diff --git a/Project.toml b/Project.toml index 8aa6252e..f34ba4c8 100644 --- a/Project.toml +++ b/Project.toml @@ -7,7 +7,6 @@ version = "0.8.0" AbstractAlgebra = "c3fe647b-3220-5bb0-a1ea-a7954cac585d" Atomix = "a9b6321e-bd34-4604-b9c9-b65b8de01458" Combinatorics = "861a8166-3701-5b0c-9a16-15d98fcdc6aa" -HostCPUFeatures = "3e5b6fbb-0976-4d2c-9146-d79de83f2fb0" Logging = "56ddb016-857b-54e1-b83d-db4d58db5568" Nemo = "2edaba10-b0f1-5616-af89-8c11ac63239a" PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a" @@ -27,7 +26,6 @@ Atomix = "0.1" BenchmarkTools = "1" Combinatorics = "1" DynamicPolynomials = "0.6.0" -HostCPUFeatures = "0.1" Nemo = "0.45.4, 0.46, 0.47" PrecompileTools = "1" Primes = "0.5" diff --git a/benchmark/scripts/arithmetic-bench.jl b/benchmark/scripts/arithmetic-bench.jl deleted file mode 100644 index 1613c96c..00000000 --- a/benchmark/scripts/arithmetic-bench.jl +++ /dev/null @@ -1,187 +0,0 @@ -using BenchmarkTools, AbstractAlgebra, PrettyTables, Groebner -using Base.Threads, Primes - -arithm = [:basic, :signed] -coeffstight = [true] -prms = [2^25 + 35, 2^27 + 29, 2^28 + 3, 2^29 + 11, 2^30 + 3] - -Groebner.logging_enabled() = false -Groebner.invariants_enabled() = false - -#! format: off -function hexapod(p) - R,(t1,t2,t3,a,b,c) = polynomial_ring(GF(p), ["t1","t2","t3","a", "b", "c"], internal_ordering=:degrevlex) - [1000000*a^2*t1^2+1000000*a^2*t2^2+1000000*a^2*t3^2+1000000*b^2*t1^2+1000000*b^2*t2^2+1000000*b^2*t3^2+1000000*c^2*t1^2+1000000*c^2*t2^2+1000000*c^2*t3^2-1065102000*a^2*t1-1566200000*a^2*t2+359610000*a^2*t3-4000000*a*b*t2-1574352000*a*b*t3+4000000*a*c*t1+273640000*a*c*t3-1065102000*b^2*t1+8152000*b^2*t2+355610000*b^2*t3-1574352000*b*c*t1-273640000*b*c*t2-791462000*c^2*t1-1566200000*c^2*t2+355610000*c^2*t3+740236705137*a^2-279943961360*a*b+47071636200*a*c+1574352000*a*t1-273640000*a*t2+126292488913*b^2+837307375312*b*c+4000000*b*t1-273640000*b*t3+612513941897*c^2+4000000*c*t2-1574352000*c*t3+1000000*t1^2+1000000*t2^2+1000000*t3^2-624135247952*a-50784764200*b-283060057360*c-791462000*t1+8152000*t2+359610000*t3+165673, 1000000*a^2*t1^2+1000000*a^2*t2^2+1000000*a^2*t3^2+1000000*b^2*t1^2+1000000*b^2*t2^2+1000000*b^2*t3^2+1000000*c^2*t1^2+1000000*c^2*t2^2+1000000*c^2*t3^2-1889130000*a^2*t1-139016000*a^2*t2+357608000*a^2*t3+550492000*a*b*t3+1500376000*a*c*t3-1889130000*b^2*t1-689508000*b^2*t2+357608000*b^2*t3+550492000*b*c*t1-1500376000*b*c*t2-388754000*c^2*t1-139016000*c^2*t2+357608000*c^2*t3+740396599024*a^2+98430171568*a*b+268273230304*a*c-550492000*a*t1-1500376000*a*t2+854420557476*b^2-2714848476*b*c-1500376000*b*t3-114024022072*c^2+550492000*c*t3+1000000*t1^2+1000000*t2^2+1000000*t3^2+624263610988*a-268273230304*b+98430171568*c-388754000*t1-689508000*t2+357608000*t3-63620, 4000000*a^2*t1^2+4000000*a^2*t2^2+4000000*a^2*t3^2+4000000*b^2*t1^2+4000000*b^2*t2^2+4000000*b^2*t3^2+4000000*c^2*t1^2+4000000*c^2*t2^2+4000000*c^2*t3^2-3295636000*a^2*t1+6825304000*a^2*t2+1438448000*a^2*t3-16000000*a*b*t2+4096192000*a*b*t3+16000000*a*c*t1+4906624000*a*c*t3-3295636000*b^2*t1+2729112000*b^2*t2+1422448000*b^2*t3+4096192000*b*c*t1-4906624000*b*c*t2+1610988000*c^2*t1+6825304000*c^2*t2+1422448000*c^2*t3+2962666483625*a^2+722869290752*a*b+875649162944*a*c-4096192000*a*t1-4906624000*a*t2+513760438633*b^2-3361285532000*b*c+16000000*b*t1-4906624000*b*t3+2443184693353*c^2+16000000*c*t2+4096192000*c*t3+4000000*t1^2+4000000*t2^2+4000000*t3^2-2498705324448*a-879018458944*b+741978122752*c+1610988000*t1+2729112000*t2+1438448000*t3+440361,4000000*a^2*t1^2+4000000*a^2*t2^2+4000000*a^2*t3^2+4000000*b^2*t1^2+4000000*b^2*t2^2+4000000*b^2*t3^2+4000000*c^2*t1^2+4000000*c^2*t2^2+4000000*c^2*t3^2+3295636000*a^2*t1+6824896000*a^2*t2+1430432000*a^2*t3+4094592000*a*b*t3-4906624000*a*c*t3+3295636000*b^2*t1+2730304000*b^2*t2+1430432000*b^2*t3+4094592000*b*c*t1+4906624000*b*c*t2-1610988000*c^2*t1+6824896000*c^2*t2+1430432000*c^2*t3+2961910911797*a^2+732129427968*a*b-877323997696*a*c-4094592000*a*t1+4906624000*a*t2+516620569397*b^2+3361357491776*b*c+4906624000*b*t3+2445290017525*c^2+4094592000*c*t3+4000000*t1^2+4000000*t2^2+4000000*t3^2+2499114213824*a+877323997696*b+732129427968*c-1610988000*t1+2730304000*t2+1430432000*t3-324875, 1000000*a^2*t1^2+1000000*a^2*t2^2+1000000*a^2*t3^2+1000000*b^2*t1^2+1000000*b^2*t2^2+1000000*b^2*t3^2+1000000*c^2*t1^2+1000000*c^2*t2^2+1000000*c^2*t3^2+1889602000*a^2*t1-138926000*a^2*t2+359604000*a^2*t3-4000000*a*b*t2+550036000*a*b*t3+4000000*a*c*t1-1500228000*a*c*t3+1889602000*b^2*t1-688962000*b^2*t2+355604000*b^2*t3+550036000*b*c*t1+1500228000*b*c*t2+389374000*c^2*t1-138926000*c^2*t2+355604000*c^2*t3+740903906549*a^2+99175424872*a*b-265964790856*a*c-550036000*a*t1+1500228000*a*t2+854030749541*b^2+2874521168*b*c+4000000*b*t1+1500228000*b*t3-114557203083*c^2+4000000*c*t2+550036000*c*t3+1000000*t1^2+1000000*t2^2+1000000*t3^2-623884900400*a+270522742856*b+97519648872*c+389374000*t1-688962000*t2+359604000*t3+55909, 250000*a^2*t1^2+250000*a^2*t2^2+250000*a^2*t3^2+250000*b^2*t1^2+250000*b^2*t2^2+250000*b^2*t3^2+250000*c^2*t1^2+250000*c^2*t2^2+250000*c^2*t3^2+266341000*a^2*t1-391502000*a^2*t2+89402000*a^2*t3-393620000*a*b*t3-68228000*a*c*t3+266341000*b^2*t1+2118000*b^2*t2+89402000*b^2*t3-393620000*b*c*t1+68228000*b*c*t2+198113000*c^2*t1-391502000*c^2*t2+89402000*c^2*t3+184958257568*a^2-70380830480*a*b-12199439312*a*c+393620000*a*t1+68228000*a*t2+31688927488*b^2-209385275032*b*c+68228000*b*t3+153269490056*c^2-393620000*c*t3+250000*t1^2+250000*t2^2+250000*t3^2+156251491928*a+12199439312*b-70380830480*c+198113000*t1+2118000*t2+89402000*t3+159976] -end -#! format: on - -function benchmark_system(system, trials=20; kwargs...) - timings = [] - GC.gc() - j = 1 - gb = nothing - while j < trials - time = @elapsed gb = Groebner.groebner(system; kwargs...) - push!(timings, time) - if time > 100e-3 - trials = 3 - end - j += 1 - end - gb, minimum(timings) -end - -function create_systems(p) - [ - ( - "kat5", - Groebner.Examples.katsuran(5, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ( - "kat6", - Groebner.Examples.katsuran(6, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ( - "kat7", - Groebner.Examples.katsuran(7, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ( - "kat8", - Groebner.Examples.katsuran(8, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ( - "kat9", - Groebner.Examples.katsuran(9, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ( - "kat10", - Groebner.Examples.katsuran(10, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ( - "kat11", - Groebner.Examples.katsuran(11, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ("hen5", Groebner.Examples.henrion5(internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - ( - "reim4", - Groebner.Examples.reimern(4, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ( - "reim5", - Groebner.Examples.reimern(5, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ( - "cyc4", - Groebner.Examples.cyclicn(4, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ( - "cyc5", - Groebner.Examples.cyclicn(5, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ( - "cyc6", - Groebner.Examples.cyclicn(6, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ( - "cyc7", - Groebner.Examples.cyclicn(7, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ( - "cyc8", - Groebner.Examples.cyclicn(8, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ("eco10", Groebner.Examples.eco10(internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - ("eco11", Groebner.Examples.eco11(internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - ("eco12", Groebner.Examples.eco12(internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - ("eco13", Groebner.Examples.eco12(internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - ( - "noon4", - Groebner.Examples.noonn(4, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ( - "noon5", - Groebner.Examples.noonn(5, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ( - "noon6", - Groebner.Examples.noonn(6, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ( - "noon7", - Groebner.Examples.noonn(7, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ( - "noon8", - Groebner.Examples.noonn(8, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ("hexapod", hexapod(p)) - ] -end - -table = Matrix{Any}(undef, (length(create_systems(2)), length(arithm) * length(prms))) -table_num = Matrix{Any}(undef, (length(create_systems(2)), length(arithm) * length(prms))) - -for (j, p) in enumerate(prms) - systems = create_systems(p) - @assert length(systems) == size(table, 1) - - @info "p < 2^$(floor(Int, log(2, p)+1))" - - gbs = [] - for (k, ar) in enumerate(arithm) - @info "arithmetic: $ar" - - push!(gbs, []) - for (i, (name, sys)) in enumerate(systems) - @info "$name.." - gb1, ti1 = benchmark_system(sys, arithmetic=ar) - table[i, k + (j - 1) * length(arithm)] = BenchmarkTools.prettytime(ti1 * 1e9) - table_num[i, k + (j - 1) * length(arithm)] = ti1 - push!(gbs[end], gb1) - end - end - - @assert allequal(gbs) -end - -ps = map(p -> "< 2^$(floor(Int, log(2, p)+1))", prms) -header = reduce(vcat, map(p -> map(a -> "$p, $a", arithm), ps)) - -hl = Highlighter((data, i, j) -> all(table_num[i, j] .<= table_num[i, :]), crayon"green bold") -highlighter = pretty_table( - table, - header=header, - tf=tf_markdown, - highlighters=(hl,), - row_labels=map(first, create_systems(2)) -) - -#= -| | < 2^26, basic | < 2^26, delayed | < 2^28, basic | < 2^28, delayed | < 2^29, basic | < 2^29, delayed | < 2^30, basic | < 2^30, delayed | < 2^31, basic | < 2^31, delayed | -|---------|---------------|-----------------|---------------|-----------------|---------------|-----------------|---------------|-----------------|---------------|-----------------| -| kat5 | 730.800 μs | 788.500 μs | 617.500 μs | 566.200 μs | 633.500 μs | 613.100 μs | 657.000 μs | 706.000 μs | 615.600 μs | 702.200 μs | -| kat6 | 1.784 ms | 1.750 ms | 1.791 ms | 1.733 ms | 1.938 ms | 1.898 ms | 1.735 ms | 2.033 ms | 1.809 ms | 2.547 ms | -| kat7 | 6.885 ms | 6.635 ms | 6.746 ms | 6.425 ms | 6.551 ms | 7.412 ms | 6.076 ms | 9.662 ms | 6.546 ms | 15.591 ms | -| kat8 | 28.246 ms | 24.333 ms | 27.613 ms | 24.947 ms | 25.912 ms | 32.133 ms | 25.023 ms | 59.271 ms | 28.239 ms | 93.528 ms | -| kat9 | 142.830 ms | 121.198 ms | 135.497 ms | 119.091 ms | 137.884 ms | 197.900 ms | 122.112 ms | 441.779 ms | 165.224 ms | 705.643 ms | -| kat10 | 812.048 ms | 671.743 ms | 830.687 ms | 677.113 ms | 810.229 ms | 1.103 s | 714.078 ms | 2.875 s | 1.094 s | 6.902 s | -| kat11 | 4.932 s | 4.050 s | 5.196 s | 4.361 s | 4.401 s | 7.496 s | 4.428 s | 20.507 s | 5.678 s | 60.104 s | -| hen5 | 1.881 ms | 1.657 ms | 1.908 ms | 1.585 ms | 1.757 ms | 1.784 ms | 1.771 ms | 1.699 ms | 1.862 ms | 2.018 ms | -| reim4 | 15.376 ms | 14.751 ms | 16.662 ms | 13.430 ms | 13.555 ms | 12.792 ms | 13.168 ms | 17.269 ms | 16.295 ms | 15.651 ms | -| reim5 | 781.772 ms | 842.125 ms | 775.096 ms | 763.221 ms | 701.023 ms | 858.490 ms | 675.663 ms | 1.456 s | 852.027 ms | 3.039 s | -| cyc4 | 105.200 μs | 114.800 μs | 100.100 μs | 99.800 μs | 100.500 μs | 102.600 μs | 100.300 μs | 110.400 μs | 105.700 μs | 104.400 μs | -| cyc5 | 711.300 μs | 821.000 μs | 658.600 μs | 646.300 μs | 644.500 μs | 667.300 μs | 642.400 μs | 765.000 μs | 740.600 μs | 696.200 μs | -| cyc6 | 2.884 ms | 3.090 ms | 2.727 ms | 2.526 ms | 2.616 ms | 2.606 ms | 2.508 ms | 2.734 ms | 2.874 ms | 3.120 ms | -| cyc7 | 73.650 ms | 70.406 ms | 72.386 ms | 67.035 ms | 75.787 ms | 72.931 ms | 71.618 ms | 106.726 ms | 79.233 ms | 158.859 ms | -| cyc8 | 1.157 s | 981.642 ms | 1.131 s | 1.010 s | 1.394 s | 1.197 s | 1.093 s | 2.208 s | 1.530 s | 4.763 s | -| eco10 | 57.877 ms | 61.051 ms | 55.883 ms | 55.968 ms | 63.984 ms | 68.353 ms | 54.592 ms | 132.491 ms | 68.345 ms | 300.625 ms | -| eco11 | 304.619 ms | 306.374 ms | 313.741 ms | 317.257 ms | 499.326 ms | 493.978 ms | 299.208 ms | 965.387 ms | 441.400 ms | 2.528 s | -| eco12 | 2.007 s | 1.968 s | 1.878 s | 2.424 s | 1.895 s | 3.359 s | 2.099 s | 9.267 s | 2.794 s | 27.133 s | -| eco13 | 2.059 s | 1.852 s | 1.828 s | 2.824 s | 2.246 s | 3.242 s | 2.523 s | 9.233 s | 2.235 s | 28.807 s | -| noon4 | 602.600 μs | 631.700 μs | 566.900 μs | 764.800 μs | 611.600 μs | 562.000 μs | 668.000 μs | 616.400 μs | 800.000 μs | 734.000 μs | -| noon5 | 3.545 ms | 3.478 ms | 3.140 ms | 4.212 ms | 3.666 ms | 3.385 ms | 4.066 ms | 3.849 ms | 4.363 ms | 5.974 ms | -| noon6 | 20.533 ms | 22.407 ms | 19.337 ms | 23.667 ms | 20.692 ms | 25.880 ms | 24.329 ms | 45.775 ms | 21.513 ms | 95.320 ms | -| noon7 | 144.968 ms | 146.774 ms | 128.802 ms | 162.340 ms | 133.974 ms | 252.806 ms | 170.418 ms | 731.718 ms | 214.646 ms | 2.270 s | -| noon8 | 1.166 s | 1.337 s | 1.093 s | 2.393 s | 1.687 s | 4.680 s | 1.173 s | 16.254 s | 1.564 s | 59.645 s | -| hexapod | 3.722 ms | 3.357 ms | 3.233 ms | 3.237 ms | 3.561 ms | 3.070 ms | 3.731 ms | 3.376 ms | 3.337 ms | 4.965 ms | -=# diff --git a/benchmark/scripts/bench-apply.jl b/benchmark/scripts/bench-apply.jl deleted file mode 100644 index 655d902f..00000000 --- a/benchmark/scripts/bench-apply.jl +++ /dev/null @@ -1,108 +0,0 @@ -using BenchmarkTools, AbstractAlgebra, PrettyTables # Groebner -using Base.Threads - -Groebner.logging_enabled() = false -Groebner.invariants_enabled() = false - -#! format: off -R,(t1,t2,t3,a,b,c) = polynomial_ring(QQ, ["t1","t2","t3","a", "b", "c"], internal_ordering=:degrevlex) -hexapod = [1000000*a^2*t1^2+1000000*a^2*t2^2+1000000*a^2*t3^2+1000000*b^2*t1^2+1000000*b^2*t2^2+1000000*b^2*t3^2+1000000*c^2*t1^2+1000000*c^2*t2^2+1000000*c^2*t3^2-1065102000*a^2*t1-1566200000*a^2*t2+359610000*a^2*t3-4000000*a*b*t2-1574352000*a*b*t3+4000000*a*c*t1+273640000*a*c*t3-1065102000*b^2*t1+8152000*b^2*t2+355610000*b^2*t3-1574352000*b*c*t1-273640000*b*c*t2-791462000*c^2*t1-1566200000*c^2*t2+355610000*c^2*t3+740236705137*a^2-279943961360*a*b+47071636200*a*c+1574352000*a*t1-273640000*a*t2+126292488913*b^2+837307375312*b*c+4000000*b*t1-273640000*b*t3+612513941897*c^2+4000000*c*t2-1574352000*c*t3+1000000*t1^2+1000000*t2^2+1000000*t3^2-624135247952*a-50784764200*b-283060057360*c-791462000*t1+8152000*t2+359610000*t3+165673, 1000000*a^2*t1^2+1000000*a^2*t2^2+1000000*a^2*t3^2+1000000*b^2*t1^2+1000000*b^2*t2^2+1000000*b^2*t3^2+1000000*c^2*t1^2+1000000*c^2*t2^2+1000000*c^2*t3^2-1889130000*a^2*t1-139016000*a^2*t2+357608000*a^2*t3+550492000*a*b*t3+1500376000*a*c*t3-1889130000*b^2*t1-689508000*b^2*t2+357608000*b^2*t3+550492000*b*c*t1-1500376000*b*c*t2-388754000*c^2*t1-139016000*c^2*t2+357608000*c^2*t3+740396599024*a^2+98430171568*a*b+268273230304*a*c-550492000*a*t1-1500376000*a*t2+854420557476*b^2-2714848476*b*c-1500376000*b*t3-114024022072*c^2+550492000*c*t3+1000000*t1^2+1000000*t2^2+1000000*t3^2+624263610988*a-268273230304*b+98430171568*c-388754000*t1-689508000*t2+357608000*t3-63620, 4000000*a^2*t1^2+4000000*a^2*t2^2+4000000*a^2*t3^2+4000000*b^2*t1^2+4000000*b^2*t2^2+4000000*b^2*t3^2+4000000*c^2*t1^2+4000000*c^2*t2^2+4000000*c^2*t3^2-3295636000*a^2*t1+6825304000*a^2*t2+1438448000*a^2*t3-16000000*a*b*t2+4096192000*a*b*t3+16000000*a*c*t1+4906624000*a*c*t3-3295636000*b^2*t1+2729112000*b^2*t2+1422448000*b^2*t3+4096192000*b*c*t1-4906624000*b*c*t2+1610988000*c^2*t1+6825304000*c^2*t2+1422448000*c^2*t3+2962666483625*a^2+722869290752*a*b+875649162944*a*c-4096192000*a*t1-4906624000*a*t2+513760438633*b^2-3361285532000*b*c+16000000*b*t1-4906624000*b*t3+2443184693353*c^2+16000000*c*t2+4096192000*c*t3+4000000*t1^2+4000000*t2^2+4000000*t3^2-2498705324448*a-879018458944*b+741978122752*c+1610988000*t1+2729112000*t2+1438448000*t3+440361,4000000*a^2*t1^2+4000000*a^2*t2^2+4000000*a^2*t3^2+4000000*b^2*t1^2+4000000*b^2*t2^2+4000000*b^2*t3^2+4000000*c^2*t1^2+4000000*c^2*t2^2+4000000*c^2*t3^2+3295636000*a^2*t1+6824896000*a^2*t2+1430432000*a^2*t3+4094592000*a*b*t3-4906624000*a*c*t3+3295636000*b^2*t1+2730304000*b^2*t2+1430432000*b^2*t3+4094592000*b*c*t1+4906624000*b*c*t2-1610988000*c^2*t1+6824896000*c^2*t2+1430432000*c^2*t3+2961910911797*a^2+732129427968*a*b-877323997696*a*c-4094592000*a*t1+4906624000*a*t2+516620569397*b^2+3361357491776*b*c+4906624000*b*t3+2445290017525*c^2+4094592000*c*t3+4000000*t1^2+4000000*t2^2+4000000*t3^2+2499114213824*a+877323997696*b+732129427968*c-1610988000*t1+2730304000*t2+1430432000*t3-324875, 1000000*a^2*t1^2+1000000*a^2*t2^2+1000000*a^2*t3^2+1000000*b^2*t1^2+1000000*b^2*t2^2+1000000*b^2*t3^2+1000000*c^2*t1^2+1000000*c^2*t2^2+1000000*c^2*t3^2+1889602000*a^2*t1-138926000*a^2*t2+359604000*a^2*t3-4000000*a*b*t2+550036000*a*b*t3+4000000*a*c*t1-1500228000*a*c*t3+1889602000*b^2*t1-688962000*b^2*t2+355604000*b^2*t3+550036000*b*c*t1+1500228000*b*c*t2+389374000*c^2*t1-138926000*c^2*t2+355604000*c^2*t3+740903906549*a^2+99175424872*a*b-265964790856*a*c-550036000*a*t1+1500228000*a*t2+854030749541*b^2+2874521168*b*c+4000000*b*t1+1500228000*b*t3-114557203083*c^2+4000000*c*t2+550036000*c*t3+1000000*t1^2+1000000*t2^2+1000000*t3^2-623884900400*a+270522742856*b+97519648872*c+389374000*t1-688962000*t2+359604000*t3+55909, 250000*a^2*t1^2+250000*a^2*t2^2+250000*a^2*t3^2+250000*b^2*t1^2+250000*b^2*t2^2+250000*b^2*t3^2+250000*c^2*t1^2+250000*c^2*t2^2+250000*c^2*t3^2+266341000*a^2*t1-391502000*a^2*t2+89402000*a^2*t3-393620000*a*b*t3-68228000*a*c*t3+266341000*b^2*t1+2118000*b^2*t2+89402000*b^2*t3-393620000*b*c*t1+68228000*b*c*t2+198113000*c^2*t1-391502000*c^2*t2+89402000*c^2*t3+184958257568*a^2-70380830480*a*b-12199439312*a*c+393620000*a*t1+68228000*a*t2+31688927488*b^2-209385275032*b*c+68228000*b*t3+153269490056*c^2-393620000*c*t3+250000*t1^2+250000*t2^2+250000*t3^2+156251491928*a+12199439312*b-70380830480*c+198113000*t1+2118000*t2+89402000*t3+159976] -#! format: on - -systems = [ - # ("kat5", Groebner.Examples.katsuran(5, internal_ordering=:degrevlex, k=QQ)), - ("kat6", Groebner.Examples.katsuran(6, internal_ordering=:degrevlex, k=QQ)), - ("kat7", Groebner.Examples.katsuran(7, internal_ordering=:degrevlex, k=QQ)), - ("kat8", Groebner.Examples.katsuran(8, internal_ordering=:degrevlex, k=QQ)), - ("kat9", Groebner.Examples.katsuran(9, internal_ordering=:degrevlex, k=QQ)), - ("kat10", Groebner.Examples.katsuran(10, internal_ordering=:degrevlex, k=QQ)), - # ("kat11", Groebner.Examples.katsuran(11, internal_ordering=:degrevlex, k=QQ)), - # ("kat12", Groebner.Examples.katsuran(12, internal_ordering=:degrevlex, k=QQ)), - ("hen5", Groebner.Examples.henrion5(internal_ordering=:degrevlex, k=QQ)), - ("hen6", Groebner.Examples.henrion6(internal_ordering=:degrevlex, k=QQ)), - ("reim4", Groebner.Examples.reimern(4, internal_ordering=:degrevlex, k=QQ)), - # ("reim5", Groebner.Examples.reimern(5, internal_ordering=:degrevlex, k=QQ)), - # ("cyc4", Groebner.Examples.cyclicn(4, internal_ordering=:degrevlex, k=QQ)), - # ("cyc5", Groebner.Examples.cyclicn(5, internal_ordering=:degrevlex, k=QQ)), - ("cyc6", Groebner.Examples.cyclicn(6, internal_ordering=:degrevlex, k=QQ)), - ("cyc7", Groebner.Examples.cyclicn(7, internal_ordering=:degrevlex, k=QQ)), - ("cyc8", Groebner.Examples.cyclicn(8, internal_ordering=:degrevlex, k=QQ)), - ("eco10", Groebner.Examples.eco10(internal_ordering=:degrevlex, k=QQ)), - ("eco11", Groebner.Examples.eco11(internal_ordering=:degrevlex, k=QQ)), - ("eco12", Groebner.Examples.eco12(internal_ordering=:degrevlex, k=QQ)), - # ("eco13", Groebner.Examples.eco13(internal_ordering=:degrevlex, k=QQ)), - # ("noon4", Groebner.Examples.noonn(4, internal_ordering=:degrevlex, k=QQ)), - ("noon5", Groebner.Examples.noonn(5, internal_ordering=:degrevlex, k=QQ)), - ("noon6", Groebner.Examples.noonn(6, internal_ordering=:degrevlex, k=QQ)), - ("noon7", Groebner.Examples.noonn(7, internal_ordering=:degrevlex, k=QQ)), - ("noon8", Groebner.Examples.noonn(8, internal_ordering=:degrevlex, k=QQ)), - ("hexapod", hexapod) -] - -table = Matrix{Any}(undef, (length(systems), 3)) - -function benchmark_system(system, trials=20; kwargs...) - timings = [] - GC.gc() - j = 1 - gb = nothing - while j < trials - time = @elapsed gb = Groebner.groebner(system; kwargs...) - push!(timings, time) - if time > 100e-3 - trials = 5 - end - if time > 10 - trials = 1 - end - j += 1 - end - gb, minimum(timings) -end - -for (i, (name, s)) in enumerate(systems) - @info """ - $name: - classic multi-modular / learn & apply / learn & apply N=4""" - gb3, ti3 = benchmark_system(s; modular=:classic_modular) - gb4, ti4 = benchmark_system(s; modular=:learn_and_apply, batched=false) - gb5, ti5 = benchmark_system(s; modular=:learn_and_apply, batched=true) - - (ti3, ti4, ti5) = map(t -> BenchmarkTools.prettytime(t * 1e9), (ti3, ti4, ti5)) - - table[i, :] .= (ti3, ti4, ti5) - println("$ti3 / $ti4 / $ti5") - - @assert gb3 == gb4 == gb5 -end - -pretty_table( - table, - header=["classic multi-modular", "learn & apply", "learn & apply N=4"], - tf=tf_markdown, - row_labels=map(first, systems) -) - -#= -| | classic multi-modular | learn & apply | learn & apply N=4 | -|---------|-----------------------|---------------|-------------------| -| kat6 | 37.169 ms | 22.459 ms | 18.573 ms | -| kat7 | 140.579 ms | 97.749 ms | 81.444 ms | -| kat8 | 987.475 ms | 633.818 ms | 506.742 ms | -| kat9 | 7.434 s | 4.626 s | 3.931 s | -| kat10 | 76.061 s | 37.614 s | 25.093 s | -| hen5 | 470.852 ms | 395.549 ms | 328.494 ms | -| hen6 | 1.086 s | 655.668 ms | 522.634 ms | -| reim4 | 151.234 ms | 106.118 ms | 81.168 ms | -| cyc6 | 12.657 ms | 8.853 ms | 8.884 ms | -| cyc7 | 2.255 s | 1.245 s | 884.418 ms | -| cyc8 | 86.251 s | 47.330 s | 22.606 s | -| eco10 | 559.307 ms | 426.300 ms | 394.343 ms | -| eco11 | 5.185 s | 3.924 s | 2.952 s | -| eco12 | 31.792 s | 27.085 s | 19.377 s | -| noon5 | 9.839 ms | 8.558 ms | 8.236 ms | -| noon6 | 114.301 ms | 65.704 ms | 65.833 ms | -| noon7 | 653.635 ms | 392.572 ms | 396.666 ms | -| noon8 | 5.148 s | 2.725 s | 2.816 s | -| hexapod | 15.053 s | 13.172 s | 13.193 s | -=# diff --git a/benchmark/scripts/char-bench.jl b/benchmark/scripts/char-bench.jl deleted file mode 100644 index db9aa216..00000000 --- a/benchmark/scripts/char-bench.jl +++ /dev/null @@ -1,158 +0,0 @@ -using BenchmarkTools, AbstractAlgebra, PrettyTables, Groebner -using Base.Threads, Primes - -prms = vcat( - [Primes.prevprime(BigInt(2)^i) for i in 63:-1:59], - [Primes.prevprime(2^i) for i in 31:-1:26] -) - -Groebner.logging_enabled() = false -Groebner.invariants_enabled() = false - -#! format: off -R,(t1,t2,t3,a,b,c) = polynomial_ring(GF(2^27+29), ["t1","t2","t3","a", "b", "c"], internal_ordering=:degrevlex) -hexapod = [1000000*a^2*t1^2+1000000*a^2*t2^2+1000000*a^2*t3^2+1000000*b^2*t1^2+1000000*b^2*t2^2+1000000*b^2*t3^2+1000000*c^2*t1^2+1000000*c^2*t2^2+1000000*c^2*t3^2-1065102000*a^2*t1-1566200000*a^2*t2+359610000*a^2*t3-4000000*a*b*t2-1574352000*a*b*t3+4000000*a*c*t1+273640000*a*c*t3-1065102000*b^2*t1+8152000*b^2*t2+355610000*b^2*t3-1574352000*b*c*t1-273640000*b*c*t2-791462000*c^2*t1-1566200000*c^2*t2+355610000*c^2*t3+740236705137*a^2-279943961360*a*b+47071636200*a*c+1574352000*a*t1-273640000*a*t2+126292488913*b^2+837307375312*b*c+4000000*b*t1-273640000*b*t3+612513941897*c^2+4000000*c*t2-1574352000*c*t3+1000000*t1^2+1000000*t2^2+1000000*t3^2-624135247952*a-50784764200*b-283060057360*c-791462000*t1+8152000*t2+359610000*t3+165673, 1000000*a^2*t1^2+1000000*a^2*t2^2+1000000*a^2*t3^2+1000000*b^2*t1^2+1000000*b^2*t2^2+1000000*b^2*t3^2+1000000*c^2*t1^2+1000000*c^2*t2^2+1000000*c^2*t3^2-1889130000*a^2*t1-139016000*a^2*t2+357608000*a^2*t3+550492000*a*b*t3+1500376000*a*c*t3-1889130000*b^2*t1-689508000*b^2*t2+357608000*b^2*t3+550492000*b*c*t1-1500376000*b*c*t2-388754000*c^2*t1-139016000*c^2*t2+357608000*c^2*t3+740396599024*a^2+98430171568*a*b+268273230304*a*c-550492000*a*t1-1500376000*a*t2+854420557476*b^2-2714848476*b*c-1500376000*b*t3-114024022072*c^2+550492000*c*t3+1000000*t1^2+1000000*t2^2+1000000*t3^2+624263610988*a-268273230304*b+98430171568*c-388754000*t1-689508000*t2+357608000*t3-63620, 4000000*a^2*t1^2+4000000*a^2*t2^2+4000000*a^2*t3^2+4000000*b^2*t1^2+4000000*b^2*t2^2+4000000*b^2*t3^2+4000000*c^2*t1^2+4000000*c^2*t2^2+4000000*c^2*t3^2-3295636000*a^2*t1+6825304000*a^2*t2+1438448000*a^2*t3-16000000*a*b*t2+4096192000*a*b*t3+16000000*a*c*t1+4906624000*a*c*t3-3295636000*b^2*t1+2729112000*b^2*t2+1422448000*b^2*t3+4096192000*b*c*t1-4906624000*b*c*t2+1610988000*c^2*t1+6825304000*c^2*t2+1422448000*c^2*t3+2962666483625*a^2+722869290752*a*b+875649162944*a*c-4096192000*a*t1-4906624000*a*t2+513760438633*b^2-3361285532000*b*c+16000000*b*t1-4906624000*b*t3+2443184693353*c^2+16000000*c*t2+4096192000*c*t3+4000000*t1^2+4000000*t2^2+4000000*t3^2-2498705324448*a-879018458944*b+741978122752*c+1610988000*t1+2729112000*t2+1438448000*t3+440361,4000000*a^2*t1^2+4000000*a^2*t2^2+4000000*a^2*t3^2+4000000*b^2*t1^2+4000000*b^2*t2^2+4000000*b^2*t3^2+4000000*c^2*t1^2+4000000*c^2*t2^2+4000000*c^2*t3^2+3295636000*a^2*t1+6824896000*a^2*t2+1430432000*a^2*t3+4094592000*a*b*t3-4906624000*a*c*t3+3295636000*b^2*t1+2730304000*b^2*t2+1430432000*b^2*t3+4094592000*b*c*t1+4906624000*b*c*t2-1610988000*c^2*t1+6824896000*c^2*t2+1430432000*c^2*t3+2961910911797*a^2+732129427968*a*b-877323997696*a*c-4094592000*a*t1+4906624000*a*t2+516620569397*b^2+3361357491776*b*c+4906624000*b*t3+2445290017525*c^2+4094592000*c*t3+4000000*t1^2+4000000*t2^2+4000000*t3^2+2499114213824*a+877323997696*b+732129427968*c-1610988000*t1+2730304000*t2+1430432000*t3-324875, 1000000*a^2*t1^2+1000000*a^2*t2^2+1000000*a^2*t3^2+1000000*b^2*t1^2+1000000*b^2*t2^2+1000000*b^2*t3^2+1000000*c^2*t1^2+1000000*c^2*t2^2+1000000*c^2*t3^2+1889602000*a^2*t1-138926000*a^2*t2+359604000*a^2*t3-4000000*a*b*t2+550036000*a*b*t3+4000000*a*c*t1-1500228000*a*c*t3+1889602000*b^2*t1-688962000*b^2*t2+355604000*b^2*t3+550036000*b*c*t1+1500228000*b*c*t2+389374000*c^2*t1-138926000*c^2*t2+355604000*c^2*t3+740903906549*a^2+99175424872*a*b-265964790856*a*c-550036000*a*t1+1500228000*a*t2+854030749541*b^2+2874521168*b*c+4000000*b*t1+1500228000*b*t3-114557203083*c^2+4000000*c*t2+550036000*c*t3+1000000*t1^2+1000000*t2^2+1000000*t3^2-623884900400*a+270522742856*b+97519648872*c+389374000*t1-688962000*t2+359604000*t3+55909, 250000*a^2*t1^2+250000*a^2*t2^2+250000*a^2*t3^2+250000*b^2*t1^2+250000*b^2*t2^2+250000*b^2*t3^2+250000*c^2*t1^2+250000*c^2*t2^2+250000*c^2*t3^2+266341000*a^2*t1-391502000*a^2*t2+89402000*a^2*t3-393620000*a*b*t3-68228000*a*c*t3+266341000*b^2*t1+2118000*b^2*t2+89402000*b^2*t3-393620000*b*c*t1+68228000*b*c*t2+198113000*c^2*t1-391502000*c^2*t2+89402000*c^2*t3+184958257568*a^2-70380830480*a*b-12199439312*a*c+393620000*a*t1+68228000*a*t2+31688927488*b^2-209385275032*b*c+68228000*b*t3+153269490056*c^2-393620000*c*t3+250000*t1^2+250000*t2^2+250000*t3^2+156251491928*a+12199439312*b-70380830480*c+198113000*t1+2118000*t2+89402000*t3+159976] -#! format: on - -table = Matrix{Any}(undef, (23, length(prms))) - -function benchmark_system(system, trials=5; kwargs...) - timings = [] - GC.gc() - gb = nothing - for _ in 1:trials - time = @elapsed gb = Groebner.groebner(system; kwargs...) - push!(timings, time) - end - gb, minimum(timings) -end - -function create_systems(p) - systems = [ - ( - "kat5", - Groebner.Examples.katsuran(5, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ( - "kat6", - Groebner.Examples.katsuran(6, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ( - "kat7", - Groebner.Examples.katsuran(7, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ( - "kat8", - Groebner.Examples.katsuran(8, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ( - "kat9", - Groebner.Examples.katsuran(9, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ( - "kat10", - Groebner.Examples.katsuran(10, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ("hen5", Groebner.Examples.henrion5(internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - ( - "reim4", - Groebner.Examples.reimern(4, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ( - "reim5", - Groebner.Examples.reimern(5, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ( - "cyc4", - Groebner.Examples.cyclicn(4, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ( - "cyc5", - Groebner.Examples.cyclicn(5, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ( - "cyc6", - Groebner.Examples.cyclicn(6, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ( - "cyc7", - Groebner.Examples.cyclicn(7, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ( - "cyc8", - Groebner.Examples.cyclicn(8, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ("eco10", Groebner.Examples.eco10(internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - ("eco11", Groebner.Examples.eco11(internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - ("eco12", Groebner.Examples.eco12(internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - ( - "noon4", - Groebner.Examples.noonn(4, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ( - "noon5", - Groebner.Examples.noonn(5, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ( - "noon6", - Groebner.Examples.noonn(6, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ( - "noon7", - Groebner.Examples.noonn(7, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ( - "noon8", - Groebner.Examples.noonn(8, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p)) - ), - ("hexapod", hexapod) - ] -end - -for (j, p) in enumerate(prms) - systems = create_systems(p) - @assert length(systems) == size(table, 1) - - @info "p < 2^$(floor(Int, log(2, p)+1))" - - for (i, (name, s)) in enumerate(systems) - @info "$name.." - gb1, ti1 = benchmark_system(s) - table[i, j] = BenchmarkTools.prettytime(ti1 * 1e9) - end -end - -pretty_table( - table, - header=map(p -> "< 2^$(floor(Int, log(2, p)+1))", prms), - tf=tf_markdown, - row_labels=map(first, create_systems(2^31 - 1)) -) - -#= -| | linalg #1 | linalg #1 threaded | linalg #2 (default) | linalg #2 threaded | -|---------|------------|--------------------|---------------------|--------------------| -| kat5 | 1.435 ms | 1.325 ms | 547.100 μs | 855.700 μs | -| kat6 | 2.456 ms | 3.146 ms | 1.709 ms | 2.179 ms | -| kat7 | 12.759 ms | 9.484 ms | 6.647 ms | 6.648 ms | -| kat8 | 76.593 ms | 43.593 ms | 25.981 ms | 22.833 ms | -| kat9 | 534.610 ms | 262.078 ms | 126.060 ms | 93.090 ms | -| kat10 | 4.553 s | 2.032 s | 709.215 ms | 450.237 ms | -| hen5 | 2.047 ms | 2.835 ms | 1.776 ms | 2.538 ms | -| reim4 | 13.356 ms | 18.100 ms | 14.044 ms | 18.906 ms | -| reim5 | 719.158 ms | 707.738 ms | 637.063 ms | 639.548 ms | -| cyc4 | 99.200 μs | 259.700 μs | 105.400 μs | 168.300 μs | -| cyc5 | 681.000 μs | 1.110 ms | 619.700 μs | 897.500 μs | -| cyc6 | 3.149 ms | 4.636 ms | 2.488 ms | 3.347 ms | -| cyc7 | 152.065 ms | 100.933 ms | 74.816 ms | 61.060 ms | -| cyc8 | 3.512 s | 2.064 s | 1.068 s | 768.843 ms | -| eco10 | 131.248 ms | 82.306 ms | 54.571 ms | 50.196 ms | -| eco11 | 915.857 ms | 511.648 ms | 283.292 ms | 230.956 ms | -| eco12 | 7.624 s | 3.862 s | 1.805 s | 1.372 s | -| noon4 | 540.900 μs | 1.001 ms | 565.700 μs | 861.800 μs | -| noon5 | 3.320 ms | 4.484 ms | 3.215 ms | 3.957 ms | -| noon6 | 19.383 ms | 19.045 ms | 18.735 ms | 18.887 ms | -| noon7 | 129.403 ms | 112.976 ms | 123.975 ms | 111.059 ms | -| noon8 | 1.075 s | 855.434 ms | 1.031 s | 873.569 ms | -| hexapod | 4.296 ms | 4.843 ms | 3.444 ms | 4.146 ms | -=# diff --git a/benchmark/scripts/fillin.jl b/benchmark/scripts/fillin.jl deleted file mode 100644 index dd9673ec..00000000 --- a/benchmark/scripts/fillin.jl +++ /dev/null @@ -1,182 +0,0 @@ -using LinearAlgebra, SparseArrays -using Random - -mutable struct MyMatrix - supports::Vector{Vector{Any}} - coeffs::Vector{Vector{Any}} - m::Int - n::Int -end - -Base.size(mat::MyMatrix) = (mat.m, mat.n) - -function matrix_from_dense(arr) - inds = findall(!iszero, arr) - supports = [findall(!iszero, arr[i, :]) for i in 1:size(arr, 1)] - coeffs = [[arr[i, j] for j in supports[i]] for i in 1:size(arr, 1)] - MyMatrix(supports, coeffs, size(arr)...) -end - -function matrix_to_sparse(mat::MyMatrix) - m, n = size(mat) - arr = spzeros(Int, m, n) - for i in 1:m - for j in 1:length(mat.supports[i]) - row, col = i, mat.supports[i][j] - arr[row, col] = 1 - end - end - sparse(arr) -end - -function build_graph(mat) - m, n = size(mat) - graph = [Int[] for _ in 1:(m + n)] - for i in 1:m - for j in 1:length(mat.supports[i]) - row, col = i, mat.supports[i][j] - push!(graph[row], m + col) - push!(graph[m + col], row) - end - end - graph -end - -function dfs!(graph, src, components, color) - if components[src] != 0 - return 0 - end - queue = Int[src] - while !isempty(queue) - src = pop!(queue) - components[src] = color - for dst in graph[src] - if components[dst] == 0 - push!(queue, dst) - end - end - end - return 1 -end - -function connected_components(graph) - components = [0 for _ in 1:length(graph)] - color = 1 - for i in 1:length(graph) - color += dfs!(graph, i, components, color) - end - components -end - -function decompose(mat::MyMatrix) - graph = build_graph(mat) - components = connected_components(graph) - components -end - -A = [ - 1 0 1 - 0 1 0 - 0 0 1 -] -B = matrix_from_dense(A) -A = matrix_to_sparse(B) -cc = decompose(B) - -begin - n = 100 - A = sprand(Int, n, n, 0.2) + I - for i in 1:n - for j in (i + 1):n - A[j, i] = 0 - end - end - dropzeros!(A) - @info "" A - B = matrix_from_dense(A) - cc = decompose(B) - length(unique(cc)), map(i -> sum(cc .== i), 1:length(unique(cc))) -end - -#= -Int32[2, 3, 4, 5] -UInt32[0x00000001, 0x40000002, 0x20000002, 0x20000001] - -Int32[2, 3, 4, 5] -UInt32[0x00000001, 0x40000002, 0x20000002, 0x20000001] -=# - -include("../../../Groebner.jl/src/Groebner.jl") -using AbstractAlgebra, JLD2, Random -c = Groebner.Examples.noonn(8, k=GF(2^30 + 3), internal_ordering=:degrevlex) - -Groebner.__SAVE[] = true -gb1 = Groebner.groebner(c, loglevel=-0, linalg=:deterministic); -Groebner.__SAVE[] = false -gb2 = Groebner.groebner(c, loglevel=-0, linalg=:experimental_2); -gb1 == gb2 - -for fn in readdir((@__DIR__), join=true) - if !startswith(last(split(fn, "/")), "matrix") - continue - end - begin - mat = load(fn)["matrix"] - (n, _) = Groebner.matrix_block_sizes(mat) - rows = map(row -> filter(col -> col <= n, row), mat.upper_rows) - # B = MyMatrix(rows, [[]], n, n) - # A = matrix_to_sparse(B) - # @time cc = decompose(B) - # nc = length(unique(cc)) - # cnt = map(i -> floor(Int, sum(cc .== unique(cc)[i]) / 2), 1:length(unique(cc))) - # display(A) - @info "" n - end -end - -for fn in readdir((@__DIR__), join=true) - if !startswith(last(split(fn, "/")), "matrix") - continue - end - begin - matrix = load(fn)["matrix"] - basis = load(fn)["basis"] - println(Groebner.matrix_block_sizes(matrix)) - arithmetic = Groebner.SpecializedArithmeticZp(UInt64, UInt32, 2^30 + 3) - @time Groebner.linalg_deterministic_sparse!( - matrix, - basis, - Groebner.LinearAlgebra(:a, :b), - arithmetic - ) - - matrix = load(fn)["matrix"] - basis = load(fn)["basis"] - @time Groebner.linalg_randomized_sparse!( - matrix, - basis, - Groebner.LinearAlgebra(:a, :b), - arithmetic, - Random.MersenneTwister(42) - ) - - matrix = load(fn)["matrix"] - basis = load(fn)["basis"] - @time Groebner.linalg_randomized_hashcolumns_sparse!( - matrix, - basis, - Groebner.LinearAlgebra(:a, :b), - arithmetic, - Random.MersenneTwister(42) - ) - end -end - -if true - for fn in readdir((@__DIR__), join=true) - if !startswith(last(split(fn, "/")), "matrix") - continue - end - rm(fn) - end -end diff --git a/benchmark/scripts/hashtable/benchmark.jl b/benchmark/scripts/hashtable/benchmark.jl deleted file mode 100644 index 96d5d4cb..00000000 --- a/benchmark/scripts/hashtable/benchmark.jl +++ /dev/null @@ -1,67 +0,0 @@ -using Random, BenchmarkTools - -include("common.jl") -include("hashtable-1.jl") -include("hashtable-2.jl") - -n = 10 -sz = 2^16 - -function setup_random_monoms(n, d, s; T=UInt8) - monoms = Vector{Vector{T}}(undef, s) - for i in 1:s - monoms[i] = rand(T(0):T(d), n) - end - monoms -end - -function setup_1(n, sz, s) - ht = hashtable_initialize1(n, Random.MersenneTwister(42), Vector{UInt8}, sz) - monoms = setup_random_monoms(n, 5, s) - ht, monoms -end - -function setup_2(n, sz, s) - ht = hashtable_initialize1(n, Random.MersenneTwister(42), Vector{UInt8}, sz) - monoms = setup_random_monoms(n, 5, s) - for i in 1:length(monoms) - hashtable_insert!(ht, monoms[i]) - end - monoms2 = setup_random_monoms(n, 5, s) - for j in 1:length(monoms) - if iszero(j % 1_000) - monoms[j] = monoms2[j] - end - end - ht, monoms -end - -# Inserts, almost no collisions -for k in 8:16 - sz = 2^k - s = div(sz, 2) - @info "n = $n, sz = 2^$k, s = $s" - - @btime begin - for i in 1:($s) - hashtable_insert!(ht, monoms[i]) - end - end setup = begin - ht, monoms = setup_1($n, $sz, $s) - end -end - -# Inserts, almost all are hits -for k in 8:16 - sz = 2^k - s = div(sz, 2) - @info "n = $n, sz = 2^$k, s = $s" - - @btime begin - for i in 1:($s) - hashtable_insert!(ht, monoms[i]) - end - end setup = begin - ht, monoms = setup_2($n, $sz, $s) - end -end diff --git a/benchmark/scripts/hashtable/common.jl b/benchmark/scripts/hashtable/common.jl deleted file mode 100644 index 35ed0a7d..00000000 --- a/benchmark/scripts/hashtable/common.jl +++ /dev/null @@ -1,7 +0,0 @@ - -const Monom = Vector{UInt8} - -# The idenfifier of a monomial. This idenfifier is guaranteed to be unique -# within a particular hashtable. This allows one to use this idenfifier when -# working with monomials -const MonomId = Int32 diff --git a/benchmark/scripts/hashtable/hashtable-1.jl b/benchmark/scripts/hashtable/hashtable-1.jl deleted file mode 100644 index 87e78c8d..00000000 --- a/benchmark/scripts/hashtable/hashtable-1.jl +++ /dev/null @@ -1,187 +0,0 @@ - -# Hash of a monomial in the hashtable -const MonomHash = UInt32 - -# Hashvalue1 of a single monomial -struct Hashvalue1 - # index of the monomial in the F4 matrix (defaults to NON_PIVOT_COLUMN, or 0), - idx::Int32 - # hash of the monomial, - hash::MonomHash - # total degree of the monomial - deg::MonomHash -end - -# Hashtable implements open addressing with linear scan. -mutable struct MonomialHashtable1{M <: Monom} - #= Data =# - monoms::Vector{M} - # Maps monomial id to its position in the `monoms` array - hashtable::Vector{MonomId} - # Stores hashes, division masks, and other valuable info for each hashtable - # enrty - hashdata::Vector{Hashvalue1} - # Hash vector. Hash of a monomial is a dot product of the `hasher` vector - # and the monomial exponent vector - hasher::Vector{MonomHash} - - #= Ring information =# - # number of variables - nvars::Int - - # Hashtable size - # (always a power of two) - # (always greater than 1) - size::Int - # Elements currently added - load::Int - offset::Int - - # If the hashtable is frozen, any operation that tries to modify it will - # result in an error. - frozen::Bool -end - -### -# Initialization and resizing - -# Resize hashtable if load factor exceeds hashtable_resize_threshold. Load factor of a -# hashtable must be smaller than hashtable_resize_threshold at any point of its -# lifetime -hashtable_resize_threshold() = 0.4 -hashtable_needs_resize(size, load, added) = (load + added) / size > hashtable_resize_threshold() - -function hashtable_initialize1(nvars, rng::AbstractRNG, MonomT::T, initial_size::Int) where {T} - exponents = Vector{MonomT}(undef, initial_size) - hashdata = Vector{Hashvalue1}(undef, initial_size) - hashtable = zeros(MonomId, initial_size) - - # initialize hashing vector - hasher = [rand(MonomHash) for i in 1:nvars] - - # exponents[1:load] covers all stored exponents - # , also exponents[1] is [0, 0, ..., 0] by default - load = 1 - @assert initial_size > 1 - size = initial_size - - # exponents array starts from index offset, - # We store buffer array at index 1 - offset = 2 - - # first stored exponent used as buffer lately - exponents[1] = zeros(UInt8, nvars) - - MonomialHashtable1(exponents, hashtable, hashdata, hasher, nvars, size, load, offset, false) -end - -function hashtable_resize_if_needed!(ht::MonomialHashtable1, added::Int) - newsize = ht.size - while hashtable_needs_resize(newsize, ht.load, added) - newsize *= 2 - end - newsize == ht.size && return nothing - - ht.size = newsize - - resize!(ht.hashdata, ht.size) - resize!(ht.monoms, ht.size) - resize!(ht.hashtable, ht.size) - @inbounds for i in 1:(ht.size) - ht.hashtable[i] = zero(MonomId) - end - - mod = MonomHash(ht.size - 1) - - @inbounds for i in (ht.offset):(ht.load) - # hash for this elem is already computed - he = ht.hashdata[i].hash - hidx = he - for j in MonomHash(0):MonomHash(ht.size) - hidx = hashtable_next_lookup_index(he, j, mod) - !iszero(ht.hashtable[hidx]) && continue - ht.hashtable[hidx] = i - break - end - end - nothing -end - -### -# Insertion of monomials - -# Returns the next look-up position in the table. -# Must be within 1 <= ... <= mod+1 -function hashtable_next_lookup_index(h::MonomHash, j::MonomHash, mod::MonomHash) - ((h + j) & mod) + MonomHash(1) -end - -# if hash collision happened -function hashtable_is_hash_collision(ht::MonomialHashtable1, vidx, e, he) - # if not free and not same hash - @inbounds if ht.hashdata[vidx].hash != he - return true - end - # if not free and not same monomial - @inbounds if !(ht.monoms[vidx] == e) - return true - end - false -end - -function monom_hash(x::Vector{T}, b::Vector{MH}) where {T, MH} - h = zero(MH) - @inbounds for i in eachindex(x, b) - h = h + MH(x[i]) * b[i] - end - mod(h, MonomHash) -end - -function hashtable_insert!(ht::MonomialHashtable1{M}, e::M) where {M <: Monom} - # NOTE: trying to optimize for the case when the monomial is already in the - # table. - # NOTE: all of the functions called here are inlined. The only potential - # exception is monom_create_divmask - - # generate hash - he = monom_hash(e, ht.hash_vector) - - hsize = ht.size - mod = (hsize - 1) % MonomHash - hidx = hashtable_next_lookup_index(he, 0 % MonomHash, mod) - @inbounds vidx = ht.hashtable[hidx] - - hit = !iszero(vidx) - @inbounds if hit && !hashtable_is_hash_collision(ht, vidx, e, he) - # Hit! - return vidx - end - - # Miss or collision - i = 1 % MonomHash - mhhsize = hsize % MonomHash - @inbounds while hit && i < mhhsize - hidx = hashtable_next_lookup_index(he, i, mod) - vidx = ht.hashtable[hidx] - - iszero(vidx) && break - - if hashtable_is_hash_collision(ht, vidx, e, he) - i += (1 % MonomHash) - continue - end - - # already present in hashtable - return vidx - end - - # add monomial to hashtable - vidx = (ht.load + 1) % MonomId - @inbounds ht.hashtable[hidx] = vidx - @inbounds ht.monoms[vidx] = Base.copy(e) - @inbounds ht.hashdata[vidx] = Hashvalue1(0, he, e[1]) - - ht.load += 1 - - return vidx -end diff --git a/benchmark/scripts/hashtable/hashtable-2.jl b/benchmark/scripts/hashtable/hashtable-2.jl deleted file mode 100644 index 8b137891..00000000 --- a/benchmark/scripts/hashtable/hashtable-2.jl +++ /dev/null @@ -1 +0,0 @@ - diff --git a/benchmark/scripts/llvm.jl b/benchmark/scripts/llvm.jl deleted file mode 100644 index 1567f23b..00000000 --- a/benchmark/scripts/llvm.jl +++ /dev/null @@ -1,352 +0,0 @@ -using HostCPUFeatures, InteractiveUtils - -const BitInteger = Union{Int16, Int32, Int64, Int8, UInt16, UInt32, UInt64, UInt8} - -jl_to_llvm_t(::Type{T}) where {T <: BitInteger} = "i$(8*sizeof(T))" -align_to(x::Integer, N::Integer) = x ⊻ (N - 1) - -function llvm_iota(::Type{T}, N::Integer, start::Int=0) where {T <: BitInteger} - llvm_t = jl_to_llvm_t(T) - llvm_vec_t = "<$N x $llvm_t>" - llvm_vec = "<" * join(["$llvm_t $(T(i))" for i in start:(N + start - 1)], ", ") * ">" - llvm_vec_t, llvm_vec -end - -function pick_vector_width_clamp_8(::Type{T}) where {T} - N = pick_vector_width(T) - if N in (8, 16, 32) - return Int(N) - end - if N == 64 - return 32 - end - 1 -end - -# Vector functions in this file assume that -# - input vectors are non-negative. -# - input vectors have the same length. - -# Returns false if a[i] < b[i] for ANY index i, and true otherwise. -@inline @generated function _vec_not_any_lt_NEW( - a::Vector{T}, - b::Vector{T}, - offset::Int=1 -) where {T <: BitInteger} - N = pick_vector_width_clamp_8(T) - - # Unfortunate case. Default to scalar code. - if N == 1 - return quote - @inbounds for j in (1 + offset):length(a) - if a[j] < b[j] - return false - end - end - return true - end - end - - # The case when IntN exists. - @assert N in (8, 16, 32, 64) - B = sizeof(T) - llvm_t = jl_to_llvm_t(T) - mask = align_to(typemax(Int), N) - _, iota = llvm_iota(Int8, N) - textir = """ - declare <$N x $llvm_t> @llvm.masked.load.v$(N)$(llvm_t)(<$N x $llvm_t>*, i32, <$N x i1>, <$N x $llvm_t>); - define i8 @entry(i8* %0, i8* %1, i64 %2) #0 { - top: - %a = bitcast i8* %0 to $llvm_t* - %b = bitcast i8* %1 to $llvm_t* - %lenm$(N-1) = add nsw i64 %2, -$(N-1) - %dosimditer = icmp ugt i64 %2, $(N-1) - br i1 %dosimditer, label %L9.lr.ph, label %L32 - L9.lr.ph: - %len$N = and i64 %2, $mask ; divisible by N - br label %L9 - - L9: - %i = phi i64 [ 0, %L9.lr.ph ], [ %vinc, %L30 ] - %api = getelementptr inbounds $llvm_t, $llvm_t* %a, i64 %i - %bpi = getelementptr inbounds $llvm_t, $llvm_t* %b, i64 %i - %avi = bitcast $llvm_t* %api to <$N x $llvm_t>* - %bvi = bitcast $llvm_t* %bpi to <$N x $llvm_t>* - %ai = load <$N x $llvm_t>, <$N x $llvm_t>* %avi, align $B - %bi = load <$N x $llvm_t>, <$N x $llvm_t>* %bvi, align $B - %mask = icmp ult <$N x $llvm_t> %ai, %bi - %compressed = bitcast <$N x i1> %mask to i$N - %matchnotfound = icmp eq i$N %compressed, 0 - br i1 %matchnotfound, label %L30, label %common.ret - - common.ret: - %retval = phi i8 [ 0, %L9 ], [ 1, %L32 ], [ 0, %L51 ], [ 1, %L67 ] - ret i8 %retval - - L30: - %vinc = add nuw nsw i64 %i, $N - %continue = icmp slt i64 %vinc, %lenm$(N-1) - br i1 %continue, label %L9, label %L32 - - L32: - %cumi = phi i64 [ 0, %top ], [ %len$N, %L30 ] - %done = icmp eq i64 %cumi, %2 - br i1 %done, label %common.ret, label %L51 - - L51: - %si = phi i64 [ %inc, %L67 ], [ %cumi, %L32 ] - %sapi = getelementptr inbounds $llvm_t, $llvm_t* %a, i64 %si - %sbpi = getelementptr inbounds $llvm_t, $llvm_t* %b, i64 %si - %savi = load $llvm_t, $llvm_t* %sapi, align $B - %sbvi = load $llvm_t, $llvm_t* %sbpi, align $B - %match = icmp ult $llvm_t %savi, %sbvi - br i1 %match, label %common.ret, label %L67 - - L67: - %inc = add i64 %si, 1 - %dobreak = icmp eq i64 %inc, %2 - br i1 %dobreak, label %common.ret, label %L51 - } - attributes #0 = { alwaysinline } - """ - quote - GC.@preserve a b begin - Base.llvmcall( - ($textir, "entry"), - Bool, - Tuple{Ptr{T}, Ptr{T}, Int64}, - pointer(a) + sizeof(T) * offset, - pointer(b) + sizeof(T) * offset, - length(a) - offset - ) - end - end -end - -@inline @generated function _vec_not_any_lt_OLD( - a::Vector{T}, - b::Vector{T}, - offset::Int=1 -) where {T <: BitInteger} - N = pick_vector_width_clamp_8(T) - - # Unfortunate case. Default to scalar code. - if N == 1 - return quote - @inbounds for j in (1 + offset):length(a) - if a[j] < b[j] - return false - end - end - return true - end - end - - # The case when IntN exists. - @assert N in (8, 16, 32, 64) - B = sizeof(T) - llvm_t = jl_to_llvm_t(T) - mask = align_to(typemax(Int), N) - textir = """ - define i8 @entry(i64 %0, i64 %1, i64 %2) #0 { - top: - %a = inttoptr i64 %0 to $llvm_t* - %b = inttoptr i64 %1 to $llvm_t* - %lenm$(N-1) = add nsw i64 %2, -$(N-1) - %dosimditer = icmp ugt i64 %2, $(N-1) - br i1 %dosimditer, label %L9.lr.ph, label %L32 - - L9.lr.ph: - %len$N = and i64 %2, $mask ; divisible by N - br label %L9 - - L9: - %i = phi i64 [ 0, %L9.lr.ph ], [ %vinc, %L30 ] - %api = getelementptr inbounds $llvm_t, $llvm_t* %a, i64 %i - %bpi = getelementptr inbounds $llvm_t, $llvm_t* %b, i64 %i - %avi = bitcast $llvm_t* %api to <$N x $llvm_t>* - %bvi = bitcast $llvm_t* %bpi to <$N x $llvm_t>* - %ai = load <$N x $llvm_t>, <$N x $llvm_t>* %avi, align $B - %bi = load <$N x $llvm_t>, <$N x $llvm_t>* %bvi, align $B - %mask = icmp ult <$N x $llvm_t> %ai, %bi - %compressed = bitcast <$N x i1> %mask to i$N - %matchnotfound = icmp eq i$N %compressed, 0 - br i1 %matchnotfound, label %L30, label %common.ret - - common.ret: - %retval = phi i8 [ 0, %L9 ], [ 1, %L32 ], [ 0, %L51 ], [ 1, %L67 ] - ret i8 %retval - - L30: - %vinc = add nuw nsw i64 %i, $N - %continue = icmp slt i64 %vinc, %lenm$(N-1) - br i1 %continue, label %L9, label %L32 - - L32: - %cumi = phi i64 [ 0, %top ], [ %len$N, %L30 ] - %done = icmp eq i64 %cumi, %2 - br i1 %done, label %common.ret, label %L51 - - L51: - %si = phi i64 [ %inc, %L67 ], [ %cumi, %L32 ] - %sapi = getelementptr inbounds $llvm_t, $llvm_t* %a, i64 %si - %sbpi = getelementptr inbounds $llvm_t, $llvm_t* %b, i64 %si - %savi = load $llvm_t, $llvm_t* %sapi, align $B - %sbvi = load $llvm_t, $llvm_t* %sbpi, align $B - %match = icmp ult $llvm_t %savi, %sbvi - br i1 %match, label %common.ret, label %L67 - - L67: - %inc = add i64 %si, 1 - %dobreak = icmp eq i64 %inc, %2 - br i1 %dobreak, label %common.ret, label %L51 - } - attributes #0 = { alwaysinline } - """ - quote - GC.@preserve a b begin - Base.llvmcall( - ($textir, "entry"), - Bool, - Tuple{Ptr{T}, Ptr{T}, Int64}, - pointer(a) + sizeof(T) * offset, - pointer(b) + sizeof(T) * offset, - length(a) - offset - ) - end - end -end - -@inline function foo_old(a::Vector{UInt32}) - textir = """ - define i32 @entry(i64 %0, i64 %1) #0 { - top: - %arr = inttoptr i64 %0 to i32* - %x = getelementptr inbounds i32, i32* %a, i64 0 - ret i32 %x - } - attributes #0 = { alwaysinline } - """ - quote - GC.@preserve a begin - Base.llvmcall(($textir, "entry"), Bool, Tuple{Ptr{T}, Int64}, pointer(a), length(a)) - end - end -end - -for i in 1:5 - n = 2^i - a, b = rand(UInt8, n), rand(UInt8, n) - res1 = @btime _vec_not_any_lt_OLD($a, $b) - res2 = @btime _vec_not_any_lt_NEW($a, $b) - @assert res1 == res2 -end - -_vec_not_any_lt(UInt32[1, 2, 3, 4, 5, 6, 7, 8, 8], UInt32[1, 2, 3, 4, 5, 6, 7, 8, 9]) -@code_llvm _vec_not_any_lt(UInt32[1, 0, 3], UInt32[1, 2, 3]) -@code_native _vec_not_any_lt(UInt32[1, 0, 3], UInt32[1, 2, 3]) - -io = open((@__DIR__) * "/llvm.ll", "w") -code_native(io, _vec_not_any_lt, map(typeof, (UInt16[1, 0, 3], UInt16[1, 2, 3]))) -close(io) - -#= -L9.lr.ph: - %len$N = and i64 %2, $mask ; divisible by N - br label %L9 - - L9: - %i = phi i64 [ 0, %L9.lr.ph ], [ %vinc, %L30 ] - %api = getelementptr inbounds $llvm_t, $llvm_t* %a, i64 %i - %bpi = getelementptr inbounds $llvm_t, $llvm_t* %b, i64 %i - %avi = bitcast $llvm_t* %api to <$N x $llvm_t>* - %bvi = bitcast $llvm_t* %bpi to <$N x $llvm_t>* - %ai = load <$N x $llvm_t>, <$N x $llvm_t>* %avi, align $B - %bi = load <$N x $llvm_t>, <$N x $llvm_t>* %bvi, align $B - %mask = icmp ult <$N x $llvm_t> %ai, %bi - %compressed = bitcast <$N x i1> %mask to i$N - %matchnotfound = icmp eq i$N %compressed, 0 - br i1 %matchnotfound, label %L30, label %common.ret - - common.ret: - %retval = phi i8 [ 0, %L9 ], [ 1, %L32 ], [ %smatchnotfound.i8, %L51 ] - ret i8 %retval - - L30: - %vinc = add nuw nsw i64 %i, $N - %continue = icmp slt i64 %vinc, %lenm$(N-1) - br i1 %continue, label %L9, label %L32 - - L32: - %cumi = phi i64 [ 0, %top ], [ %len$N, %L30 ] - %done = icmp eq i64 %cumi, %2 - br i1 %done, label %common.ret, label %L51 - - L51: - ; %si = phi i64 [ %inc, %L67 ], [ %cumi, %L32 ] - %lenmod = and i64 %2, $(N-1) ; mod N - %lenmod.t = trunc i64 %lenmod to i8 - %lenmod.vec = insertelement <$N x i8> undef, i8 %lenmod.t, i64 0 - %res.si = shufflevector <$N x i8> %lenmod.vec, <$N x i8> undef, <$N x i32> zeroinitializer - %loadmask = icmp ugt <$N x i8> %res.si, $iota - %sapi = getelementptr inbounds $llvm_t, $llvm_t* %a, i64 %cumi - %sbpi = getelementptr inbounds $llvm_t, $llvm_t* %b, i64 %cumi - %savi = bitcast $llvm_t* %sapi to <$N x $llvm_t>* - %sbvi = bitcast $llvm_t* %sbpi to <$N x $llvm_t>* - %sai = call <$N x $llvm_t> @llvm.masked.load.v$(N)$(llvm_t)(<$N x $llvm_t>* %savi, i32 $B, <$N x i1> %loadmask, <$N x $llvm_t> zeroinitializer) - %sbi = call <$N x $llvm_t> @llvm.masked.load.v$(N)$(llvm_t)(<$N x $llvm_t>* %sbvi, i32 $B, <$N x i1> %loadmask, <$N x $llvm_t> zeroinitializer) - %smask = icmp ult <$N x $llvm_t> %sai, %sbi - %scompressed = bitcast <$N x i1> %smask to i$N - %smatchnotfound = icmp eq i$N %scompressed, 0 - %smatchnotfound.i8 = zext i1 %smatchnotfound to i8 - br label %common.ret - } - attributes #0 = { alwaysinline } -=# - -######################## - -@generated function foo_old(a::Vector{UInt32}) - textir = """ - define i32 @entry(i64 %0) #0 { - %arr = inttoptr i64 %0 to i32* - %arr.i = getelementptr inbounds i32, i32* %arr, i64 0 - %x = load i32, i32* %arr.i, align 4 - ret i32 %x - } - attributes #0 = { alwaysinline } - """ - quote - GC.@preserve a begin - Base.llvmcall(($textir, "entry"), UInt32, Tuple{Ptr{UInt32}}, pointer(a)) - end - end -end - -@generated function foo_new(a::Vector{UInt32}) - textir = """ - define i32 @entry(i8* %0) #0 { - %arr = bitcast i8* %0 to i32* - %arr.i = getelementptr inbounds i32, i32* %arr, i64 0 - %x = load i32, i32* %arr.i, align 4 - ret i32 %x - } - attributes #0 = { alwaysinline } - """ - quote - GC.@preserve a begin - Base.llvmcall(($textir, "entry"), UInt32, Tuple{Ptr{UInt32}}, pointer(a)) - end - end -end - -@assert foo_old([UInt32(9)]) === foo_new([UInt32(9)]) === UInt32(9) - -@code_native foo_old([UInt32(1)]) -@code_native foo_new([UInt32(1)]) - -@code_llvm debuginfo = :none foo_old([UInt32(1)]) -@code_llvm debuginfo = :none foo_new([UInt32(1)]) - -@btime foo_old($([UInt32(9)])); -@btime foo_new($([UInt32(9)])); diff --git a/benchmark/scripts/llvm.ll b/benchmark/scripts/llvm.ll deleted file mode 100644 index a8a16e93..00000000 --- a/benchmark/scripts/llvm.ll +++ /dev/null @@ -1,389 +0,0 @@ - .text - .file "_vec_not_any_lt" - .section .rodata.cst16,"aM",@progbits,16 - .p2align 4 # -- Begin function julia__vec_not_any_lt_5899 -.LCPI0_0: - .byte 0 # 0x0 - .byte 1 # 0x1 - .byte 2 # 0x2 - .byte 3 # 0x3 - .byte 4 # 0x4 - .byte 5 # 0x5 - .byte 6 # 0x6 - .byte 7 # 0x7 - .byte 8 # 0x8 - .byte 9 # 0x9 - .byte 10 # 0xa - .byte 11 # 0xb - .byte 12 # 0xc - .byte 13 # 0xd - .byte 14 # 0xe - .byte 15 # 0xf - .text - .globl julia__vec_not_any_lt_5899 - .p2align 4, 0x90 - .type julia__vec_not_any_lt_5899,@function -julia__vec_not_any_lt_5899: # @julia__vec_not_any_lt_5899 -; ┌ @ none within `_vec_not_any_lt` - .cfi_startproc -# %bb.0: # %top - push rbp - .cfi_def_cfa_offset 16 - .cfi_offset rbp, -16 - mov rbp, rsp - .cfi_def_cfa_register rbp -; │ @ none within `_vec_not_any_lt` @ none:0 -; │┌ @ none within `macro expansion` @ c:\data\projects\gbgb\Groebner.jl\benchmark\scripts\llvm.jl:120 -; ││┌ @ abstractarray.jl:1237 within `pointer` -; │││┌ @ pointer.jl:65 within `unsafe_convert` - mov r9, qword ptr [rcx] -; ││└└ -; ││┌ @ essentials.jl:10 within `length` - mov rax, qword ptr [rcx + 8] -; ││└ -; ││┌ @ pointer.jl:282 within `+` - add r9, 2 -; ││└ -; ││┌ @ abstractarray.jl:1237 within `pointer` -; │││┌ @ pointer.jl:65 within `unsafe_convert` - mov r10, qword ptr [rdx] -; ││└└ -; ││┌ @ pointer.jl:282 within `+` - add r10, 2 -; ││└ -; ││┌ @ int.jl:86 within `-` - lea r11, [rax - 1] -; ││└ - cmp r11, 16 - jb .LBB0_1 -# %bb.2: # %L9.lr.ph.i - add rax, -16 - movabs r8, 9223372036854775792 - and r8, r11 - xor ecx, ecx - .p2align 4, 0x90 -.LBB0_3: # %L9.i - # =>This Inner Loop Header: Depth=1 - vmovdqu ymm0, ymmword ptr [r9 + 2*rcx] - vpmaxuw ymm1, ymm0, ymmword ptr [r10 + 2*rcx] - vpcmpeqw ymm0, ymm0, ymm1 - vpmovmskb edx, ymm0 - not edx - test edx, edx - jne .LBB0_4 -# %bb.5: # %L30.i - # in Loop: Header=BB0_3 Depth=1 - add rcx, 16 - cmp rcx, rax - jl .LBB0_3 - jmp .LBB0_6 -.LBB0_1: - xor r8d, r8d -.LBB0_6: # %L32.i - mov al, 1 - cmp r8, r11 - je .LBB0_72 -# %bb.7: # %L51.i - and r11b, 15 - vmovd xmm0, r11d - vpbroadcastb xmm0, xmm0 - lea rdx, [r9 + 2*r8] - movabs rax, offset .LCPI0_0 - vpcmpgtb xmm0, xmm0, xmmword ptr [rax] - vpmovmskb eax, xmm0 - vpxor xmm0, xmm0, xmm0 - test al, 1 - jne .LBB0_8 -# %bb.9: # %else - test al, 2 - jne .LBB0_10 -.LBB0_11: # %else12 - test al, 4 - jne .LBB0_12 -.LBB0_13: # %else15 - test al, 8 - jne .LBB0_14 -.LBB0_15: # %else18 - test al, 16 - jne .LBB0_16 -.LBB0_17: # %else21 - test al, 32 - jne .LBB0_18 -.LBB0_19: # %else24 - test al, 64 - jne .LBB0_20 -.LBB0_21: # %else27 - test al, -128 - jne .LBB0_22 -.LBB0_23: # %else30 - test eax, 256 - jne .LBB0_24 -.LBB0_25: # %else33 - test eax, 512 - jne .LBB0_26 -.LBB0_27: # %else36 - test eax, 1024 - jne .LBB0_28 -.LBB0_29: # %else39 - test eax, 2048 - jne .LBB0_30 -.LBB0_31: # %else42 - test eax, 4096 - jne .LBB0_32 -.LBB0_33: # %else45 - test eax, 8192 - jne .LBB0_34 -.LBB0_35: # %else48 - test eax, 16384 - jne .LBB0_36 -.LBB0_37: # %else51 - test eax, 32768 - je .LBB0_39 -.LBB0_38: # %cond.load53 - vpbroadcastw ymm1, word ptr [rdx + 30] - vpblendw ymm1, ymm0, ymm1, 128 # ymm1 = ymm0[0,1,2,3,4,5,6],ymm1[7],ymm0[8,9,10,11,12,13,14],ymm1[15] - vpblendd ymm0, ymm0, ymm1, 240 # ymm0 = ymm0[0,1,2,3],ymm1[4,5,6,7] -.LBB0_39: # %else54 - lea rcx, [r10 + 2*r8] - vpxor xmm1, xmm1, xmm1 - test al, 1 - jne .LBB0_40 -# %bb.41: # %else58 - test al, 2 - jne .LBB0_42 -.LBB0_43: # %else61 - test al, 4 - jne .LBB0_44 -.LBB0_45: # %else64 - test al, 8 - jne .LBB0_46 -.LBB0_47: # %else67 - test al, 16 - jne .LBB0_48 -.LBB0_49: # %else70 - test al, 32 - jne .LBB0_50 -.LBB0_51: # %else73 - test al, 64 - jne .LBB0_52 -.LBB0_53: # %else76 - test al, -128 - jne .LBB0_54 -.LBB0_55: # %else79 - test eax, 256 - jne .LBB0_56 -.LBB0_57: # %else82 - test eax, 512 - jne .LBB0_58 -.LBB0_59: # %else85 - test eax, 1024 - jne .LBB0_60 -.LBB0_61: # %else88 - test eax, 2048 - jne .LBB0_62 -.LBB0_63: # %else91 - test eax, 4096 - jne .LBB0_64 -.LBB0_65: # %else94 - test eax, 8192 - jne .LBB0_66 -.LBB0_67: # %else97 - test eax, 16384 - jne .LBB0_68 -.LBB0_69: # %else100 - test eax, 32768 - je .LBB0_71 -.LBB0_70: # %cond.load102 - vpbroadcastw ymm2, word ptr [rcx + 30] - vpblendw ymm2, ymm1, ymm2, 128 # ymm2 = ymm1[0,1,2,3,4,5,6],ymm2[7],ymm1[8,9,10,11,12,13,14],ymm2[15] - vpblendd ymm1, ymm1, ymm2, 240 # ymm1 = ymm1[0,1,2,3],ymm2[4,5,6,7] -.LBB0_71: # %else103 - vpmaxuw ymm1, ymm0, ymm1 - vpcmpeqw ymm0, ymm0, ymm1 - vpmovmskb eax, ymm0 - not eax - test eax, eax - sete al -.LBB0_72: # %julia__vec_not_any_lt_5899u5901.exit - # kill: def $al killed $al killed $eax - pop rbp - vzeroupper - ret -.LBB0_4: - xor eax, eax - # kill: def $al killed $al killed $eax - pop rbp - vzeroupper - ret -.LBB0_8: # %cond.load - movzx ecx, word ptr [rdx] - vmovd xmm0, ecx - test al, 2 - je .LBB0_11 -.LBB0_10: # %cond.load11 - vpinsrw xmm1, xmm0, word ptr [rdx + 2], 1 - vpblendd ymm0, ymm0, ymm1, 15 # ymm0 = ymm1[0,1,2,3],ymm0[4,5,6,7] - test al, 4 - je .LBB0_13 -.LBB0_12: # %cond.load14 - vpinsrw xmm1, xmm0, word ptr [rdx + 4], 2 - vpblendd ymm0, ymm0, ymm1, 15 # ymm0 = ymm1[0,1,2,3],ymm0[4,5,6,7] - test al, 8 - je .LBB0_15 -.LBB0_14: # %cond.load17 - vpinsrw xmm1, xmm0, word ptr [rdx + 6], 3 - vpblendd ymm0, ymm0, ymm1, 15 # ymm0 = ymm1[0,1,2,3],ymm0[4,5,6,7] - test al, 16 - je .LBB0_17 -.LBB0_16: # %cond.load20 - vpinsrw xmm1, xmm0, word ptr [rdx + 8], 4 - vpblendd ymm0, ymm0, ymm1, 15 # ymm0 = ymm1[0,1,2,3],ymm0[4,5,6,7] - test al, 32 - je .LBB0_19 -.LBB0_18: # %cond.load23 - vpinsrw xmm1, xmm0, word ptr [rdx + 10], 5 - vpblendd ymm0, ymm0, ymm1, 15 # ymm0 = ymm1[0,1,2,3],ymm0[4,5,6,7] - test al, 64 - je .LBB0_21 -.LBB0_20: # %cond.load26 - vpinsrw xmm1, xmm0, word ptr [rdx + 12], 6 - vpblendd ymm0, ymm0, ymm1, 15 # ymm0 = ymm1[0,1,2,3],ymm0[4,5,6,7] - test al, -128 - je .LBB0_23 -.LBB0_22: # %cond.load29 - vpinsrw xmm1, xmm0, word ptr [rdx + 14], 7 - vpblendd ymm0, ymm0, ymm1, 15 # ymm0 = ymm1[0,1,2,3],ymm0[4,5,6,7] - test eax, 256 - je .LBB0_25 -.LBB0_24: # %cond.load32 - vpbroadcastw ymm1, word ptr [rdx + 16] - vpblendw ymm1, ymm0, ymm1, 1 # ymm1 = ymm1[0],ymm0[1,2,3,4,5,6,7],ymm1[8],ymm0[9,10,11,12,13,14,15] - vpblendd ymm0, ymm0, ymm1, 240 # ymm0 = ymm0[0,1,2,3],ymm1[4,5,6,7] - test eax, 512 - je .LBB0_27 -.LBB0_26: # %cond.load35 - vpbroadcastw ymm1, word ptr [rdx + 18] - vpblendw ymm1, ymm0, ymm1, 2 # ymm1 = ymm0[0],ymm1[1],ymm0[2,3,4,5,6,7,8],ymm1[9],ymm0[10,11,12,13,14,15] - vpblendd ymm0, ymm0, ymm1, 240 # ymm0 = ymm0[0,1,2,3],ymm1[4,5,6,7] - test eax, 1024 - je .LBB0_29 -.LBB0_28: # %cond.load38 - vpbroadcastw ymm1, word ptr [rdx + 20] - vpblendw ymm1, ymm0, ymm1, 4 # ymm1 = ymm0[0,1],ymm1[2],ymm0[3,4,5,6,7,8,9],ymm1[10],ymm0[11,12,13,14,15] - vpblendd ymm0, ymm0, ymm1, 240 # ymm0 = ymm0[0,1,2,3],ymm1[4,5,6,7] - test eax, 2048 - je .LBB0_31 -.LBB0_30: # %cond.load41 - vpbroadcastw ymm1, word ptr [rdx + 22] - vpblendw ymm1, ymm0, ymm1, 8 # ymm1 = ymm0[0,1,2],ymm1[3],ymm0[4,5,6,7,8,9,10],ymm1[11],ymm0[12,13,14,15] - vpblendd ymm0, ymm0, ymm1, 240 # ymm0 = ymm0[0,1,2,3],ymm1[4,5,6,7] - test eax, 4096 - je .LBB0_33 -.LBB0_32: # %cond.load44 - vpbroadcastw ymm1, word ptr [rdx + 24] - vpblendw ymm1, ymm0, ymm1, 16 # ymm1 = ymm0[0,1,2,3],ymm1[4],ymm0[5,6,7,8,9,10,11],ymm1[12],ymm0[13,14,15] - vpblendd ymm0, ymm0, ymm1, 240 # ymm0 = ymm0[0,1,2,3],ymm1[4,5,6,7] - test eax, 8192 - je .LBB0_35 -.LBB0_34: # %cond.load47 - vpbroadcastw ymm1, word ptr [rdx + 26] - vpblendw ymm1, ymm0, ymm1, 32 # ymm1 = ymm0[0,1,2,3,4],ymm1[5],ymm0[6,7,8,9,10,11,12],ymm1[13],ymm0[14,15] - vpblendd ymm0, ymm0, ymm1, 240 # ymm0 = ymm0[0,1,2,3],ymm1[4,5,6,7] - test eax, 16384 - je .LBB0_37 -.LBB0_36: # %cond.load50 - vpbroadcastw ymm1, word ptr [rdx + 28] - vpblendw ymm1, ymm0, ymm1, 64 # ymm1 = ymm0[0,1,2,3,4,5],ymm1[6],ymm0[7,8,9,10,11,12,13],ymm1[14],ymm0[15] - vpblendd ymm0, ymm0, ymm1, 240 # ymm0 = ymm0[0,1,2,3],ymm1[4,5,6,7] - test eax, 32768 - je .LBB0_39 - jmp .LBB0_38 -.LBB0_40: # %cond.load57 - movzx edx, word ptr [rcx] - vmovd xmm1, edx - test al, 2 - je .LBB0_43 -.LBB0_42: # %cond.load60 - vpinsrw xmm2, xmm1, word ptr [rcx + 2], 1 - vpblendd ymm1, ymm1, ymm2, 15 # ymm1 = ymm2[0,1,2,3],ymm1[4,5,6,7] - test al, 4 - je .LBB0_45 -.LBB0_44: # %cond.load63 - vpinsrw xmm2, xmm1, word ptr [rcx + 4], 2 - vpblendd ymm1, ymm1, ymm2, 15 # ymm1 = ymm2[0,1,2,3],ymm1[4,5,6,7] - test al, 8 - je .LBB0_47 -.LBB0_46: # %cond.load66 - vpinsrw xmm2, xmm1, word ptr [rcx + 6], 3 - vpblendd ymm1, ymm1, ymm2, 15 # ymm1 = ymm2[0,1,2,3],ymm1[4,5,6,7] - test al, 16 - je .LBB0_49 -.LBB0_48: # %cond.load69 - vpinsrw xmm2, xmm1, word ptr [rcx + 8], 4 - vpblendd ymm1, ymm1, ymm2, 15 # ymm1 = ymm2[0,1,2,3],ymm1[4,5,6,7] - test al, 32 - je .LBB0_51 -.LBB0_50: # %cond.load72 - vpinsrw xmm2, xmm1, word ptr [rcx + 10], 5 - vpblendd ymm1, ymm1, ymm2, 15 # ymm1 = ymm2[0,1,2,3],ymm1[4,5,6,7] - test al, 64 - je .LBB0_53 -.LBB0_52: # %cond.load75 - vpinsrw xmm2, xmm1, word ptr [rcx + 12], 6 - vpblendd ymm1, ymm1, ymm2, 15 # ymm1 = ymm2[0,1,2,3],ymm1[4,5,6,7] - test al, -128 - je .LBB0_55 -.LBB0_54: # %cond.load78 - vpinsrw xmm2, xmm1, word ptr [rcx + 14], 7 - vpblendd ymm1, ymm1, ymm2, 15 # ymm1 = ymm2[0,1,2,3],ymm1[4,5,6,7] - test eax, 256 - je .LBB0_57 -.LBB0_56: # %cond.load81 - vpbroadcastw ymm2, word ptr [rcx + 16] - vpblendw ymm2, ymm1, ymm2, 1 # ymm2 = ymm2[0],ymm1[1,2,3,4,5,6,7],ymm2[8],ymm1[9,10,11,12,13,14,15] - vpblendd ymm1, ymm1, ymm2, 240 # ymm1 = ymm1[0,1,2,3],ymm2[4,5,6,7] - test eax, 512 - je .LBB0_59 -.LBB0_58: # %cond.load84 - vpbroadcastw ymm2, word ptr [rcx + 18] - vpblendw ymm2, ymm1, ymm2, 2 # ymm2 = ymm1[0],ymm2[1],ymm1[2,3,4,5,6,7,8],ymm2[9],ymm1[10,11,12,13,14,15] - vpblendd ymm1, ymm1, ymm2, 240 # ymm1 = ymm1[0,1,2,3],ymm2[4,5,6,7] - test eax, 1024 - je .LBB0_61 -.LBB0_60: # %cond.load87 - vpbroadcastw ymm2, word ptr [rcx + 20] - vpblendw ymm2, ymm1, ymm2, 4 # ymm2 = ymm1[0,1],ymm2[2],ymm1[3,4,5,6,7,8,9],ymm2[10],ymm1[11,12,13,14,15] - vpblendd ymm1, ymm1, ymm2, 240 # ymm1 = ymm1[0,1,2,3],ymm2[4,5,6,7] - test eax, 2048 - je .LBB0_63 -.LBB0_62: # %cond.load90 - vpbroadcastw ymm2, word ptr [rcx + 22] - vpblendw ymm2, ymm1, ymm2, 8 # ymm2 = ymm1[0,1,2],ymm2[3],ymm1[4,5,6,7,8,9,10],ymm2[11],ymm1[12,13,14,15] - vpblendd ymm1, ymm1, ymm2, 240 # ymm1 = ymm1[0,1,2,3],ymm2[4,5,6,7] - test eax, 4096 - je .LBB0_65 -.LBB0_64: # %cond.load93 - vpbroadcastw ymm2, word ptr [rcx + 24] - vpblendw ymm2, ymm1, ymm2, 16 # ymm2 = ymm1[0,1,2,3],ymm2[4],ymm1[5,6,7,8,9,10,11],ymm2[12],ymm1[13,14,15] - vpblendd ymm1, ymm1, ymm2, 240 # ymm1 = ymm1[0,1,2,3],ymm2[4,5,6,7] - test eax, 8192 - je .LBB0_67 -.LBB0_66: # %cond.load96 - vpbroadcastw ymm2, word ptr [rcx + 26] - vpblendw ymm2, ymm1, ymm2, 32 # ymm2 = ymm1[0,1,2,3,4],ymm2[5],ymm1[6,7,8,9,10,11,12],ymm2[13],ymm1[14,15] - vpblendd ymm1, ymm1, ymm2, 240 # ymm1 = ymm1[0,1,2,3],ymm2[4,5,6,7] - test eax, 16384 - je .LBB0_69 -.LBB0_68: # %cond.load99 - vpbroadcastw ymm2, word ptr [rcx + 28] - vpblendw ymm2, ymm1, ymm2, 64 # ymm2 = ymm1[0,1,2,3,4,5],ymm2[6],ymm1[7,8,9,10,11,12,13],ymm2[14],ymm1[15] - vpblendd ymm1, ymm1, ymm2, 240 # ymm1 = ymm1[0,1,2,3],ymm2[4,5,6,7] - test eax, 32768 - je .LBB0_71 - jmp .LBB0_70 -.Lfunc_end0: - .size julia__vec_not_any_lt_5899, .Lfunc_end0-julia__vec_not_any_lt_5899 - .cfi_endproc -; └└ - # -- End function - .section ".note.GNU-stack","",@progbits diff --git a/benchmark/scripts/monom.jl b/benchmark/scripts/monom.jl deleted file mode 100644 index c3386584..00000000 --- a/benchmark/scripts/monom.jl +++ /dev/null @@ -1,109 +0,0 @@ -using BenchmarkTools, PrettyTables, IOCapture - -using HostCPUFeatures -using HostCPUFeatures: - register_size, - pick_vector_width, - pick_vector_width_shift, - simd_integer_register_size, - fma_fast, - has_feature, - register_count, - cpu_name, - register_size - -######### - -function setup_data(n, T, kind=:randeq) - if kind === :randeq - a, b = zeros(T, n), zeros(T, n) - inds = rand(1:n, 10) - a[inds] .= 1 - b[inds] .= 1 - end - a, b -end - -function setup_dense(n, T) - a, b = setup_data(n, T) - x = Groebner.monom_construct_from_vector(Groebner.ExponentVector{T}, a) - y = Groebner.monom_construct_from_vector(Groebner.ExponentVector{T}, b) - x, y -end - -packed_type(n) = - if n < 8 - Groebner.PackedTuple1 - elseif n < 16 - Groebner.PackedTuple2 - elseif n < 24 - Groebner.PackedTuple3 - elseif n < 32 - Groebner.PackedTuple4 - else - nothing - end - -function setup_packed(n, T) - a, b = setup_data(n, T) - type = packed_type(n) - isnothing(type) && return nothing - x_packed = Groebner.monom_construct_from_vector(type{UInt64, T}, a) - y_packed = Groebner.monom_construct_from_vector(type{UInt64, T}, b) - x_packed, y_packed -end - -function setup_sparse(n, T) - a, b = setup_data(n, T) - x_sparse = Groebner.monom_construct_from_vector(Groebner.SparseExponentVector{T}, a) - y_sparse = Groebner.monom_construct_from_vector(Groebner.SparseExponentVector{T}, b) - x_sparse, y_sparse -end - -funcs = ["monom_lcm!", "monom_is_divisible"] -execs = [ - ((n, setup) -> @btime Groebner.monom_lcm!(z, x, y) setup = begin - x, y = $(setup)($n) - z = Groebner.monom_copy(x) - end), - ((n, setup) -> @btime Groebner.monom_is_divisible(x, y) setup = begin - x, y = $(setup)($n) - end) -] -impls = ["dense:u8", "dense:u32", "packed", "sparse"] -setup = [ - n -> setup_dense(n, UInt8), - n -> setup_dense(n, UInt32), - n -> setup_packed(n, UInt8), - n -> setup_sparse(n, UInt8) -] -ns = [7, 8, 15, 16, 23, 24, 31, 32, 63, 64, 127, 128, 255, 256] -# ns = [255, 256, 400, 511, 512, 1023, 1024] - -begin - for (k, func) in enumerate(funcs[2:2]) - table = Matrix{Any}(undef, (length(ns), length(impls))) - exec = execs[k] - @info "func = $func" - for (i, n) in enumerate(ns) - @info "n = $n" - row = Vector{Any}(undef, length(impls)) - for (j, impl) in enumerate(impls) - print("$func:$impl\t") - if (setup[j])(n) === nothing - println("-") - row[j] = "-" - continue - end - c = IOCapture.capture() do - exec(n, setup[j]) - end - s = strip(c.output) - println(s) - row[j] = parse(Float64, s[1:findfirst(' ', s)]) - end - table[i, :] .= row - end - pretty_table(table, title=func, header=impls, tf=tf_markdown, row_labels=ns) - end -end diff --git a/benchmark/scripts/pairset/pairset.jl b/benchmark/scripts/pairset/pairset.jl deleted file mode 100644 index e4e8e0f7..00000000 --- a/benchmark/scripts/pairset/pairset.jl +++ /dev/null @@ -1,127 +0,0 @@ -using LinuxPerf, JLD2, BenchmarkTools - -function clear_data() - for (root, dirs, files) in walkdir((@__DIR__)) - for file in files - if endswith((@__DIR__) * "/" * file, "jld2") - rm((@__DIR__) * "/" * file) - end - end - break - end -end - -function load_data() - data = [] - for (root, dirs, files) in walkdir((@__DIR__)) - @info "" files - for file in files - !endswith(file, "jld2") && continue - a = load((@__DIR__) * "/" * file) - push!(data, a) - end - break - end - data -end - -function describe_data(data) - println("$(length(data)) entries") - println("#\tb:filled\tps:load\t\tupdht:load\tupdht:sz\tpairs") - println("-------------------------------------------------------------------------") - res = [] - for (j, x) in enumerate(data) - ht, update_ht, basis, pairset, i = x["ht"], x["update_ht"], x["basis"], x["pairset"], x["i"] - # println("$j\t$(basis.nfilled)\t\t$(pairset.load)\t\t$(update_ht.load)/$(update_ht.size)") - push!(res, [basis.nfilled, pairset.load, update_ht.load, update_ht.size, i]) - end - println("avg\t", join(string.(round.(Int, mean(res, dims=1)[1])), "\t\t")) - println("tot\t", join(string.(sum(res, dims=1)[1]), "\t\t")) -end - -function multiple_data(data, n=1) - newdata = deepcopy(data) - for i in 1:n - append!(newdata, deepcopy(data)) - end - newdata -end - -clear_data() - -# data = load_data(); -# describe_data(data) - -_data = deepcopy(data); -@time begin - for x in data - ht, update_ht, basis, pairset, i = x["ht"], x["update_ht"], x["basis"], x["pairset"], x["i"] - Groebner.pairset_update!(pairset, basis, ht, update_ht, i) - end -end -# 0.005203 seconds (187 allocations: 5.844 KiB) -# 0.005697 seconds (187 allocations: 5.844 KiB) -# 0.005263 seconds (187 allocations: 5.844 KiB) - -# _data = multiple_data(data); -_data = deepcopy(data); -@pstats "(cpu-cycles,task-clock),(instructions,branch-instructions,branch-misses), (L1-dcache-load-misses, L1-dcache-loads, cache-misses, cache-references)" begin - for x in _data - ht, update_ht, basis, pairset, i = x["ht"], x["update_ht"], x["basis"], x["pairset"], x["i"] - Groebner.pairset_update!(pairset, basis, ht, update_ht, i) - end -end - -############################## - -function gather_pairs(x::Vector{T}, pairs) where {T} - s = T(0) - @inbounds for p in pairs - i, j = p - s += x[i] + x[j] - end - s -end - -n, m = 1000, 1000 * 1000 -x = rand(UInt64, n) - -pairs_i8 = [(rand(1:n), rand(1:n)) for i in 1:m] -pairs_i4 = [(Int32.(rand(1:n)), Int32.(rand(1:n))) for i in 1:m] -pairs_i2 = [(Int16.(rand(1:n)), Int16.(rand(1:n))) for i in 1:m] - -@code_llvm debuginfo = :none gather_pairs(x, pairs_i8) -@code_native debuginfo = :none gather_pairs(x, pairs_i8) -@btime gather_pairs($x, pairs_i8) setup = begin - pairs_i8 = [(Int64.(rand(1:n)), Int64.(rand(1:n))) for i in 1:m] -end - -@code_llvm debuginfo = :none gather_pairs(x, pairs_i4) -@code_native debuginfo = :none gather_pairs(x, pairs_i4) -@btime gather_pairs($x, pairs_i4) setup = begin - pairs_i4 = [(Int32.(rand(1:n)), Int32.(rand(1:n))) for i in 1:m] -end - -@code_llvm debuginfo = :none gather_pairs(x, pairs_i2) -@code_native debuginfo = :none gather_pairs(x, pairs_i2) -@btime gather_pairs($x, pairs_i2) setup = begin - pairs_i2 = [(Int16.(rand(1:n)), Int16.(rand(1:n))) for i in 1:m] -end - -@pstats "(cpu-cycles,task-clock),(instructions,branch-instructions,branch-misses), (L1-dcache-load-misses, L1-dcache-loads, cache-misses, cache-references), (alignment-faults,page-faults,minor-faults)" begin - for _ in 1:100 - gather_pairs(x, pairs_i8) - end -end - -@pstats "(cpu-cycles,task-clock),(instructions,branch-instructions,branch-misses), (L1-dcache-load-misses, L1-dcache-loads, cache-misses, cache-references), (alignment-faults,page-faults,minor-faults)" begin - for _ in 1:100 - gather_pairs(x, pairs_i4) - end -end - -@pstats "(cpu-cycles,task-clock),(instructions,branch-instructions,branch-misses), (L1-dcache-load-misses, L1-dcache-loads, cache-misses, cache-references), (alignment-faults,page-faults,minor-faults)" begin - for _ in 1:100 - gather_pairs(x, pairs_i2) - end -end diff --git a/benchmark/scripts/runge-kutta/RK-6-6.mpl b/benchmark/scripts/runge-kutta/RK-6-6.mpl deleted file mode 100644 index ef824664..00000000 --- a/benchmark/scripts/runge-kutta/RK-6-6.mpl +++ /dev/null @@ -1,52 +0,0 @@ -with(Groebner): -with(PolynomialIdeals): - -kernelopts(numcpus=4); - -J := [ - b_1 + b_2 + b_3 + b_4 + b_5 + b_6 - 1, - 2*a_21*b_2 + 2*a_31*b_3 + 2*a_32*b_3 + 2*a_41*b_4 + 2*a_42*b_4 + 2*a_43*b_4 + 2*a_51*b_5 + 2*a_52*b_5 + 2*a_53*b_5 + 2*a_54*b_5 + 2*a_61*b_6 + 2*a_62*b_6 + 2*a_63*b_6 + 2*a_64*b_6 + 2*a_65*b_6 - 1, - 6*a_21*a_32*b_3 + 6*a_21*a_42*b_4 + 6*a_21*a_52*b_5 + 6*a_21*a_62*b_6 + 6*a_31*a_43*b_4 + 6*a_31*a_53*b_5 + 6*a_31*a_63*b_6 + 6*a_32*a_43*b_4 + 6*a_32*a_53*b_5 + 6*a_32*a_63*b_6 + 6*a_41*a_54*b_5 + 6*a_41*a_64*b_6 + 6*a_42*a_54*b_5 + 6*a_42*a_64*b_6 + 6*a_43*a_54*b_5 + 6*a_43*a_64*b_6 + 6*a_51*a_65*b_6 + 6*a_52*a_65*b_6 + 6*a_53*a_65*b_6 + 6*a_54*a_65*b_6 - 1, - 3*a_21^2*b_2 + 3*a_31^2*b_3 + 6*a_31*a_32*b_3 + 3*a_32^2*b_3 + 3*a_41^2*b_4 + 6*a_41*a_42*b_4 + 6*a_41*a_43*b_4 + 3*a_42^2*b_4 + 6*a_42*a_43*b_4 + 3*a_43^2*b_4 + 3*a_51^2*b_5 + 6*a_51*a_52*b_5 + 6*a_51*a_53*b_5 + 6*a_51*a_54*b_5 + 3*a_52^2*b_5 + 6*a_52*a_53*b_5 + 6*a_52*a_54*b_5 + 3*a_53^2*b_5 + 6*a_53*a_54*b_5 + 3*a_54^2*b_5 + 3*a_61^2*b_6 + 6*a_61*a_62*b_6 + 6*a_61*a_63*b_6 + 6*a_61*a_64*b_6 + 6*a_61*a_65*b_6 + 3*a_62^2*b_6 + 6*a_62*a_63*b_6 + 6*a_62*a_64*b_6 + 6*a_62*a_65*b_6 + 3*a_63^2*b_6 + 6*a_63*a_64*b_6 + 6*a_63*a_65*b_6 + 3*a_64^2*b_6 + 6*a_64*a_65*b_6 + 3*a_65^2*b_6 - 1, - 24*a_21*a_32*a_43*b_4 + 24*a_21*a_32*a_53*b_5 + 24*a_21*a_32*a_63*b_6 + 24*a_21*a_42*a_54*b_5 + 24*a_21*a_42*a_64*b_6 + 24*a_21*a_52*a_65*b_6 + 24*a_31*a_43*a_54*b_5 + 24*a_31*a_43*a_64*b_6 + 24*a_31*a_53*a_65*b_6 + 24*a_32*a_43*a_54*b_5 + 24*a_32*a_43*a_64*b_6 + 24*a_32*a_53*a_65*b_6 + 24*a_41*a_54*a_65*b_6 + 24*a_42*a_54*a_65*b_6 + 24*a_43*a_54*a_65*b_6 - 1, - 12*a_21^2*a_32*b_3 + 12*a_21^2*a_42*b_4 + 12*a_21^2*a_52*b_5 + 12*a_21^2*a_62*b_6 + 12*a_31^2*a_43*b_4 + 12*a_31^2*a_53*b_5 + 12*a_31^2*a_63*b_6 + 24*a_31*a_32*a_43*b_4 + 24*a_31*a_32*a_53*b_5 + 24*a_31*a_32*a_63*b_6 + 12*a_32^2*a_43*b_4 + 12*a_32^2*a_53*b_5 + 12*a_32^2*a_63*b_6 + 12*a_41^2*a_54*b_5 + 12*a_41^2*a_64*b_6 + 24*a_41*a_42*a_54*b_5 + 24*a_41*a_42*a_64*b_6 + 24*a_41*a_43*a_54*b_5 + 24*a_41*a_43*a_64*b_6 + 12*a_42^2*a_54*b_5 + 12*a_42^2*a_64*b_6 + 24*a_42*a_43*a_54*b_5 + 24*a_42*a_43*a_64*b_6 + 12*a_43^2*a_54*b_5 + 12*a_43^2*a_64*b_6 + 12*a_51^2*a_65*b_6 + 24*a_51*a_52*a_65*b_6 + 24*a_51*a_53*a_65*b_6 + 24*a_51*a_54*a_65*b_6 + 12*a_52^2*a_65*b_6 + 24*a_52*a_53*a_65*b_6 + 24*a_52*a_54*a_65*b_6 + 12*a_53^2*a_65*b_6 + 24*a_53*a_54*a_65*b_6 + 12*a_54^2*a_65*b_6 - 1, - 8*a_21*a_31*a_32*b_3 + 8*a_21*a_32^2*b_3 + 8*a_21*a_41*a_42*b_4 + 8*a_21*a_42^2*b_4 + 8*a_21*a_42*a_43*b_4 + 8*a_21*a_51*a_52*b_5 + 8*a_21*a_52^2*b_5 + 8*a_21*a_52*a_53*b_5 + 8*a_21*a_52*a_54*b_5 + 8*a_21*a_61*a_62*b_6 + 8*a_21*a_62^2*b_6 + 8*a_21*a_62*a_63*b_6 + 8*a_21*a_62*a_64*b_6 + 8*a_21*a_62*a_65*b_6 + 8*a_31*a_41*a_43*b_4 + 8*a_31*a_42*a_43*b_4 + 8*a_31*a_43^2*b_4 + 8*a_31*a_51*a_53*b_5 + 8*a_31*a_52*a_53*b_5 + 8*a_31*a_53^2*b_5 + 8*a_31*a_53*a_54*b_5 + 8*a_31*a_61*a_63*b_6 + 8*a_31*a_62*a_63*b_6 + 8*a_31*a_63^2*b_6 + 8*a_31*a_63*a_64*b_6 + 8*a_31*a_63*a_65*b_6 + 8*a_32*a_41*a_43*b_4 + 8*a_32*a_42*a_43*b_4 + 8*a_32*a_43^2*b_4 + 8*a_32*a_51*a_53*b_5 + 8*a_32*a_52*a_53*b_5 + 8*a_32*a_53^2*b_5 + 8*a_32*a_53*a_54*b_5 + 8*a_32*a_61*a_63*b_6 + 8*a_32*a_62*a_63*b_6 + 8*a_32*a_63^2*b_6 + 8*a_32*a_63*a_64*b_6 + 8*a_32*a_63*a_65*b_6 + 8*a_41*a_51*a_54*b_5 + 8*a_41*a_52*a_54*b_5 + 8*a_41*a_53*a_54*b_5 + 8*a_41*a_54^2*b_5 + 8*a_41*a_61*a_64*b_6 + 8*a_41*a_62*a_64*b_6 + 8*a_41*a_63*a_64*b_6 + 8*a_41*a_64^2*b_6 + 8*a_41*a_64*a_65*b_6 + 8*a_42*a_51*a_54*b_5 + 8*a_42*a_52*a_54*b_5 + 8*a_42*a_53*a_54*b_5 + 8*a_42*a_54^2*b_5 + 8*a_42*a_61*a_64*b_6 + 8*a_42*a_62*a_64*b_6 + 8*a_42*a_63*a_64*b_6 + 8*a_42*a_64^2*b_6 + 8*a_42*a_64*a_65*b_6 + 8*a_43*a_51*a_54*b_5 + 8*a_43*a_52*a_54*b_5 + 8*a_43*a_53*a_54*b_5 + 8*a_43*a_54^2*b_5 + 8*a_43*a_61*a_64*b_6 + 8*a_43*a_62*a_64*b_6 + 8*a_43*a_63*a_64*b_6 + 8*a_43*a_64^2*b_6 + 8*a_43*a_64*a_65*b_6 + 8*a_51*a_61*a_65*b_6 + 8*a_51*a_62*a_65*b_6 + 8*a_51*a_63*a_65*b_6 + 8*a_51*a_64*a_65*b_6 + 8*a_51*a_65^2*b_6 + 8*a_52*a_61*a_65*b_6 + 8*a_52*a_62*a_65*b_6 + 8*a_52*a_63*a_65*b_6 + 8*a_52*a_64*a_65*b_6 + 8*a_52*a_65^2*b_6 + 8*a_53*a_61*a_65*b_6 + 8*a_53*a_62*a_65*b_6 + 8*a_53*a_63*a_65*b_6 + 8*a_53*a_64*a_65*b_6 + 8*a_53*a_65^2*b_6 + 8*a_54*a_61*a_65*b_6 + 8*a_54*a_62*a_65*b_6 + 8*a_54*a_63*a_65*b_6 + 8*a_54*a_64*a_65*b_6 + 8*a_54*a_65^2*b_6 - 1, - 4*a_21^3*b_2 + 4*a_31^3*b_3 + 12*a_31^2*a_32*b_3 + 12*a_31*a_32^2*b_3 + 4*a_32^3*b_3 + 4*a_41^3*b_4 + 12*a_41^2*a_42*b_4 + 12*a_41^2*a_43*b_4 + 12*a_41*a_42^2*b_4 + 24*a_41*a_42*a_43*b_4 + 12*a_41*a_43^2*b_4 + 4*a_42^3*b_4 + 12*a_42^2*a_43*b_4 + 12*a_42*a_43^2*b_4 + 4*a_43^3*b_4 + 4*a_51^3*b_5 + 12*a_51^2*a_52*b_5 + 12*a_51^2*a_53*b_5 + 12*a_51^2*a_54*b_5 + 12*a_51*a_52^2*b_5 + 24*a_51*a_52*a_53*b_5 + 24*a_51*a_52*a_54*b_5 + 12*a_51*a_53^2*b_5 + 24*a_51*a_53*a_54*b_5 + 12*a_51*a_54^2*b_5 + 4*a_52^3*b_5 + 12*a_52^2*a_53*b_5 + 12*a_52^2*a_54*b_5 + 12*a_52*a_53^2*b_5 + 24*a_52*a_53*a_54*b_5 + 12*a_52*a_54^2*b_5 + 4*a_53^3*b_5 + 12*a_53^2*a_54*b_5 + 12*a_53*a_54^2*b_5 + 4*a_54^3*b_5 + 4*a_61^3*b_6 + 12*a_61^2*a_62*b_6 + 12*a_61^2*a_63*b_6 + 12*a_61^2*a_64*b_6 + 12*a_61^2*a_65*b_6 + 12*a_61*a_62^2*b_6 + 24*a_61*a_62*a_63*b_6 + 24*a_61*a_62*a_64*b_6 + 24*a_61*a_62*a_65*b_6 + 12*a_61*a_63^2*b_6 + 24*a_61*a_63*a_64*b_6 + 24*a_61*a_63*a_65*b_6 + 12*a_61*a_64^2*b_6 + 24*a_61*a_64*a_65*b_6 + 12*a_61*a_65^2*b_6 + 4*a_62^3*b_6 + 12*a_62^2*a_63*b_6 + 12*a_62^2*a_64*b_6 + 12*a_62^2*a_65*b_6 + 12*a_62*a_63^2*b_6 + 24*a_62*a_63*a_64*b_6 + 24*a_62*a_63*a_65*b_6 + 12*a_62*a_64^2*b_6 + 24*a_62*a_64*a_65*b_6 + 12*a_62*a_65^2*b_6 + 4*a_63^3*b_6 + 12*a_63^2*a_64*b_6 + 12*a_63^2*a_65*b_6 + 12*a_63*a_64^2*b_6 + 24*a_63*a_64*a_65*b_6 + 12*a_63*a_65^2*b_6 + 4*a_64^3*b_6 + 12*a_64^2*a_65*b_6 + 12*a_64*a_65^2*b_6 + 4*a_65^3*b_6 - 1, - 120*a_21*a_32*a_43*a_54*b_5 + 120*a_21*a_32*a_43*a_64*b_6 + 120*a_21*a_32*a_53*a_65*b_6 + 120*a_21*a_42*a_54*a_65*b_6 + 120*a_31*a_43*a_54*a_65*b_6 + 120*a_32*a_43*a_54*a_65*b_6 - 1, - 60*a_21^2*a_32*a_43*b_4 + 60*a_21^2*a_32*a_53*b_5 + 60*a_21^2*a_32*a_63*b_6 + 60*a_21^2*a_42*a_54*b_5 + 60*a_21^2*a_42*a_64*b_6 + 60*a_21^2*a_52*a_65*b_6 + 60*a_31^2*a_43*a_54*b_5 + 60*a_31^2*a_43*a_64*b_6 + 60*a_31^2*a_53*a_65*b_6 + 120*a_31*a_32*a_43*a_54*b_5 + 120*a_31*a_32*a_43*a_64*b_6 + 120*a_31*a_32*a_53*a_65*b_6 + 60*a_32^2*a_43*a_54*b_5 + 60*a_32^2*a_43*a_64*b_6 + 60*a_32^2*a_53*a_65*b_6 + 60*a_41^2*a_54*a_65*b_6 + 120*a_41*a_42*a_54*a_65*b_6 + 120*a_41*a_43*a_54*a_65*b_6 + 60*a_42^2*a_54*a_65*b_6 + 120*a_42*a_43*a_54*a_65*b_6 + 60*a_43^2*a_54*a_65*b_6 - 1, - 40*a_21*a_31*a_32*a_43*b_4 + 40*a_21*a_31*a_32*a_53*b_5 + 40*a_21*a_31*a_32*a_63*b_6 + 40*a_21*a_32^2*a_43*b_4 + 40*a_21*a_32^2*a_53*b_5 + 40*a_21*a_32^2*a_63*b_6 + 40*a_21*a_41*a_42*a_54*b_5 + 40*a_21*a_41*a_42*a_64*b_6 + 40*a_21*a_42^2*a_54*b_5 + 40*a_21*a_42^2*a_64*b_6 + 40*a_21*a_42*a_43*a_54*b_5 + 40*a_21*a_42*a_43*a_64*b_6 + 40*a_21*a_51*a_52*a_65*b_6 + 40*a_21*a_52^2*a_65*b_6 + 40*a_21*a_52*a_53*a_65*b_6 + 40*a_21*a_52*a_54*a_65*b_6 + 40*a_31*a_41*a_43*a_54*b_5 + 40*a_31*a_41*a_43*a_64*b_6 + 40*a_31*a_42*a_43*a_54*b_5 + 40*a_31*a_42*a_43*a_64*b_6 + 40*a_31*a_43^2*a_54*b_5 + 40*a_31*a_43^2*a_64*b_6 + 40*a_31*a_51*a_53*a_65*b_6 + 40*a_31*a_52*a_53*a_65*b_6 + 40*a_31*a_53^2*a_65*b_6 + 40*a_31*a_53*a_54*a_65*b_6 + 40*a_32*a_41*a_43*a_54*b_5 + 40*a_32*a_41*a_43*a_64*b_6 + 40*a_32*a_42*a_43*a_54*b_5 + 40*a_32*a_42*a_43*a_64*b_6 + 40*a_32*a_43^2*a_54*b_5 + 40*a_32*a_43^2*a_64*b_6 + 40*a_32*a_51*a_53*a_65*b_6 + 40*a_32*a_52*a_53*a_65*b_6 + 40*a_32*a_53^2*a_65*b_6 + 40*a_32*a_53*a_54*a_65*b_6 + 40*a_41*a_51*a_54*a_65*b_6 + 40*a_41*a_52*a_54*a_65*b_6 + 40*a_41*a_53*a_54*a_65*b_6 + 40*a_41*a_54^2*a_65*b_6 + 40*a_42*a_51*a_54*a_65*b_6 + 40*a_42*a_52*a_54*a_65*b_6 + 40*a_42*a_53*a_54*a_65*b_6 + 40*a_42*a_54^2*a_65*b_6 + 40*a_43*a_51*a_54*a_65*b_6 + 40*a_43*a_52*a_54*a_65*b_6 + 40*a_43*a_53*a_54*a_65*b_6 + 40*a_43*a_54^2*a_65*b_6 - 1, - 30*a_21*a_32*a_41*a_43*b_4 + 30*a_21*a_32*a_42*a_43*b_4 + 30*a_21*a_32*a_43^2*b_4 + 30*a_21*a_32*a_51*a_53*b_5 + 30*a_21*a_32*a_52*a_53*b_5 + 30*a_21*a_32*a_53^2*b_5 + 30*a_21*a_32*a_53*a_54*b_5 + 30*a_21*a_32*a_61*a_63*b_6 + 30*a_21*a_32*a_62*a_63*b_6 + 30*a_21*a_32*a_63^2*b_6 + 30*a_21*a_32*a_63*a_64*b_6 + 30*a_21*a_32*a_63*a_65*b_6 + 30*a_21*a_42*a_51*a_54*b_5 + 30*a_21*a_42*a_52*a_54*b_5 + 30*a_21*a_42*a_53*a_54*b_5 + 30*a_21*a_42*a_54^2*b_5 + 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20*a_51^3*a_53*b_5 + 20*a_51^3*a_54*b_5 + 30*a_51^2*a_52^2*b_5 + 60*a_51^2*a_52*a_53*b_5 + 60*a_51^2*a_52*a_54*b_5 + 30*a_51^2*a_53^2*b_5 + 60*a_51^2*a_53*a_54*b_5 + 30*a_51^2*a_54^2*b_5 + 20*a_51*a_52^3*b_5 + 60*a_51*a_52^2*a_53*b_5 + 60*a_51*a_52^2*a_54*b_5 + 60*a_51*a_52*a_53^2*b_5 + 120*a_51*a_52*a_53*a_54*b_5 + 60*a_51*a_52*a_54^2*b_5 + 20*a_51*a_53^3*b_5 + 60*a_51*a_53^2*a_54*b_5 + 60*a_51*a_53*a_54^2*b_5 + 20*a_51*a_54^3*b_5 + 5*a_52^4*b_5 + 20*a_52^3*a_53*b_5 + 20*a_52^3*a_54*b_5 + 30*a_52^2*a_53^2*b_5 + 60*a_52^2*a_53*a_54*b_5 + 30*a_52^2*a_54^2*b_5 + 20*a_52*a_53^3*b_5 + 60*a_52*a_53^2*a_54*b_5 + 60*a_52*a_53*a_54^2*b_5 + 20*a_52*a_54^3*b_5 + 5*a_53^4*b_5 + 20*a_53^3*a_54*b_5 + 30*a_53^2*a_54^2*b_5 + 20*a_53*a_54^3*b_5 + 5*a_54^4*b_5 + 5*a_61^4*b_6 + 20*a_61^3*a_62*b_6 + 20*a_61^3*a_63*b_6 + 20*a_61^3*a_64*b_6 + 20*a_61^3*a_65*b_6 + 30*a_61^2*a_62^2*b_6 + 60*a_61^2*a_62*a_63*b_6 + 60*a_61^2*a_62*a_64*b_6 + 60*a_61^2*a_62*a_65*b_6 + 30*a_61^2*a_63^2*b_6 + 60*a_61^2*a_63*a_64*b_6 + 60*a_61^2*a_63*a_65*b_6 + 30*a_61^2*a_64^2*b_6 + 60*a_61^2*a_64*a_65*b_6 + 30*a_61^2*a_65^2*b_6 + 20*a_61*a_62^3*b_6 + 60*a_61*a_62^2*a_63*b_6 + 60*a_61*a_62^2*a_64*b_6 + 60*a_61*a_62^2*a_65*b_6 + 60*a_61*a_62*a_63^2*b_6 + 120*a_61*a_62*a_63*a_64*b_6 + 120*a_61*a_62*a_63*a_65*b_6 + 60*a_61*a_62*a_64^2*b_6 + 120*a_61*a_62*a_64*a_65*b_6 + 60*a_61*a_62*a_65^2*b_6 + 20*a_61*a_63^3*b_6 + 60*a_61*a_63^2*a_64*b_6 + 60*a_61*a_63^2*a_65*b_6 + 60*a_61*a_63*a_64^2*b_6 + 120*a_61*a_63*a_64*a_65*b_6 + 60*a_61*a_63*a_65^2*b_6 + 20*a_61*a_64^3*b_6 + 60*a_61*a_64^2*a_65*b_6 + 60*a_61*a_64*a_65^2*b_6 + 20*a_61*a_65^3*b_6 + 5*a_62^4*b_6 + 20*a_62^3*a_63*b_6 + 20*a_62^3*a_64*b_6 + 20*a_62^3*a_65*b_6 + 30*a_62^2*a_63^2*b_6 + 60*a_62^2*a_63*a_64*b_6 + 60*a_62^2*a_63*a_65*b_6 + 30*a_62^2*a_64^2*b_6 + 60*a_62^2*a_64*a_65*b_6 + 30*a_62^2*a_65^2*b_6 + 20*a_62*a_63^3*b_6 + 60*a_62*a_63^2*a_64*b_6 + 60*a_62*a_63^2*a_65*b_6 + 60*a_62*a_63*a_64^2*b_6 + 120*a_62*a_63*a_64*a_65*b_6 + 60*a_62*a_63*a_65^2*b_6 + 20*a_62*a_64^3*b_6 + 60*a_62*a_64^2*a_65*b_6 + 60*a_62*a_64*a_65^2*b_6 + 20*a_62*a_65^3*b_6 + 5*a_63^4*b_6 + 20*a_63^3*a_64*b_6 + 20*a_63^3*a_65*b_6 + 30*a_63^2*a_64^2*b_6 + 60*a_63^2*a_64*a_65*b_6 + 30*a_63^2*a_65^2*b_6 + 20*a_63*a_64^3*b_6 + 60*a_63*a_64^2*a_65*b_6 + 60*a_63*a_64*a_65^2*b_6 + 20*a_63*a_65^3*b_6 + 5*a_64^4*b_6 + 20*a_64^3*a_65*b_6 + 30*a_64^2*a_65^2*b_6 + 20*a_64*a_65^3*b_6 + 5*a_65^4*b_6 - 1, - 720*a_21*a_32*a_43*a_54*a_65*b_6 - 1, - 360*a_21^2*a_32*a_43*a_54*b_5 + 360*a_21^2*a_32*a_43*a_64*b_6 + 360*a_21^2*a_32*a_53*a_65*b_6 + 360*a_21^2*a_42*a_54*a_65*b_6 + 360*a_31^2*a_43*a_54*a_65*b_6 + 720*a_31*a_32*a_43*a_54*a_65*b_6 + 360*a_32^2*a_43*a_54*a_65*b_6 - 1, - 240*a_21*a_31*a_32*a_43*a_54*b_5 + 240*a_21*a_31*a_32*a_43*a_64*b_6 + 240*a_21*a_31*a_32*a_53*a_65*b_6 + 240*a_21*a_32^2*a_43*a_54*b_5 + 240*a_21*a_32^2*a_43*a_64*b_6 + 240*a_21*a_32^2*a_53*a_65*b_6 + 240*a_21*a_41*a_42*a_54*a_65*b_6 + 240*a_21*a_42^2*a_54*a_65*b_6 + 240*a_21*a_42*a_43*a_54*a_65*b_6 + 240*a_31*a_41*a_43*a_54*a_65*b_6 + 240*a_31*a_42*a_43*a_54*a_65*b_6 + 240*a_31*a_43^2*a_54*a_65*b_6 + 240*a_32*a_41*a_43*a_54*a_65*b_6 + 240*a_32*a_42*a_43*a_54*a_65*b_6 + 240*a_32*a_43^2*a_54*a_65*b_6 - 1, - 180*a_21*a_32*a_41*a_43*a_54*b_5 + 180*a_21*a_32*a_41*a_43*a_64*b_6 + 180*a_21*a_32*a_42*a_43*a_54*b_5 + 180*a_21*a_32*a_42*a_43*a_64*b_6 + 180*a_21*a_32*a_43^2*a_54*b_5 + 180*a_21*a_32*a_43^2*a_64*b_6 + 180*a_21*a_32*a_51*a_53*a_65*b_6 + 180*a_21*a_32*a_52*a_53*a_65*b_6 + 180*a_21*a_32*a_53^2*a_65*b_6 + 180*a_21*a_32*a_53*a_54*a_65*b_6 + 180*a_21*a_42*a_51*a_54*a_65*b_6 + 180*a_21*a_42*a_52*a_54*a_65*b_6 + 180*a_21*a_42*a_53*a_54*a_65*b_6 + 180*a_21*a_42*a_54^2*a_65*b_6 + 180*a_31*a_43*a_51*a_54*a_65*b_6 + 180*a_31*a_43*a_52*a_54*a_65*b_6 + 180*a_31*a_43*a_53*a_54*a_65*b_6 + 180*a_31*a_43*a_54^2*a_65*b_6 + 180*a_32*a_43*a_51*a_54*a_65*b_6 + 180*a_32*a_43*a_52*a_54*a_65*b_6 + 180*a_32*a_43*a_53*a_54*a_65*b_6 + 180*a_32*a_43*a_54^2*a_65*b_6 - 1, - 144*a_21*a_32*a_43*a_51*a_54*b_5 + 144*a_21*a_32*a_43*a_52*a_54*b_5 + 144*a_21*a_32*a_43*a_53*a_54*b_5 + 144*a_21*a_32*a_43*a_54^2*b_5 + 144*a_21*a_32*a_43*a_61*a_64*b_6 + 144*a_21*a_32*a_43*a_62*a_64*b_6 + 144*a_21*a_32*a_43*a_63*a_64*b_6 + 144*a_21*a_32*a_43*a_64^2*b_6 + 144*a_21*a_32*a_43*a_64*a_65*b_6 + 144*a_21*a_32*a_53*a_61*a_65*b_6 + 144*a_21*a_32*a_53*a_62*a_65*b_6 + 144*a_21*a_32*a_53*a_63*a_65*b_6 + 144*a_21*a_32*a_53*a_64*a_65*b_6 + 144*a_21*a_32*a_53*a_65^2*b_6 + 144*a_21*a_42*a_54*a_61*a_65*b_6 + 144*a_21*a_42*a_54*a_62*a_65*b_6 + 144*a_21*a_42*a_54*a_63*a_65*b_6 + 144*a_21*a_42*a_54*a_64*a_65*b_6 + 144*a_21*a_42*a_54*a_65^2*b_6 + 144*a_31*a_43*a_54*a_61*a_65*b_6 + 144*a_31*a_43*a_54*a_62*a_65*b_6 + 144*a_31*a_43*a_54*a_63*a_65*b_6 + 144*a_31*a_43*a_54*a_64*a_65*b_6 + 144*a_31*a_43*a_54*a_65^2*b_6 + 144*a_32*a_43*a_54*a_61*a_65*b_6 + 144*a_32*a_43*a_54*a_62*a_65*b_6 + 144*a_32*a_43*a_54*a_63*a_65*b_6 + 144*a_32*a_43*a_54*a_64*a_65*b_6 + 144*a_32*a_43*a_54*a_65^2*b_6 - 1, - 120*a_21^3*a_32*a_43*b_4 + 120*a_21^3*a_32*a_53*b_5 + 120*a_21^3*a_32*a_63*b_6 + 120*a_21^3*a_42*a_54*b_5 + 120*a_21^3*a_42*a_64*b_6 + 120*a_21^3*a_52*a_65*b_6 + 120*a_31^3*a_43*a_54*b_5 + 120*a_31^3*a_43*a_64*b_6 + 120*a_31^3*a_53*a_65*b_6 + 360*a_31^2*a_32*a_43*a_54*b_5 + 360*a_31^2*a_32*a_43*a_64*b_6 + 360*a_31^2*a_32*a_53*a_65*b_6 + 360*a_31*a_32^2*a_43*a_54*b_5 + 360*a_31*a_32^2*a_43*a_64*b_6 + 360*a_31*a_32^2*a_53*a_65*b_6 + 120*a_32^3*a_43*a_54*b_5 + 120*a_32^3*a_43*a_64*b_6 + 120*a_32^3*a_53*a_65*b_6 + 120*a_41^3*a_54*a_65*b_6 + 360*a_41^2*a_42*a_54*a_65*b_6 + 360*a_41^2*a_43*a_54*a_65*b_6 + 360*a_41*a_42^2*a_54*a_65*b_6 + 720*a_41*a_42*a_43*a_54*a_65*b_6 + 360*a_41*a_43^2*a_54*a_65*b_6 + 120*a_42^3*a_54*a_65*b_6 + 360*a_42^2*a_43*a_54*a_65*b_6 + 360*a_42*a_43^2*a_54*a_65*b_6 + 120*a_43^3*a_54*a_65*b_6 - 1, - 90*a_21^2*a_31*a_32*a_43*b_4 + 90*a_21^2*a_31*a_32*a_53*b_5 + 90*a_21^2*a_31*a_32*a_63*b_6 + 90*a_21^2*a_32^2*a_43*b_4 + 90*a_21^2*a_32^2*a_53*b_5 + 90*a_21^2*a_32^2*a_63*b_6 + 90*a_21^2*a_41*a_42*a_54*b_5 + 90*a_21^2*a_41*a_42*a_64*b_6 + 90*a_21^2*a_42^2*a_54*b_5 + 90*a_21^2*a_42^2*a_64*b_6 + 90*a_21^2*a_42*a_43*a_54*b_5 + 90*a_21^2*a_42*a_43*a_64*b_6 + 90*a_21^2*a_51*a_52*a_65*b_6 + 90*a_21^2*a_52^2*a_65*b_6 + 90*a_21^2*a_52*a_53*a_65*b_6 + 90*a_21^2*a_52*a_54*a_65*b_6 + 90*a_31^2*a_41*a_43*a_54*b_5 + 90*a_31^2*a_41*a_43*a_64*b_6 + 90*a_31^2*a_42*a_43*a_54*b_5 + 90*a_31^2*a_42*a_43*a_64*b_6 + 90*a_31^2*a_43^2*a_54*b_5 + 90*a_31^2*a_43^2*a_64*b_6 + 90*a_31^2*a_51*a_53*a_65*b_6 + 90*a_31^2*a_52*a_53*a_65*b_6 + 90*a_31^2*a_53^2*a_65*b_6 + 90*a_31^2*a_53*a_54*a_65*b_6 + 180*a_31*a_32*a_41*a_43*a_54*b_5 + 180*a_31*a_32*a_41*a_43*a_64*b_6 + 180*a_31*a_32*a_42*a_43*a_54*b_5 + 180*a_31*a_32*a_42*a_43*a_64*b_6 + 180*a_31*a_32*a_43^2*a_54*b_5 + 180*a_31*a_32*a_43^2*a_64*b_6 + 180*a_31*a_32*a_51*a_53*a_65*b_6 + 180*a_31*a_32*a_52*a_53*a_65*b_6 + 180*a_31*a_32*a_53^2*a_65*b_6 + 180*a_31*a_32*a_53*a_54*a_65*b_6 + 90*a_32^2*a_41*a_43*a_54*b_5 + 90*a_32^2*a_41*a_43*a_64*b_6 + 90*a_32^2*a_42*a_43*a_54*b_5 + 90*a_32^2*a_42*a_43*a_64*b_6 + 90*a_32^2*a_43^2*a_54*b_5 + 90*a_32^2*a_43^2*a_64*b_6 + 90*a_32^2*a_51*a_53*a_65*b_6 + 90*a_32^2*a_52*a_53*a_65*b_6 + 90*a_32^2*a_53^2*a_65*b_6 + 90*a_32^2*a_53*a_54*a_65*b_6 + 90*a_41^2*a_51*a_54*a_65*b_6 + 90*a_41^2*a_52*a_54*a_65*b_6 + 90*a_41^2*a_53*a_54*a_65*b_6 + 90*a_41^2*a_54^2*a_65*b_6 + 180*a_41*a_42*a_51*a_54*a_65*b_6 + 180*a_41*a_42*a_52*a_54*a_65*b_6 + 180*a_41*a_42*a_53*a_54*a_65*b_6 + 180*a_41*a_42*a_54^2*a_65*b_6 + 180*a_41*a_43*a_51*a_54*a_65*b_6 + 180*a_41*a_43*a_52*a_54*a_65*b_6 + 180*a_41*a_43*a_53*a_54*a_65*b_6 + 180*a_41*a_43*a_54^2*a_65*b_6 + 90*a_42^2*a_51*a_54*a_65*b_6 + 90*a_42^2*a_52*a_54*a_65*b_6 + 90*a_42^2*a_53*a_54*a_65*b_6 + 90*a_42^2*a_54^2*a_65*b_6 + 180*a_42*a_43*a_51*a_54*a_65*b_6 + 180*a_42*a_43*a_52*a_54*a_65*b_6 + 180*a_42*a_43*a_53*a_54*a_65*b_6 + 180*a_42*a_43*a_54^2*a_65*b_6 + 90*a_43^2*a_51*a_54*a_65*b_6 + 90*a_43^2*a_52*a_54*a_65*b_6 + 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72*a_31^2*a_43*a_61*a_64*b_6 + 72*a_31^2*a_43*a_62*a_64*b_6 + 72*a_31^2*a_43*a_63*a_64*b_6 + 72*a_31^2*a_43*a_64^2*b_6 + 72*a_31^2*a_43*a_64*a_65*b_6 + 72*a_31^2*a_53*a_61*a_65*b_6 + 72*a_31^2*a_53*a_62*a_65*b_6 + 72*a_31^2*a_53*a_63*a_65*b_6 + 72*a_31^2*a_53*a_64*a_65*b_6 + 72*a_31^2*a_53*a_65^2*b_6 + 144*a_31*a_32*a_43*a_51*a_54*b_5 + 144*a_31*a_32*a_43*a_52*a_54*b_5 + 144*a_31*a_32*a_43*a_53*a_54*b_5 + 144*a_31*a_32*a_43*a_54^2*b_5 + 144*a_31*a_32*a_43*a_61*a_64*b_6 + 144*a_31*a_32*a_43*a_62*a_64*b_6 + 144*a_31*a_32*a_43*a_63*a_64*b_6 + 144*a_31*a_32*a_43*a_64^2*b_6 + 144*a_31*a_32*a_43*a_64*a_65*b_6 + 144*a_31*a_32*a_53*a_61*a_65*b_6 + 144*a_31*a_32*a_53*a_62*a_65*b_6 + 144*a_31*a_32*a_53*a_63*a_65*b_6 + 144*a_31*a_32*a_53*a_64*a_65*b_6 + 144*a_31*a_32*a_53*a_65^2*b_6 + 72*a_32^2*a_43*a_51*a_54*b_5 + 72*a_32^2*a_43*a_52*a_54*b_5 + 72*a_32^2*a_43*a_53*a_54*b_5 + 72*a_32^2*a_43*a_54^2*b_5 + 72*a_32^2*a_43*a_61*a_64*b_6 + 72*a_32^2*a_43*a_62*a_64*b_6 + 72*a_32^2*a_43*a_63*a_64*b_6 + 72*a_32^2*a_43*a_64^2*b_6 + 72*a_32^2*a_43*a_64*a_65*b_6 + 72*a_32^2*a_53*a_61*a_65*b_6 + 72*a_32^2*a_53*a_62*a_65*b_6 + 72*a_32^2*a_53*a_63*a_65*b_6 + 72*a_32^2*a_53*a_64*a_65*b_6 + 72*a_32^2*a_53*a_65^2*b_6 + 72*a_41^2*a_54*a_61*a_65*b_6 + 72*a_41^2*a_54*a_62*a_65*b_6 + 72*a_41^2*a_54*a_63*a_65*b_6 + 72*a_41^2*a_54*a_64*a_65*b_6 + 72*a_41^2*a_54*a_65^2*b_6 + 144*a_41*a_42*a_54*a_61*a_65*b_6 + 144*a_41*a_42*a_54*a_62*a_65*b_6 + 144*a_41*a_42*a_54*a_63*a_65*b_6 + 144*a_41*a_42*a_54*a_64*a_65*b_6 + 144*a_41*a_42*a_54*a_65^2*b_6 + 144*a_41*a_43*a_54*a_61*a_65*b_6 + 144*a_41*a_43*a_54*a_62*a_65*b_6 + 144*a_41*a_43*a_54*a_63*a_65*b_6 + 144*a_41*a_43*a_54*a_64*a_65*b_6 + 144*a_41*a_43*a_54*a_65^2*b_6 + 72*a_42^2*a_54*a_61*a_65*b_6 + 72*a_42^2*a_54*a_62*a_65*b_6 + 72*a_42^2*a_54*a_63*a_65*b_6 + 72*a_42^2*a_54*a_64*a_65*b_6 + 72*a_42^2*a_54*a_65^2*b_6 + 144*a_42*a_43*a_54*a_61*a_65*b_6 + 144*a_42*a_43*a_54*a_62*a_65*b_6 + 144*a_42*a_43*a_54*a_63*a_65*b_6 + 144*a_42*a_43*a_54*a_64*a_65*b_6 + 144*a_42*a_43*a_54*a_65^2*b_6 + 72*a_43^2*a_54*a_61*a_65*b_6 + 72*a_43^2*a_54*a_62*a_65*b_6 + 72*a_43^2*a_54*a_63*a_65*b_6 + 72*a_43^2*a_54*a_64*a_65*b_6 + 72*a_43^2*a_54*a_65^2*b_6 - 1, - 120*a_21^2*a_32^2*a_43*b_4 + 120*a_21^2*a_32^2*a_53*b_5 + 120*a_21^2*a_32^2*a_63*b_6 + 120*a_21^2*a_42^2*a_54*b_5 + 120*a_21^2*a_42^2*a_64*b_6 + 120*a_21^2*a_52^2*a_65*b_6 + 240*a_21*a_31*a_42*a_43*a_54*b_5 + 240*a_21*a_31*a_42*a_43*a_64*b_6 + 240*a_21*a_31*a_52*a_53*a_65*b_6 + 240*a_21*a_32*a_42*a_43*a_54*b_5 + 240*a_21*a_32*a_42*a_43*a_64*b_6 + 240*a_21*a_32*a_52*a_53*a_65*b_6 + 240*a_21*a_41*a_52*a_54*a_65*b_6 + 240*a_21*a_42*a_52*a_54*a_65*b_6 + 240*a_21*a_43*a_52*a_54*a_65*b_6 + 120*a_31^2*a_43^2*a_54*b_5 + 120*a_31^2*a_43^2*a_64*b_6 + 120*a_31^2*a_53^2*a_65*b_6 + 240*a_31*a_32*a_43^2*a_54*b_5 + 240*a_31*a_32*a_43^2*a_64*b_6 + 240*a_31*a_32*a_53^2*a_65*b_6 + 240*a_31*a_41*a_53*a_54*a_65*b_6 + 240*a_31*a_42*a_53*a_54*a_65*b_6 + 240*a_31*a_43*a_53*a_54*a_65*b_6 + 120*a_32^2*a_43^2*a_54*b_5 + 120*a_32^2*a_43^2*a_64*b_6 + 120*a_32^2*a_53^2*a_65*b_6 + 240*a_32*a_41*a_53*a_54*a_65*b_6 + 240*a_32*a_42*a_53*a_54*a_65*b_6 + 240*a_32*a_43*a_53*a_54*a_65*b_6 + 120*a_41^2*a_54^2*a_65*b_6 + 240*a_41*a_42*a_54^2*a_65*b_6 + 240*a_41*a_43*a_54^2*a_65*b_6 + 120*a_42^2*a_54^2*a_65*b_6 + 240*a_42*a_43*a_54^2*a_65*b_6 + 120*a_43^2*a_54^2*a_65*b_6 - 1, - 60*a_21*a_31^2*a_32*a_43*b_4 + 60*a_21*a_31^2*a_32*a_53*b_5 + 60*a_21*a_31^2*a_32*a_63*b_6 + 120*a_21*a_31*a_32^2*a_43*b_4 + 120*a_21*a_31*a_32^2*a_53*b_5 + 120*a_21*a_31*a_32^2*a_63*b_6 + 60*a_21*a_32^3*a_43*b_4 + 60*a_21*a_32^3*a_53*b_5 + 60*a_21*a_32^3*a_63*b_6 + 60*a_21*a_41^2*a_42*a_54*b_5 + 60*a_21*a_41^2*a_42*a_64*b_6 + 120*a_21*a_41*a_42^2*a_54*b_5 + 120*a_21*a_41*a_42^2*a_64*b_6 + 120*a_21*a_41*a_42*a_43*a_54*b_5 + 120*a_21*a_41*a_42*a_43*a_64*b_6 + 60*a_21*a_42^3*a_54*b_5 + 60*a_21*a_42^3*a_64*b_6 + 120*a_21*a_42^2*a_43*a_54*b_5 + 120*a_21*a_42^2*a_43*a_64*b_6 + 60*a_21*a_42*a_43^2*a_54*b_5 + 60*a_21*a_42*a_43^2*a_64*b_6 + 60*a_21*a_51^2*a_52*a_65*b_6 + 120*a_21*a_51*a_52^2*a_65*b_6 + 120*a_21*a_51*a_52*a_53*a_65*b_6 + 120*a_21*a_51*a_52*a_54*a_65*b_6 + 60*a_21*a_52^3*a_65*b_6 + 120*a_21*a_52^2*a_53*a_65*b_6 + 120*a_21*a_52^2*a_54*a_65*b_6 + 60*a_21*a_52*a_53^2*a_65*b_6 + 120*a_21*a_52*a_53*a_54*a_65*b_6 + 60*a_21*a_52*a_54^2*a_65*b_6 + 60*a_31*a_41^2*a_43*a_54*b_5 + 60*a_31*a_41^2*a_43*a_64*b_6 + 120*a_31*a_41*a_42*a_43*a_54*b_5 + 120*a_31*a_41*a_42*a_43*a_64*b_6 + 120*a_31*a_41*a_43^2*a_54*b_5 + 120*a_31*a_41*a_43^2*a_64*b_6 + 60*a_31*a_42^2*a_43*a_54*b_5 + 60*a_31*a_42^2*a_43*a_64*b_6 + 120*a_31*a_42*a_43^2*a_54*b_5 + 120*a_31*a_42*a_43^2*a_64*b_6 + 60*a_31*a_43^3*a_54*b_5 + 60*a_31*a_43^3*a_64*b_6 + 60*a_31*a_51^2*a_53*a_65*b_6 + 120*a_31*a_51*a_52*a_53*a_65*b_6 + 120*a_31*a_51*a_53^2*a_65*b_6 + 120*a_31*a_51*a_53*a_54*a_65*b_6 + 60*a_31*a_52^2*a_53*a_65*b_6 + 120*a_31*a_52*a_53^2*a_65*b_6 + 120*a_31*a_52*a_53*a_54*a_65*b_6 + 60*a_31*a_53^3*a_65*b_6 + 120*a_31*a_53^2*a_54*a_65*b_6 + 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36*a_53*a_61^2*a_65^2*b_6 + 36*a_53*a_61*a_62^2*a_65*b_6 + 72*a_53*a_61*a_62*a_63*a_65*b_6 + 72*a_53*a_61*a_62*a_64*a_65*b_6 + 72*a_53*a_61*a_62*a_65^2*b_6 + 36*a_53*a_61*a_63^2*a_65*b_6 + 72*a_53*a_61*a_63*a_64*a_65*b_6 + 72*a_53*a_61*a_63*a_65^2*b_6 + 36*a_53*a_61*a_64^2*a_65*b_6 + 72*a_53*a_61*a_64*a_65^2*b_6 + 36*a_53*a_61*a_65^3*b_6 + 12*a_53*a_62^3*a_65*b_6 + 36*a_53*a_62^2*a_63*a_65*b_6 + 36*a_53*a_62^2*a_64*a_65*b_6 + 36*a_53*a_62^2*a_65^2*b_6 + 36*a_53*a_62*a_63^2*a_65*b_6 + 72*a_53*a_62*a_63*a_64*a_65*b_6 + 72*a_53*a_62*a_63*a_65^2*b_6 + 36*a_53*a_62*a_64^2*a_65*b_6 + 72*a_53*a_62*a_64*a_65^2*b_6 + 36*a_53*a_62*a_65^3*b_6 + 12*a_53*a_63^3*a_65*b_6 + 36*a_53*a_63^2*a_64*a_65*b_6 + 36*a_53*a_63^2*a_65^2*b_6 + 36*a_53*a_63*a_64^2*a_65*b_6 + 72*a_53*a_63*a_64*a_65^2*b_6 + 36*a_53*a_63*a_65^3*b_6 + 12*a_53*a_64^3*a_65*b_6 + 36*a_53*a_64^2*a_65^2*b_6 + 36*a_53*a_64*a_65^3*b_6 + 12*a_53*a_65^4*b_6 + 12*a_54*a_61^3*a_65*b_6 + 36*a_54*a_61^2*a_62*a_65*b_6 + 36*a_54*a_61^2*a_63*a_65*b_6 + 36*a_54*a_61^2*a_64*a_65*b_6 + 36*a_54*a_61^2*a_65^2*b_6 + 36*a_54*a_61*a_62^2*a_65*b_6 + 72*a_54*a_61*a_62*a_63*a_65*b_6 + 72*a_54*a_61*a_62*a_64*a_65*b_6 + 72*a_54*a_61*a_62*a_65^2*b_6 + 36*a_54*a_61*a_63^2*a_65*b_6 + 72*a_54*a_61*a_63*a_64*a_65*b_6 + 72*a_54*a_61*a_63*a_65^2*b_6 + 36*a_54*a_61*a_64^2*a_65*b_6 + 72*a_54*a_61*a_64*a_65^2*b_6 + 36*a_54*a_61*a_65^3*b_6 + 12*a_54*a_62^3*a_65*b_6 + 36*a_54*a_62^2*a_63*a_65*b_6 + 36*a_54*a_62^2*a_64*a_65*b_6 + 36*a_54*a_62^2*a_65^2*b_6 + 36*a_54*a_62*a_63^2*a_65*b_6 + 72*a_54*a_62*a_63*a_64*a_65*b_6 + 72*a_54*a_62*a_63*a_65^2*b_6 + 36*a_54*a_62*a_64^2*a_65*b_6 + 72*a_54*a_62*a_64*a_65^2*b_6 + 36*a_54*a_62*a_65^3*b_6 + 12*a_54*a_63^3*a_65*b_6 + 36*a_54*a_63^2*a_64*a_65*b_6 + 36*a_54*a_63^2*a_65^2*b_6 + 36*a_54*a_63*a_64^2*a_65*b_6 + 72*a_54*a_63*a_64*a_65^2*b_6 + 36*a_54*a_63*a_65^3*b_6 + 12*a_54*a_64^3*a_65*b_6 + 36*a_54*a_64^2*a_65^2*b_6 + 36*a_54*a_64*a_65^3*b_6 + 12*a_54*a_65^4*b_6 - 1, - 6*a_21^5*b_2 + 6*a_31^5*b_3 + 30*a_31^4*a_32*b_3 + 60*a_31^3*a_32^2*b_3 + 60*a_31^2*a_32^3*b_3 + 30*a_31*a_32^4*b_3 + 6*a_32^5*b_3 + 6*a_41^5*b_4 + 30*a_41^4*a_42*b_4 + 30*a_41^4*a_43*b_4 + 60*a_41^3*a_42^2*b_4 + 120*a_41^3*a_42*a_43*b_4 + 60*a_41^3*a_43^2*b_4 + 60*a_41^2*a_42^3*b_4 + 180*a_41^2*a_42^2*a_43*b_4 + 180*a_41^2*a_42*a_43^2*b_4 + 60*a_41^2*a_43^3*b_4 + 30*a_41*a_42^4*b_4 + 120*a_41*a_42^3*a_43*b_4 + 180*a_41*a_42^2*a_43^2*b_4 + 120*a_41*a_42*a_43^3*b_4 + 30*a_41*a_43^4*b_4 + 6*a_42^5*b_4 + 30*a_42^4*a_43*b_4 + 60*a_42^3*a_43^2*b_4 + 60*a_42^2*a_43^3*b_4 + 30*a_42*a_43^4*b_4 + 6*a_43^5*b_4 + 6*a_51^5*b_5 + 30*a_51^4*a_52*b_5 + 30*a_51^4*a_53*b_5 + 30*a_51^4*a_54*b_5 + 60*a_51^3*a_52^2*b_5 + 120*a_51^3*a_52*a_53*b_5 + 120*a_51^3*a_52*a_54*b_5 + 60*a_51^3*a_53^2*b_5 + 120*a_51^3*a_53*a_54*b_5 + 60*a_51^3*a_54^2*b_5 + 60*a_51^2*a_52^3*b_5 + 180*a_51^2*a_52^2*a_53*b_5 + 180*a_51^2*a_52^2*a_54*b_5 + 180*a_51^2*a_52*a_53^2*b_5 + 360*a_51^2*a_52*a_53*a_54*b_5 + 180*a_51^2*a_52*a_54^2*b_5 + 60*a_51^2*a_53^3*b_5 + 180*a_51^2*a_53^2*a_54*b_5 + 180*a_51^2*a_53*a_54^2*b_5 + 60*a_51^2*a_54^3*b_5 + 30*a_51*a_52^4*b_5 + 120*a_51*a_52^3*a_53*b_5 + 120*a_51*a_52^3*a_54*b_5 + 180*a_51*a_52^2*a_53^2*b_5 + 360*a_51*a_52^2*a_53*a_54*b_5 + 180*a_51*a_52^2*a_54^2*b_5 + 120*a_51*a_52*a_53^3*b_5 + 360*a_51*a_52*a_53^2*a_54*b_5 + 360*a_51*a_52*a_53*a_54^2*b_5 + 120*a_51*a_52*a_54^3*b_5 + 30*a_51*a_53^4*b_5 + 120*a_51*a_53^3*a_54*b_5 + 180*a_51*a_53^2*a_54^2*b_5 + 120*a_51*a_53*a_54^3*b_5 + 30*a_51*a_54^4*b_5 + 6*a_52^5*b_5 + 30*a_52^4*a_53*b_5 + 30*a_52^4*a_54*b_5 + 60*a_52^3*a_53^2*b_5 + 120*a_52^3*a_53*a_54*b_5 + 60*a_52^3*a_54^2*b_5 + 60*a_52^2*a_53^3*b_5 + 180*a_52^2*a_53^2*a_54*b_5 + 180*a_52^2*a_53*a_54^2*b_5 + 60*a_52^2*a_54^3*b_5 + 30*a_52*a_53^4*b_5 + 120*a_52*a_53^3*a_54*b_5 + 180*a_52*a_53^2*a_54^2*b_5 + 120*a_52*a_53*a_54^3*b_5 + 30*a_52*a_54^4*b_5 + 6*a_53^5*b_5 + 30*a_53^4*a_54*b_5 + 60*a_53^3*a_54^2*b_5 + 60*a_53^2*a_54^3*b_5 + 30*a_53*a_54^4*b_5 + 6*a_54^5*b_5 + 6*a_61^5*b_6 + 30*a_61^4*a_62*b_6 + 30*a_61^4*a_63*b_6 + 30*a_61^4*a_64*b_6 + 30*a_61^4*a_65*b_6 + 60*a_61^3*a_62^2*b_6 + 120*a_61^3*a_62*a_63*b_6 + 120*a_61^3*a_62*a_64*b_6 + 120*a_61^3*a_62*a_65*b_6 + 60*a_61^3*a_63^2*b_6 + 120*a_61^3*a_63*a_64*b_6 + 120*a_61^3*a_63*a_65*b_6 + 60*a_61^3*a_64^2*b_6 + 120*a_61^3*a_64*a_65*b_6 + 60*a_61^3*a_65^2*b_6 + 60*a_61^2*a_62^3*b_6 + 180*a_61^2*a_62^2*a_63*b_6 + 180*a_61^2*a_62^2*a_64*b_6 + 180*a_61^2*a_62^2*a_65*b_6 + 180*a_61^2*a_62*a_63^2*b_6 + 360*a_61^2*a_62*a_63*a_64*b_6 + 360*a_61^2*a_62*a_63*a_65*b_6 + 180*a_61^2*a_62*a_64^2*b_6 + 360*a_61^2*a_62*a_64*a_65*b_6 + 180*a_61^2*a_62*a_65^2*b_6 + 60*a_61^2*a_63^3*b_6 + 180*a_61^2*a_63^2*a_64*b_6 + 180*a_61^2*a_63^2*a_65*b_6 + 180*a_61^2*a_63*a_64^2*b_6 + 360*a_61^2*a_63*a_64*a_65*b_6 + 180*a_61^2*a_63*a_65^2*b_6 + 60*a_61^2*a_64^3*b_6 + 180*a_61^2*a_64^2*a_65*b_6 + 180*a_61^2*a_64*a_65^2*b_6 + 60*a_61^2*a_65^3*b_6 + 30*a_61*a_62^4*b_6 + 120*a_61*a_62^3*a_63*b_6 + 120*a_61*a_62^3*a_64*b_6 + 120*a_61*a_62^3*a_65*b_6 + 180*a_61*a_62^2*a_63^2*b_6 + 360*a_61*a_62^2*a_63*a_64*b_6 + 360*a_61*a_62^2*a_63*a_65*b_6 + 180*a_61*a_62^2*a_64^2*b_6 + 360*a_61*a_62^2*a_64*a_65*b_6 + 180*a_61*a_62^2*a_65^2*b_6 + 120*a_61*a_62*a_63^3*b_6 + 360*a_61*a_62*a_63^2*a_64*b_6 + 360*a_61*a_62*a_63^2*a_65*b_6 + 360*a_61*a_62*a_63*a_64^2*b_6 + 720*a_61*a_62*a_63*a_64*a_65*b_6 + 360*a_61*a_62*a_63*a_65^2*b_6 + 120*a_61*a_62*a_64^3*b_6 + 360*a_61*a_62*a_64^2*a_65*b_6 + 360*a_61*a_62*a_64*a_65^2*b_6 + 120*a_61*a_62*a_65^3*b_6 + 30*a_61*a_63^4*b_6 + 120*a_61*a_63^3*a_64*b_6 + 120*a_61*a_63^3*a_65*b_6 + 180*a_61*a_63^2*a_64^2*b_6 + 360*a_61*a_63^2*a_64*a_65*b_6 + 180*a_61*a_63^2*a_65^2*b_6 + 120*a_61*a_63*a_64^3*b_6 + 360*a_61*a_63*a_64^2*a_65*b_6 + 360*a_61*a_63*a_64*a_65^2*b_6 + 120*a_61*a_63*a_65^3*b_6 + 30*a_61*a_64^4*b_6 + 120*a_61*a_64^3*a_65*b_6 + 180*a_61*a_64^2*a_65^2*b_6 + 120*a_61*a_64*a_65^3*b_6 + 30*a_61*a_65^4*b_6 + 6*a_62^5*b_6 + 30*a_62^4*a_63*b_6 + 30*a_62^4*a_64*b_6 + 30*a_62^4*a_65*b_6 + 60*a_62^3*a_63^2*b_6 + 120*a_62^3*a_63*a_64*b_6 + 120*a_62^3*a_63*a_65*b_6 + 60*a_62^3*a_64^2*b_6 + 120*a_62^3*a_64*a_65*b_6 + 60*a_62^3*a_65^2*b_6 + 60*a_62^2*a_63^3*b_6 + 180*a_62^2*a_63^2*a_64*b_6 + 180*a_62^2*a_63^2*a_65*b_6 + 180*a_62^2*a_63*a_64^2*b_6 + 360*a_62^2*a_63*a_64*a_65*b_6 + 180*a_62^2*a_63*a_65^2*b_6 + 60*a_62^2*a_64^3*b_6 + 180*a_62^2*a_64^2*a_65*b_6 + 180*a_62^2*a_64*a_65^2*b_6 + 60*a_62^2*a_65^3*b_6 + 30*a_62*a_63^4*b_6 + 120*a_62*a_63^3*a_64*b_6 + 120*a_62*a_63^3*a_65*b_6 + 180*a_62*a_63^2*a_64^2*b_6 + 360*a_62*a_63^2*a_64*a_65*b_6 + 180*a_62*a_63^2*a_65^2*b_6 + 120*a_62*a_63*a_64^3*b_6 + 360*a_62*a_63*a_64^2*a_65*b_6 + 360*a_62*a_63*a_64*a_65^2*b_6 + 120*a_62*a_63*a_65^3*b_6 + 30*a_62*a_64^4*b_6 + 120*a_62*a_64^3*a_65*b_6 + 180*a_62*a_64^2*a_65^2*b_6 + 120*a_62*a_64*a_65^3*b_6 + 30*a_62*a_65^4*b_6 + 6*a_63^5*b_6 + 30*a_63^4*a_64*b_6 + 30*a_63^4*a_65*b_6 + 60*a_63^3*a_64^2*b_6 + 120*a_63^3*a_64*a_65*b_6 + 60*a_63^3*a_65^2*b_6 + 60*a_63^2*a_64^3*b_6 + 180*a_63^2*a_64^2*a_65*b_6 + 180*a_63^2*a_64*a_65^2*b_6 + 60*a_63^2*a_65^3*b_6 + 30*a_63*a_64^4*b_6 + 120*a_63*a_64^3*a_65*b_6 + 180*a_63*a_64^2*a_65^2*b_6 + 120*a_63*a_64*a_65^3*b_6 + 30*a_63*a_65^4*b_6 + 6*a_64^5*b_6 + 30*a_64^4*a_65*b_6 + 60*a_64^3*a_65^2*b_6 + 60*a_64^2*a_65^3*b_6 + 30*a_64*a_65^4*b_6 + 6*a_65^5*b_6 - 1 -]: - -print("Running RK(6,6)"); -kernelopts(bytesalloc) / (1024 * 1024.0); -st := time[real](): -gb := Groebner[Basis](J, tdeg(a_21, a_31, a_32, a_41, a_42, a_43, a_51, a_52, a_53, a_54, a_61, a_62, a_63, a_64, a_65, b_1, b_2, b_3, b_4, b_5, b_6), method=fgb): -print(gb); -print("RK(6,6): ", time[real]() - st); -kernelopts(bytesalloc) / (1024 * 1024.0); diff --git a/benchmark/scripts/runge-kutta/RK-8-7.mpl b/benchmark/scripts/runge-kutta/RK-8-7.mpl deleted file mode 100644 index d1629dea..00000000 --- a/benchmark/scripts/runge-kutta/RK-8-7.mpl +++ /dev/null @@ -1,100 +0,0 @@ -with(Groebner): -with(PolynomialIdeals): - -kernelopts(numcpus=4); - -J := [ - b_1 + b_2 + b_3 + b_4 + b_5 + b_6 + b_7 + b_8 - 1, - 2*a_21*b_2 + 2*b_3*(a_31 + a_32) + 2*b_4*(a_41 + a_42 + a_43) + 2*b_5*(a_51 + a_52 + a_53 + a_54) + 2*b_6*(a_61 + a_62 + a_63 + a_64 + a_65) + 2*b_7*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76) + 2*b_8*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87) - 1, - 6*a_21*a_32*b_3 + 6*b_4*(a_21*a_42 + a_43*(a_31 + a_32)) + 6*b_5*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)) + 6*b_6*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54)) + 6*b_7*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)) + 6*b_8*(a_21*a_82 + a_83*(a_31 + a_32) + a_84*(a_41 + a_42 + a_43) + a_85*(a_51 + a_52 + a_53 + a_54) + a_86*(a_61 + a_62 + a_63 + a_64 + a_65) + a_87*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)) - 1, - 3*a_21^2*b_2 + 3*b_3*(a_31 + a_32)^2 + 3*b_4*(a_41 + a_42 + a_43)^2 + 3*b_5*(a_51 + a_52 + a_53 + a_54)^2 + 3*b_6*(a_61 + a_62 + a_63 + a_64 + a_65)^2 + 3*b_7*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2 + 3*b_8*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^2 - 1, - 24*a_21*a_32*a_43*b_4 + 24*b_5*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32))) + 24*b_6*(a_21*a_32*a_63 + a_64*(a_21*a_42 + a_43*(a_31 + a_32)) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))) + 24*b_7*(a_21*a_32*a_73 + a_74*(a_21*a_42 + a_43*(a_31 + a_32)) + a_75*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)) + a_76*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))) + 24*b_8*(a_21*a_32*a_83 + a_84*(a_21*a_42 + a_43*(a_31 + a_32)) + a_85*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)) + a_86*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54)) + a_87*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65))) - 1, - 12*a_21^2*a_32*b_3 + 12*b_4*(a_21^2*a_42 + a_43*(a_31 + a_32)^2) + 12*b_5*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2) + 12*b_6*(a_21^2*a_62 + a_63*(a_31 + a_32)^2 + a_64*(a_41 + a_42 + a_43)^2 + a_65*(a_51 + a_52 + a_53 + a_54)^2) + 12*b_7*(a_21^2*a_72 + a_73*(a_31 + a_32)^2 + a_74*(a_41 + a_42 + a_43)^2 + a_75*(a_51 + a_52 + a_53 + a_54)^2 + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)^2) + 12*b_8*(a_21^2*a_82 + a_83*(a_31 + a_32)^2 + a_84*(a_41 + a_42 + a_43)^2 + a_85*(a_51 + a_52 + a_53 + a_54)^2 + a_86*(a_61 + a_62 + a_63 + a_64 + a_65)^2 + a_87*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2) - 1, - 8*a_21*a_32*b_3*(a_31 + a_32) + 8*b_4*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43) + 8*b_5*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54) + 8*b_6*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))*(a_61 + a_62 + a_63 + a_64 + a_65) + 8*b_7*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65))*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76) + 8*b_8*(a_21*a_82 + a_83*(a_31 + a_32) + a_84*(a_41 + a_42 + a_43) + a_85*(a_51 + a_52 + a_53 + a_54) + a_86*(a_61 + a_62 + a_63 + a_64 + a_65) + a_87*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76))*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87) - 1, - 4*a_21^3*b_2 + 4*b_3*(a_31 + a_32)^3 + 4*b_4*(a_41 + a_42 + a_43)^3 + 4*b_5*(a_51 + a_52 + a_53 + a_54)^3 + 4*b_6*(a_61 + a_62 + a_63 + a_64 + a_65)^3 + 4*b_7*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^3 + 4*b_8*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^3 - 1, - 120*a_21*a_32*a_43*a_54*b_5 + 120*b_6*(a_21*a_32*a_43*a_64 + a_65*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32)))) + 120*b_7*(a_21*a_32*a_43*a_74 + a_75*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32))) + a_76*(a_21*a_32*a_63 + a_64*(a_21*a_42 + a_43*(a_31 + a_32)) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)))) + 120*b_8*(a_21*a_32*a_43*a_84 + a_85*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32))) + a_86*(a_21*a_32*a_63 + a_64*(a_21*a_42 + a_43*(a_31 + a_32)) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))) + a_87*(a_21*a_32*a_73 + a_74*(a_21*a_42 + a_43*(a_31 + a_32)) + a_75*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)) + a_76*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54)))) - 1, - 60*a_21^2*a_32*a_43*b_4 + 60*b_5*(a_21^2*a_32*a_53 + a_54*(a_21^2*a_42 + a_43*(a_31 + a_32)^2)) + 60*b_6*(a_21^2*a_32*a_63 + a_64*(a_21^2*a_42 + a_43*(a_31 + a_32)^2) + a_65*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2)) + 60*b_7*(a_21^2*a_32*a_73 + a_74*(a_21^2*a_42 + a_43*(a_31 + a_32)^2) + a_75*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2) + a_76*(a_21^2*a_62 + a_63*(a_31 + a_32)^2 + a_64*(a_41 + a_42 + a_43)^2 + a_65*(a_51 + a_52 + a_53 + a_54)^2)) + 60*b_8*(a_21^2*a_32*a_83 + a_84*(a_21^2*a_42 + a_43*(a_31 + a_32)^2) + a_85*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2) + a_86*(a_21^2*a_62 + a_63*(a_31 + a_32)^2 + a_64*(a_41 + a_42 + a_43)^2 + a_65*(a_51 + a_52 + a_53 + a_54)^2) + a_87*(a_21^2*a_72 + a_73*(a_31 + a_32)^2 + a_74*(a_41 + a_42 + a_43)^2 + a_75*(a_51 + a_52 + a_53 + a_54)^2 + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)^2)) - 1, - 40*a_21*a_32*a_43*b_4*(a_31 + a_32) + 40*b_5*(a_21*a_32*a_53*(a_31 + a_32) + a_54*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43)) + 40*b_6*(a_21*a_32*a_63*(a_31 + a_32) + a_64*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54)) + 40*b_7*(a_21*a_32*a_73*(a_31 + a_32) + a_74*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43) + a_75*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54) + a_76*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))*(a_61 + a_62 + a_63 + a_64 + a_65)) + 40*b_8*(a_21*a_32*a_83*(a_31 + a_32) + a_84*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43) + a_85*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54) + a_86*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))*(a_61 + a_62 + a_63 + a_64 + a_65) + a_87*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65))*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)) - 1, - 30*a_21*a_32*a_43*b_4*(a_41 + a_42 + a_43) + 30*b_5*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32)))*(a_51 + a_52 + a_53 + a_54) + 30*b_6*(a_21*a_32*a_63 + a_64*(a_21*a_42 + a_43*(a_31 + a_32)) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)))*(a_61 + a_62 + a_63 + a_64 + a_65) + 30*b_7*(a_21*a_32*a_73 + a_74*(a_21*a_42 + a_43*(a_31 + a_32)) + a_75*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)) + a_76*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54)))*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76) + 30*b_8*(a_21*a_32*a_83 + a_84*(a_21*a_42 + a_43*(a_31 + a_32)) + a_85*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)) + a_86*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54)) + a_87*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)))*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87) - 1, - 20*a_21^3*a_32*b_3 + 20*b_4*(a_21^3*a_42 + a_43*(a_31 + a_32)^3) + 20*b_5*(a_21^3*a_52 + a_53*(a_31 + a_32)^3 + a_54*(a_41 + a_42 + a_43)^3) + 20*b_6*(a_21^3*a_62 + a_63*(a_31 + a_32)^3 + a_64*(a_41 + a_42 + a_43)^3 + a_65*(a_51 + a_52 + a_53 + a_54)^3) + 20*b_7*(a_21^3*a_72 + a_73*(a_31 + a_32)^3 + a_74*(a_41 + a_42 + a_43)^3 + a_75*(a_51 + a_52 + a_53 + a_54)^3 + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)^3) + 20*b_8*(a_21^3*a_82 + a_83*(a_31 + a_32)^3 + a_84*(a_41 + a_42 + a_43)^3 + a_85*(a_51 + a_52 + a_53 + a_54)^3 + a_86*(a_61 + a_62 + a_63 + a_64 + a_65)^3 + a_87*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^3) - 1, - 15*a_21^2*a_32*b_3*(a_31 + a_32) + 15*b_4*(a_21^2*a_42 + a_43*(a_31 + a_32)^2)*(a_41 + a_42 + a_43) + 15*b_5*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2)*(a_51 + a_52 + a_53 + a_54) + 15*b_6*(a_21^2*a_62 + a_63*(a_31 + a_32)^2 + a_64*(a_41 + a_42 + a_43)^2 + a_65*(a_51 + a_52 + a_53 + a_54)^2)*(a_61 + a_62 + a_63 + a_64 + a_65) + 15*b_7*(a_21^2*a_72 + a_73*(a_31 + a_32)^2 + a_74*(a_41 + a_42 + a_43)^2 + a_75*(a_51 + a_52 + a_53 + a_54)^2 + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)^2)*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76) + 15*b_8*(a_21^2*a_82 + a_83*(a_31 + a_32)^2 + a_84*(a_41 + a_42 + a_43)^2 + a_85*(a_51 + a_52 + a_53 + a_54)^2 + a_86*(a_61 + a_62 + a_63 + a_64 + a_65)^2 + a_87*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2)*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87) - 1, - 20*a_21^2*a_32^2*b_3 + 20*b_4*(a_21*a_42 + a_43*(a_31 + a_32))^2 + 20*b_5*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))^2 + 20*b_6*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))^2 + 20*b_7*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65))^2 + 20*b_8*(a_21*a_82 + a_83*(a_31 + a_32) + a_84*(a_41 + a_42 + a_43) + a_85*(a_51 + a_52 + a_53 + a_54) + a_86*(a_61 + a_62 + a_63 + a_64 + a_65) + a_87*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76))^2 - 1, - 10*a_21*a_32*b_3*(a_31 + a_32)^2 + 10*b_4*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43)^2 + 10*b_5*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54)^2 + 10*b_6*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))*(a_61 + a_62 + a_63 + a_64 + a_65)^2 + 10*b_7*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65))*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2 + 10*b_8*(a_21*a_82 + a_83*(a_31 + a_32) + a_84*(a_41 + a_42 + a_43) + a_85*(a_51 + a_52 + a_53 + a_54) + a_86*(a_61 + a_62 + a_63 + a_64 + a_65) + a_87*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76))*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^2 - 1, - 5*a_21^4*b_2 + 5*b_3*(a_31 + a_32)^4 + 5*b_4*(a_41 + a_42 + a_43)^4 + 5*b_5*(a_51 + a_52 + a_53 + a_54)^4 + 5*b_6*(a_61 + a_62 + a_63 + a_64 + a_65)^4 + 5*b_7*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^4 + 5*b_8*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^4 - 1, - 720*a_21*a_32*a_43*a_54*a_65*b_6 + 720*b_7*(a_21*a_32*a_43*a_54*a_75 + a_76*(a_21*a_32*a_43*a_64 + a_65*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32))))) + 720*b_8*(a_21*a_32*a_43*a_54*a_85 + a_86*(a_21*a_32*a_43*a_64 + a_65*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32)))) + a_87*(a_21*a_32*a_43*a_74 + a_75*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32))) + a_76*(a_21*a_32*a_63 + a_64*(a_21*a_42 + a_43*(a_31 + a_32)) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))))) - 1, - 360*a_21^2*a_32*a_43*a_54*b_5 + 360*b_6*(a_21^2*a_32*a_43*a_64 + a_65*(a_21^2*a_32*a_53 + a_54*(a_21^2*a_42 + a_43*(a_31 + a_32)^2))) + 360*b_7*(a_21^2*a_32*a_43*a_74 + a_75*(a_21^2*a_32*a_53 + a_54*(a_21^2*a_42 + a_43*(a_31 + a_32)^2)) + a_76*(a_21^2*a_32*a_63 + a_64*(a_21^2*a_42 + a_43*(a_31 + a_32)^2) + a_65*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2))) + 360*b_8*(a_21^2*a_32*a_43*a_84 + a_85*(a_21^2*a_32*a_53 + a_54*(a_21^2*a_42 + a_43*(a_31 + a_32)^2)) + a_86*(a_21^2*a_32*a_63 + a_64*(a_21^2*a_42 + a_43*(a_31 + a_32)^2) + a_65*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2)) + a_87*(a_21^2*a_32*a_73 + a_74*(a_21^2*a_42 + a_43*(a_31 + a_32)^2) + a_75*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2) + a_76*(a_21^2*a_62 + a_63*(a_31 + a_32)^2 + a_64*(a_41 + a_42 + a_43)^2 + a_65*(a_51 + a_52 + a_53 + a_54)^2))) - 1, - 240*a_21*a_32*a_43*a_54*b_5*(a_31 + a_32) + 240*b_6*(a_21*a_32*a_43*a_64*(a_31 + a_32) + a_65*(a_21*a_32*a_53*(a_31 + a_32) + a_54*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43))) + 240*b_7*(a_21*a_32*a_43*a_74*(a_31 + a_32) + a_75*(a_21*a_32*a_53*(a_31 + a_32) + a_54*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43)) + a_76*(a_21*a_32*a_63*(a_31 + a_32) + a_64*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54))) + 240*b_8*(a_21*a_32*a_43*a_84*(a_31 + a_32) + a_85*(a_21*a_32*a_53*(a_31 + a_32) + a_54*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43)) + a_86*(a_21*a_32*a_63*(a_31 + a_32) + a_64*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54)) + a_87*(a_21*a_32*a_73*(a_31 + a_32) + a_74*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43) + a_75*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54) + a_76*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))*(a_61 + a_62 + a_63 + a_64 + a_65))) - 1, - 180*a_21*a_32*a_43*a_54*b_5*(a_41 + a_42 + a_43) + 180*b_6*(a_21*a_32*a_43*a_64*(a_41 + a_42 + a_43) + a_65*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32)))*(a_51 + a_52 + a_53 + a_54)) + 180*b_7*(a_21*a_32*a_43*a_74*(a_41 + a_42 + a_43) + a_75*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32)))*(a_51 + a_52 + a_53 + a_54) + a_76*(a_21*a_32*a_63 + a_64*(a_21*a_42 + a_43*(a_31 + a_32)) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)))*(a_61 + a_62 + a_63 + a_64 + a_65)) + 180*b_8*(a_21*a_32*a_43*a_84*(a_41 + a_42 + a_43) + a_85*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32)))*(a_51 + a_52 + a_53 + a_54) + a_86*(a_21*a_32*a_63 + a_64*(a_21*a_42 + a_43*(a_31 + a_32)) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)))*(a_61 + a_62 + a_63 + a_64 + a_65) + a_87*(a_21*a_32*a_73 + a_74*(a_21*a_42 + a_43*(a_31 + a_32)) + a_75*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)) + a_76*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54)))*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)) - 1, - 144*a_21*a_32*a_43*a_54*b_5*(a_51 + a_52 + a_53 + a_54) + 144*b_6*(a_21*a_32*a_43*a_64 + a_65*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32))))*(a_61 + a_62 + a_63 + a_64 + a_65) + 144*b_7*(a_21*a_32*a_43*a_74 + a_75*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32))) + a_76*(a_21*a_32*a_63 + a_64*(a_21*a_42 + a_43*(a_31 + a_32)) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))))*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76) + 144*b_8*(a_21*a_32*a_43*a_84 + a_85*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32))) + a_86*(a_21*a_32*a_63 + a_64*(a_21*a_42 + a_43*(a_31 + a_32)) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))) + a_87*(a_21*a_32*a_73 + a_74*(a_21*a_42 + a_43*(a_31 + a_32)) + a_75*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)) + a_76*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))))*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87) - 1, - 120*a_21^3*a_32*a_43*b_4 + 120*b_5*(a_21^3*a_32*a_53 + a_54*(a_21^3*a_42 + a_43*(a_31 + a_32)^3)) + 120*b_6*(a_21^3*a_32*a_63 + a_64*(a_21^3*a_42 + a_43*(a_31 + a_32)^3) + a_65*(a_21^3*a_52 + a_53*(a_31 + a_32)^3 + a_54*(a_41 + a_42 + a_43)^3)) + 120*b_7*(a_21^3*a_32*a_73 + a_74*(a_21^3*a_42 + a_43*(a_31 + a_32)^3) + a_75*(a_21^3*a_52 + a_53*(a_31 + a_32)^3 + a_54*(a_41 + a_42 + a_43)^3) + a_76*(a_21^3*a_62 + a_63*(a_31 + a_32)^3 + a_64*(a_41 + a_42 + a_43)^3 + a_65*(a_51 + a_52 + a_53 + a_54)^3)) + 120*b_8*(a_21^3*a_32*a_83 + a_84*(a_21^3*a_42 + a_43*(a_31 + a_32)^3) + a_85*(a_21^3*a_52 + a_53*(a_31 + a_32)^3 + a_54*(a_41 + a_42 + a_43)^3) + a_86*(a_21^3*a_62 + a_63*(a_31 + a_32)^3 + a_64*(a_41 + a_42 + a_43)^3 + a_65*(a_51 + a_52 + a_53 + a_54)^3) + a_87*(a_21^3*a_72 + a_73*(a_31 + a_32)^3 + a_74*(a_41 + a_42 + a_43)^3 + a_75*(a_51 + a_52 + a_53 + a_54)^3 + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)^3)) - 1, - 90*a_21^2*a_32*a_43*b_4*(a_31 + a_32) + 90*b_5*(a_21^2*a_32*a_53*(a_31 + a_32) + a_54*(a_21^2*a_42 + a_43*(a_31 + a_32)^2)*(a_41 + a_42 + a_43)) + 90*b_6*(a_21^2*a_32*a_63*(a_31 + a_32) + a_64*(a_21^2*a_42 + a_43*(a_31 + a_32)^2)*(a_41 + a_42 + a_43) + a_65*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2)*(a_51 + a_52 + a_53 + a_54)) + 90*b_7*(a_21^2*a_32*a_73*(a_31 + a_32) + a_74*(a_21^2*a_42 + a_43*(a_31 + a_32)^2)*(a_41 + a_42 + a_43) + a_75*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2)*(a_51 + a_52 + a_53 + a_54) + a_76*(a_21^2*a_62 + a_63*(a_31 + a_32)^2 + a_64*(a_41 + a_42 + a_43)^2 + a_65*(a_51 + a_52 + a_53 + a_54)^2)*(a_61 + a_62 + a_63 + a_64 + a_65)) + 90*b_8*(a_21^2*a_32*a_83*(a_31 + a_32) + a_84*(a_21^2*a_42 + a_43*(a_31 + a_32)^2)*(a_41 + a_42 + a_43) + a_85*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2)*(a_51 + a_52 + a_53 + a_54) + a_86*(a_21^2*a_62 + a_63*(a_31 + a_32)^2 + a_64*(a_41 + a_42 + a_43)^2 + a_65*(a_51 + a_52 + a_53 + a_54)^2)*(a_61 + a_62 + a_63 + a_64 + a_65) + a_87*(a_21^2*a_72 + a_73*(a_31 + a_32)^2 + a_74*(a_41 + a_42 + a_43)^2 + a_75*(a_51 + a_52 + a_53 + a_54)^2 + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)^2)*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)) - 1, - 72*a_21^2*a_32*a_43*b_4*(a_41 + a_42 + a_43) + 72*b_5*(a_21^2*a_32*a_53 + a_54*(a_21^2*a_42 + a_43*(a_31 + a_32)^2))*(a_51 + a_52 + a_53 + a_54) + 72*b_6*(a_21^2*a_32*a_63 + a_64*(a_21^2*a_42 + a_43*(a_31 + a_32)^2) + a_65*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2))*(a_61 + a_62 + a_63 + a_64 + a_65) + 72*b_7*(a_21^2*a_32*a_73 + a_74*(a_21^2*a_42 + a_43*(a_31 + a_32)^2) + a_75*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2) + a_76*(a_21^2*a_62 + a_63*(a_31 + a_32)^2 + a_64*(a_41 + a_42 + a_43)^2 + a_65*(a_51 + a_52 + a_53 + a_54)^2))*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76) + 72*b_8*(a_21^2*a_32*a_83 + a_84*(a_21^2*a_42 + a_43*(a_31 + a_32)^2) + a_85*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2) + a_86*(a_21^2*a_62 + a_63*(a_31 + a_32)^2 + a_64*(a_41 + a_42 + a_43)^2 + a_65*(a_51 + a_52 + a_53 + a_54)^2) + a_87*(a_21^2*a_72 + a_73*(a_31 + a_32)^2 + a_74*(a_41 + a_42 + a_43)^2 + a_75*(a_51 + a_52 + a_53 + a_54)^2 + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)^2))*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87) - 1, - 120*a_21^2*a_32^2*a_43*b_4 + 120*b_5*(a_21^2*a_32^2*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32))^2) + 120*b_6*(a_21^2*a_32^2*a_63 + a_64*(a_21*a_42 + a_43*(a_31 + a_32))^2 + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))^2) + 120*b_7*(a_21^2*a_32^2*a_73 + a_74*(a_21*a_42 + a_43*(a_31 + a_32))^2 + a_75*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))^2 + a_76*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))^2) + 120*b_8*(a_21^2*a_32^2*a_83 + a_84*(a_21*a_42 + a_43*(a_31 + a_32))^2 + a_85*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))^2 + a_86*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))^2 + a_87*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65))^2) - 1, - 60*a_21*a_32*a_43*b_4*(a_31 + a_32)^2 + 60*b_5*(a_21*a_32*a_53*(a_31 + a_32)^2 + a_54*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43)^2) + 60*b_6*(a_21*a_32*a_63*(a_31 + a_32)^2 + a_64*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43)^2 + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54)^2) + 60*b_7*(a_21*a_32*a_73*(a_31 + a_32)^2 + a_74*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43)^2 + a_75*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54)^2 + a_76*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))*(a_61 + a_62 + a_63 + a_64 + a_65)^2) + 60*b_8*(a_21*a_32*a_83*(a_31 + a_32)^2 + a_84*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43)^2 + a_85*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54)^2 + a_86*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))*(a_61 + a_62 + a_63 + a_64 + a_65)^2 + a_87*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65))*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2) - 1, - 48*a_21*a_32*a_43*b_4*(a_31 + a_32)*(a_41 + a_42 + a_43) + 48*b_5*(a_21*a_32*a_53*(a_31 + a_32) + a_54*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54) + 48*b_6*(a_21*a_32*a_63*(a_31 + a_32) + a_64*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54))*(a_61 + a_62 + a_63 + a_64 + a_65) + 48*b_7*(a_21*a_32*a_73*(a_31 + a_32) + a_74*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43) + a_75*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54) + a_76*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))*(a_61 + a_62 + a_63 + a_64 + a_65))*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76) + 48*b_8*(a_21*a_32*a_83*(a_31 + a_32) + a_84*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43) + a_85*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54) + a_86*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))*(a_61 + a_62 + a_63 + a_64 + a_65) + a_87*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65))*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76))*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87) - 1, - 72*a_21*a_32*a_43*b_4*(a_21*a_42 + a_43*(a_31 + a_32)) + 72*b_5*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32)))*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)) + 72*b_6*(a_21*a_32*a_63 + a_64*(a_21*a_42 + a_43*(a_31 + a_32)) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)))*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54)) + 72*b_7*(a_21*a_32*a_73 + a_74*(a_21*a_42 + a_43*(a_31 + a_32)) + a_75*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)) + a_76*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54)))*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)) + 72*b_8*(a_21*a_32*a_83 + a_84*(a_21*a_42 + a_43*(a_31 + a_32)) + a_85*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)) + a_86*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54)) + a_87*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)))*(a_21*a_82 + a_83*(a_31 + a_32) + a_84*(a_41 + a_42 + a_43) + a_85*(a_51 + a_52 + a_53 + a_54) + a_86*(a_61 + a_62 + a_63 + a_64 + a_65) + a_87*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)) - 1, - 36*a_21*a_32*a_43*b_4*(a_41 + a_42 + a_43)^2 + 36*b_5*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32)))*(a_51 + a_52 + a_53 + a_54)^2 + 36*b_6*(a_21*a_32*a_63 + a_64*(a_21*a_42 + a_43*(a_31 + a_32)) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)))*(a_61 + a_62 + a_63 + a_64 + a_65)^2 + 36*b_7*(a_21*a_32*a_73 + a_74*(a_21*a_42 + a_43*(a_31 + a_32)) + a_75*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)) + a_76*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54)))*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2 + 36*b_8*(a_21*a_32*a_83 + a_84*(a_21*a_42 + a_43*(a_31 + a_32)) + a_85*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)) + a_86*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54)) + a_87*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)))*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^2 - 1, - 30*a_21^4*a_32*b_3 + 30*b_4*(a_21^4*a_42 + a_43*(a_31 + a_32)^4) + 30*b_5*(a_21^4*a_52 + a_53*(a_31 + a_32)^4 + a_54*(a_41 + a_42 + a_43)^4) + 30*b_6*(a_21^4*a_62 + a_63*(a_31 + a_32)^4 + a_64*(a_41 + a_42 + a_43)^4 + a_65*(a_51 + a_52 + a_53 + a_54)^4) + 30*b_7*(a_21^4*a_72 + a_73*(a_31 + a_32)^4 + a_74*(a_41 + a_42 + a_43)^4 + a_75*(a_51 + a_52 + a_53 + a_54)^4 + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)^4) + 30*b_8*(a_21^4*a_82 + a_83*(a_31 + a_32)^4 + a_84*(a_41 + a_42 + a_43)^4 + a_85*(a_51 + a_52 + a_53 + a_54)^4 + a_86*(a_61 + a_62 + a_63 + a_64 + a_65)^4 + a_87*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^4) - 1, - 24*a_21^3*a_32*b_3*(a_31 + a_32) + 24*b_4*(a_21^3*a_42 + a_43*(a_31 + a_32)^3)*(a_41 + a_42 + a_43) + 24*b_5*(a_21^3*a_52 + a_53*(a_31 + a_32)^3 + a_54*(a_41 + a_42 + a_43)^3)*(a_51 + a_52 + a_53 + a_54) + 24*b_6*(a_21^3*a_62 + a_63*(a_31 + a_32)^3 + a_64*(a_41 + a_42 + a_43)^3 + a_65*(a_51 + a_52 + a_53 + a_54)^3)*(a_61 + a_62 + a_63 + a_64 + a_65) + 24*b_7*(a_21^3*a_72 + a_73*(a_31 + a_32)^3 + a_74*(a_41 + a_42 + a_43)^3 + a_75*(a_51 + a_52 + a_53 + a_54)^3 + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)^3)*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76) + 24*b_8*(a_21^3*a_82 + a_83*(a_31 + a_32)^3 + a_84*(a_41 + a_42 + a_43)^3 + a_85*(a_51 + a_52 + a_53 + a_54)^3 + a_86*(a_61 + a_62 + a_63 + a_64 + a_65)^3 + a_87*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^3)*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87) - 1, - 36*a_21^3*a_32^2*b_3 + 36*b_4*(a_21*a_42 + a_43*(a_31 + a_32))*(a_21^2*a_42 + a_43*(a_31 + a_32)^2) + 36*b_5*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2) + 36*b_6*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))*(a_21^2*a_62 + a_63*(a_31 + a_32)^2 + a_64*(a_41 + a_42 + a_43)^2 + a_65*(a_51 + a_52 + a_53 + a_54)^2) + 36*b_7*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65))*(a_21^2*a_72 + a_73*(a_31 + a_32)^2 + a_74*(a_41 + a_42 + a_43)^2 + a_75*(a_51 + a_52 + a_53 + a_54)^2 + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)^2) + 36*b_8*(a_21*a_82 + a_83*(a_31 + a_32) + a_84*(a_41 + a_42 + a_43) + a_85*(a_51 + a_52 + a_53 + a_54) + a_86*(a_61 + a_62 + a_63 + a_64 + a_65) + a_87*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76))*(a_21^2*a_82 + a_83*(a_31 + a_32)^2 + a_84*(a_41 + a_42 + a_43)^2 + a_85*(a_51 + a_52 + a_53 + a_54)^2 + a_86*(a_61 + a_62 + a_63 + a_64 + a_65)^2 + a_87*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2) - 1, - 18*a_21^2*a_32*b_3*(a_31 + a_32)^2 + 18*b_4*(a_21^2*a_42 + a_43*(a_31 + a_32)^2)*(a_41 + a_42 + a_43)^2 + 18*b_5*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2)*(a_51 + a_52 + a_53 + a_54)^2 + 18*b_6*(a_21^2*a_62 + a_63*(a_31 + a_32)^2 + a_64*(a_41 + a_42 + a_43)^2 + a_65*(a_51 + a_52 + a_53 + a_54)^2)*(a_61 + a_62 + a_63 + a_64 + a_65)^2 + 18*b_7*(a_21^2*a_72 + a_73*(a_31 + a_32)^2 + a_74*(a_41 + a_42 + a_43)^2 + a_75*(a_51 + a_52 + a_53 + a_54)^2 + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)^2)*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2 + 18*b_8*(a_21^2*a_82 + a_83*(a_31 + a_32)^2 + a_84*(a_41 + a_42 + a_43)^2 + a_85*(a_51 + a_52 + a_53 + a_54)^2 + a_86*(a_61 + a_62 + a_63 + a_64 + a_65)^2 + a_87*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2)*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^2 - 1, - 24*a_21^2*a_32^2*b_3*(a_31 + a_32) + 24*b_4*(a_21*a_42 + a_43*(a_31 + a_32))^2*(a_41 + a_42 + a_43) + 24*b_5*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))^2*(a_51 + a_52 + a_53 + a_54) + 24*b_6*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))^2*(a_61 + a_62 + a_63 + a_64 + a_65) + 24*b_7*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65))^2*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76) + 24*b_8*(a_21*a_82 + a_83*(a_31 + a_32) + a_84*(a_41 + a_42 + a_43) + a_85*(a_51 + a_52 + a_53 + a_54) + a_86*(a_61 + a_62 + a_63 + a_64 + a_65) + a_87*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76))^2*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87) - 1, - 12*a_21*a_32*b_3*(a_31 + a_32)^3 + 12*b_4*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43)^3 + 12*b_5*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54)^3 + 12*b_6*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))*(a_61 + a_62 + a_63 + a_64 + a_65)^3 + 12*b_7*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65))*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^3 + 12*b_8*(a_21*a_82 + a_83*(a_31 + a_32) + a_84*(a_41 + a_42 + a_43) + a_85*(a_51 + a_52 + a_53 + a_54) + a_86*(a_61 + a_62 + a_63 + a_64 + a_65) + a_87*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76))*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^3 - 1, - 6*a_21^5*b_2 + 6*b_3*(a_31 + a_32)^5 + 6*b_4*(a_41 + a_42 + a_43)^5 + 6*b_5*(a_51 + a_52 + a_53 + a_54)^5 + 6*b_6*(a_61 + a_62 + a_63 + a_64 + a_65)^5 + 6*b_7*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^5 + 6*b_8*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^5 - 1, - 5040*a_21*a_32*a_43*a_54*a_65*a_76*b_7 + 5040*b_8*(a_21*a_32*a_43*a_54*a_65*a_86 + a_87*(a_21*a_32*a_43*a_54*a_75 + a_76*(a_21*a_32*a_43*a_64 + a_65*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32)))))) - 1, - 2520*a_21^2*a_32*a_43*a_54*a_65*b_6 + 2520*b_7*(a_21^2*a_32*a_43*a_54*a_75 + a_76*(a_21^2*a_32*a_43*a_64 + a_65*(a_21^2*a_32*a_53 + a_54*(a_21^2*a_42 + a_43*(a_31 + a_32)^2)))) + 2520*b_8*(a_21^2*a_32*a_43*a_54*a_85 + a_86*(a_21^2*a_32*a_43*a_64 + a_65*(a_21^2*a_32*a_53 + a_54*(a_21^2*a_42 + a_43*(a_31 + a_32)^2))) + a_87*(a_21^2*a_32*a_43*a_74 + a_75*(a_21^2*a_32*a_53 + a_54*(a_21^2*a_42 + a_43*(a_31 + a_32)^2)) + a_76*(a_21^2*a_32*a_63 + a_64*(a_21^2*a_42 + a_43*(a_31 + a_32)^2) + a_65*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2)))) - 1, - 1680*a_21*a_32*a_43*a_54*a_65*b_6*(a_31 + a_32) + 1680*b_7*(a_21*a_32*a_43*a_54*a_75*(a_31 + a_32) + a_76*(a_21*a_32*a_43*a_64*(a_31 + a_32) + a_65*(a_21*a_32*a_53*(a_31 + a_32) + a_54*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43)))) + 1680*b_8*(a_21*a_32*a_43*a_54*a_85*(a_31 + a_32) + a_86*(a_21*a_32*a_43*a_64*(a_31 + a_32) + a_65*(a_21*a_32*a_53*(a_31 + a_32) + a_54*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43))) + a_87*(a_21*a_32*a_43*a_74*(a_31 + a_32) + a_75*(a_21*a_32*a_53*(a_31 + a_32) + a_54*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43)) + a_76*(a_21*a_32*a_63*(a_31 + a_32) + a_64*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54)))) - 1, - 1260*a_21*a_32*a_43*a_54*a_65*b_6*(a_41 + a_42 + a_43) + 1260*b_7*(a_21*a_32*a_43*a_54*a_75*(a_41 + a_42 + a_43) + a_76*(a_21*a_32*a_43*a_64*(a_41 + a_42 + a_43) + a_65*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32)))*(a_51 + a_52 + a_53 + a_54))) + 1260*b_8*(a_21*a_32*a_43*a_54*a_85*(a_41 + a_42 + a_43) + a_86*(a_21*a_32*a_43*a_64*(a_41 + a_42 + a_43) + a_65*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32)))*(a_51 + a_52 + a_53 + a_54)) + a_87*(a_21*a_32*a_43*a_74*(a_41 + a_42 + a_43) + a_75*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32)))*(a_51 + a_52 + a_53 + a_54) + a_76*(a_21*a_32*a_63 + a_64*(a_21*a_42 + a_43*(a_31 + a_32)) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)))*(a_61 + a_62 + a_63 + a_64 + a_65))) - 1, - 1008*a_21*a_32*a_43*a_54*a_65*b_6*(a_51 + a_52 + a_53 + a_54) + 1008*b_7*(a_21*a_32*a_43*a_54*a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_21*a_32*a_43*a_64 + a_65*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32))))*(a_61 + a_62 + a_63 + a_64 + a_65)) + 1008*b_8*(a_21*a_32*a_43*a_54*a_85*(a_51 + a_52 + a_53 + a_54) + a_86*(a_21*a_32*a_43*a_64 + a_65*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32))))*(a_61 + a_62 + a_63 + a_64 + a_65) + a_87*(a_21*a_32*a_43*a_74 + a_75*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32))) + a_76*(a_21*a_32*a_63 + a_64*(a_21*a_42 + a_43*(a_31 + a_32)) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))))*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)) - 1, - 840*a_21*a_32*a_43*a_54*a_65*b_6*(a_61 + a_62 + a_63 + a_64 + a_65) + 840*b_7*(a_21*a_32*a_43*a_54*a_75 + a_76*(a_21*a_32*a_43*a_64 + a_65*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32)))))*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76) + 840*b_8*(a_21*a_32*a_43*a_54*a_85 + a_86*(a_21*a_32*a_43*a_64 + a_65*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32)))) + a_87*(a_21*a_32*a_43*a_74 + a_75*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32))) + a_76*(a_21*a_32*a_63 + a_64*(a_21*a_42 + a_43*(a_31 + a_32)) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)))))*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87) - 1, - 840*a_21^3*a_32*a_43*a_54*b_5 + 840*b_6*(a_21^3*a_32*a_43*a_64 + a_65*(a_21^3*a_32*a_53 + a_54*(a_21^3*a_42 + a_43*(a_31 + a_32)^3))) + 840*b_7*(a_21^3*a_32*a_43*a_74 + a_75*(a_21^3*a_32*a_53 + a_54*(a_21^3*a_42 + a_43*(a_31 + a_32)^3)) + a_76*(a_21^3*a_32*a_63 + a_64*(a_21^3*a_42 + a_43*(a_31 + a_32)^3) + a_65*(a_21^3*a_52 + a_53*(a_31 + a_32)^3 + a_54*(a_41 + a_42 + a_43)^3))) + 840*b_8*(a_21^3*a_32*a_43*a_84 + a_85*(a_21^3*a_32*a_53 + a_54*(a_21^3*a_42 + a_43*(a_31 + a_32)^3)) + a_86*(a_21^3*a_32*a_63 + a_64*(a_21^3*a_42 + a_43*(a_31 + a_32)^3) + a_65*(a_21^3*a_52 + a_53*(a_31 + a_32)^3 + a_54*(a_41 + a_42 + a_43)^3)) + a_87*(a_21^3*a_32*a_73 + a_74*(a_21^3*a_42 + a_43*(a_31 + a_32)^3) + a_75*(a_21^3*a_52 + a_53*(a_31 + a_32)^3 + a_54*(a_41 + a_42 + a_43)^3) + a_76*(a_21^3*a_62 + a_63*(a_31 + a_32)^3 + a_64*(a_41 + a_42 + a_43)^3 + a_65*(a_51 + a_52 + a_53 + a_54)^3))) - 1, - 630*a_21^2*a_32*a_43*a_54*b_5*(a_31 + a_32) + 630*b_6*(a_21^2*a_32*a_43*a_64*(a_31 + a_32) + a_65*(a_21^2*a_32*a_53*(a_31 + a_32) + a_54*(a_21^2*a_42 + a_43*(a_31 + a_32)^2)*(a_41 + a_42 + a_43))) + 630*b_7*(a_21^2*a_32*a_43*a_74*(a_31 + a_32) + a_75*(a_21^2*a_32*a_53*(a_31 + a_32) + a_54*(a_21^2*a_42 + a_43*(a_31 + a_32)^2)*(a_41 + a_42 + a_43)) + a_76*(a_21^2*a_32*a_63*(a_31 + a_32) + a_64*(a_21^2*a_42 + a_43*(a_31 + a_32)^2)*(a_41 + a_42 + a_43) + a_65*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2)*(a_51 + a_52 + a_53 + a_54))) + 630*b_8*(a_21^2*a_32*a_43*a_84*(a_31 + a_32) + a_85*(a_21^2*a_32*a_53*(a_31 + a_32) + a_54*(a_21^2*a_42 + a_43*(a_31 + a_32)^2)*(a_41 + a_42 + a_43)) + a_86*(a_21^2*a_32*a_63*(a_31 + a_32) + a_64*(a_21^2*a_42 + a_43*(a_31 + a_32)^2)*(a_41 + a_42 + a_43) + a_65*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2)*(a_51 + a_52 + a_53 + a_54)) + a_87*(a_21^2*a_32*a_73*(a_31 + a_32) + a_74*(a_21^2*a_42 + a_43*(a_31 + a_32)^2)*(a_41 + a_42 + a_43) + a_75*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2)*(a_51 + a_52 + a_53 + a_54) + a_76*(a_21^2*a_62 + a_63*(a_31 + a_32)^2 + a_64*(a_41 + a_42 + a_43)^2 + a_65*(a_51 + a_52 + a_53 + a_54)^2)*(a_61 + a_62 + a_63 + a_64 + a_65))) - 1, - 504*a_21^2*a_32*a_43*a_54*b_5*(a_41 + a_42 + a_43) + 504*b_6*(a_21^2*a_32*a_43*a_64*(a_41 + a_42 + a_43) + a_65*(a_21^2*a_32*a_53 + a_54*(a_21^2*a_42 + a_43*(a_31 + a_32)^2))*(a_51 + a_52 + a_53 + a_54)) + 504*b_7*(a_21^2*a_32*a_43*a_74*(a_41 + a_42 + a_43) + a_75*(a_21^2*a_32*a_53 + a_54*(a_21^2*a_42 + a_43*(a_31 + a_32)^2))*(a_51 + a_52 + a_53 + a_54) + a_76*(a_21^2*a_32*a_63 + a_64*(a_21^2*a_42 + a_43*(a_31 + a_32)^2) + a_65*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2))*(a_61 + a_62 + a_63 + a_64 + a_65)) + 504*b_8*(a_21^2*a_32*a_43*a_84*(a_41 + a_42 + a_43) + a_85*(a_21^2*a_32*a_53 + a_54*(a_21^2*a_42 + a_43*(a_31 + a_32)^2))*(a_51 + a_52 + a_53 + a_54) + a_86*(a_21^2*a_32*a_63 + a_64*(a_21^2*a_42 + a_43*(a_31 + a_32)^2) + a_65*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2))*(a_61 + a_62 + a_63 + a_64 + a_65) + a_87*(a_21^2*a_32*a_73 + a_74*(a_21^2*a_42 + a_43*(a_31 + a_32)^2) + a_75*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2) + a_76*(a_21^2*a_62 + a_63*(a_31 + a_32)^2 + a_64*(a_41 + a_42 + a_43)^2 + a_65*(a_51 + a_52 + a_53 + a_54)^2))*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)) - 1, - 420*a_21^2*a_32*a_43*a_54*b_5*(a_51 + a_52 + a_53 + a_54) + 420*b_6*(a_21^2*a_32*a_43*a_64 + a_65*(a_21^2*a_32*a_53 + a_54*(a_21^2*a_42 + a_43*(a_31 + a_32)^2)))*(a_61 + a_62 + a_63 + a_64 + a_65) + 420*b_7*(a_21^2*a_32*a_43*a_74 + a_75*(a_21^2*a_32*a_53 + a_54*(a_21^2*a_42 + a_43*(a_31 + a_32)^2)) + a_76*(a_21^2*a_32*a_63 + a_64*(a_21^2*a_42 + a_43*(a_31 + a_32)^2) + a_65*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2)))*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76) + 420*b_8*(a_21^2*a_32*a_43*a_84 + a_85*(a_21^2*a_32*a_53 + a_54*(a_21^2*a_42 + a_43*(a_31 + a_32)^2)) + a_86*(a_21^2*a_32*a_63 + a_64*(a_21^2*a_42 + a_43*(a_31 + a_32)^2) + a_65*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2)) + a_87*(a_21^2*a_32*a_73 + a_74*(a_21^2*a_42 + a_43*(a_31 + a_32)^2) + a_75*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2) + a_76*(a_21^2*a_62 + a_63*(a_31 + a_32)^2 + a_64*(a_41 + a_42 + a_43)^2 + a_65*(a_51 + a_52 + a_53 + a_54)^2)))*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87) - 1, - 840*a_21^2*a_32^2*a_43*a_54*b_5 + 840*b_6*(a_21^2*a_32^2*a_43*a_64 + a_65*(a_21^2*a_32^2*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32))^2)) + 840*b_7*(a_21^2*a_32^2*a_43*a_74 + a_75*(a_21^2*a_32^2*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32))^2) + a_76*(a_21^2*a_32^2*a_63 + a_64*(a_21*a_42 + a_43*(a_31 + a_32))^2 + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))^2)) + 840*b_8*(a_21^2*a_32^2*a_43*a_84 + a_85*(a_21^2*a_32^2*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32))^2) + a_86*(a_21^2*a_32^2*a_63 + a_64*(a_21*a_42 + a_43*(a_31 + a_32))^2 + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))^2) + a_87*(a_21^2*a_32^2*a_73 + a_74*(a_21*a_42 + a_43*(a_31 + a_32))^2 + a_75*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))^2 + a_76*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))^2)) - 1, - 420*a_21*a_32*a_43*a_54*b_5*(a_31 + a_32)^2 + 420*b_6*(a_21*a_32*a_43*a_64*(a_31 + a_32)^2 + a_65*(a_21*a_32*a_53*(a_31 + a_32)^2 + a_54*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43)^2)) + 420*b_7*(a_21*a_32*a_43*a_74*(a_31 + a_32)^2 + a_75*(a_21*a_32*a_53*(a_31 + a_32)^2 + a_54*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43)^2) + a_76*(a_21*a_32*a_63*(a_31 + a_32)^2 + a_64*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43)^2 + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54)^2)) + 420*b_8*(a_21*a_32*a_43*a_84*(a_31 + a_32)^2 + a_85*(a_21*a_32*a_53*(a_31 + a_32)^2 + a_54*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43)^2) + a_86*(a_21*a_32*a_63*(a_31 + a_32)^2 + a_64*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43)^2 + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54)^2) + a_87*(a_21*a_32*a_73*(a_31 + a_32)^2 + a_74*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43)^2 + a_75*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54)^2 + a_76*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))*(a_61 + a_62 + a_63 + a_64 + a_65)^2)) - 1, - 336*a_21*a_32*a_43*a_54*b_5*(a_31 + a_32)*(a_41 + a_42 + a_43) + 336*b_6*(a_21*a_32*a_43*a_64*(a_31 + a_32)*(a_41 + a_42 + a_43) + a_65*(a_21*a_32*a_53*(a_31 + a_32) + a_54*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54)) + 336*b_7*(a_21*a_32*a_43*a_74*(a_31 + a_32)*(a_41 + a_42 + a_43) + a_75*(a_21*a_32*a_53*(a_31 + a_32) + a_54*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54) + a_76*(a_21*a_32*a_63*(a_31 + a_32) + a_64*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54))*(a_61 + a_62 + a_63 + a_64 + a_65)) + 336*b_8*(a_21*a_32*a_43*a_84*(a_31 + a_32)*(a_41 + a_42 + a_43) + a_85*(a_21*a_32*a_53*(a_31 + a_32) + a_54*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54) + a_86*(a_21*a_32*a_63*(a_31 + a_32) + a_64*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54))*(a_61 + a_62 + a_63 + a_64 + a_65) + a_87*(a_21*a_32*a_73*(a_31 + a_32) + a_74*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43) + a_75*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54) + a_76*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))*(a_61 + a_62 + a_63 + a_64 + a_65))*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)) - 1, - 280*a_21*a_32*a_43*a_54*b_5*(a_31 + a_32)*(a_51 + a_52 + a_53 + a_54) + 280*b_6*(a_21*a_32*a_43*a_64*(a_31 + a_32) + a_65*(a_21*a_32*a_53*(a_31 + a_32) + a_54*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43)))*(a_61 + a_62 + a_63 + a_64 + a_65) + 280*b_7*(a_21*a_32*a_43*a_74*(a_31 + a_32) + a_75*(a_21*a_32*a_53*(a_31 + a_32) + a_54*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43)) + a_76*(a_21*a_32*a_63*(a_31 + a_32) + a_64*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54)))*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76) + 280*b_8*(a_21*a_32*a_43*a_84*(a_31 + a_32) + a_85*(a_21*a_32*a_53*(a_31 + a_32) + a_54*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43)) + a_86*(a_21*a_32*a_63*(a_31 + a_32) + a_64*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54)) + a_87*(a_21*a_32*a_73*(a_31 + a_32) + a_74*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43) + a_75*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54) + a_76*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))*(a_61 + a_62 + a_63 + a_64 + a_65)))*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87) - 1, - 504*a_21*a_32*a_43*a_54*b_5*(a_21*a_42 + a_43*(a_31 + a_32)) + 504*b_6*(a_21*a_32*a_43*a_64*(a_21*a_42 + a_43*(a_31 + a_32)) + a_65*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32)))*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))) + 504*b_7*(a_21*a_32*a_43*a_74*(a_21*a_42 + a_43*(a_31 + a_32)) + a_75*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32)))*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)) + a_76*(a_21*a_32*a_63 + a_64*(a_21*a_42 + a_43*(a_31 + a_32)) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)))*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))) + 504*b_8*(a_21*a_32*a_43*a_84*(a_21*a_42 + a_43*(a_31 + a_32)) + a_85*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32)))*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)) + a_86*(a_21*a_32*a_63 + a_64*(a_21*a_42 + a_43*(a_31 + a_32)) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)))*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54)) + a_87*(a_21*a_32*a_73 + a_74*(a_21*a_42 + a_43*(a_31 + a_32)) + a_75*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)) + a_76*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54)))*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65))) - 1, - 252*a_21*a_32*a_43*a_54*b_5*(a_41 + a_42 + a_43)^2 + 252*b_6*(a_21*a_32*a_43*a_64*(a_41 + a_42 + a_43)^2 + a_65*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32)))*(a_51 + a_52 + a_53 + a_54)^2) + 252*b_7*(a_21*a_32*a_43*a_74*(a_41 + a_42 + a_43)^2 + a_75*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32)))*(a_51 + a_52 + a_53 + a_54)^2 + a_76*(a_21*a_32*a_63 + a_64*(a_21*a_42 + a_43*(a_31 + a_32)) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)))*(a_61 + a_62 + a_63 + a_64 + a_65)^2) + 252*b_8*(a_21*a_32*a_43*a_84*(a_41 + a_42 + a_43)^2 + a_85*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32)))*(a_51 + a_52 + a_53 + a_54)^2 + a_86*(a_21*a_32*a_63 + a_64*(a_21*a_42 + a_43*(a_31 + a_32)) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)))*(a_61 + a_62 + a_63 + a_64 + a_65)^2 + a_87*(a_21*a_32*a_73 + a_74*(a_21*a_42 + a_43*(a_31 + a_32)) + a_75*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)) + a_76*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54)))*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2) - 1, - 210*a_21*a_32*a_43*a_54*b_5*(a_41 + a_42 + a_43)*(a_51 + a_52 + a_53 + a_54) + 210*b_6*(a_21*a_32*a_43*a_64*(a_41 + a_42 + a_43) + a_65*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32)))*(a_51 + a_52 + a_53 + a_54))*(a_61 + a_62 + a_63 + a_64 + a_65) + 210*b_7*(a_21*a_32*a_43*a_74*(a_41 + a_42 + a_43) + a_75*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32)))*(a_51 + a_52 + a_53 + a_54) + a_76*(a_21*a_32*a_63 + a_64*(a_21*a_42 + a_43*(a_31 + a_32)) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)))*(a_61 + a_62 + a_63 + a_64 + a_65))*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76) + 210*b_8*(a_21*a_32*a_43*a_84*(a_41 + a_42 + a_43) + a_85*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32)))*(a_51 + a_52 + a_53 + a_54) + a_86*(a_21*a_32*a_63 + a_64*(a_21*a_42 + a_43*(a_31 + a_32)) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)))*(a_61 + a_62 + a_63 + a_64 + a_65) + a_87*(a_21*a_32*a_73 + a_74*(a_21*a_42 + a_43*(a_31 + a_32)) + a_75*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)) + a_76*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54)))*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76))*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87) - 1, - 336*a_21*a_32*a_43*a_54*b_5*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)) + 336*b_6*(a_21*a_32*a_43*a_64 + a_65*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32))))*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54)) + 336*b_7*(a_21*a_32*a_43*a_74 + a_75*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32))) + a_76*(a_21*a_32*a_63 + a_64*(a_21*a_42 + a_43*(a_31 + a_32)) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))))*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)) + 336*b_8*(a_21*a_32*a_43*a_84 + a_85*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32))) + a_86*(a_21*a_32*a_63 + a_64*(a_21*a_42 + a_43*(a_31 + a_32)) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))) + a_87*(a_21*a_32*a_73 + a_74*(a_21*a_42 + a_43*(a_31 + a_32)) + a_75*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)) + a_76*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))))*(a_21*a_82 + a_83*(a_31 + a_32) + a_84*(a_41 + a_42 + a_43) + a_85*(a_51 + a_52 + a_53 + a_54) + a_86*(a_61 + a_62 + a_63 + a_64 + a_65) + a_87*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)) - 1, - 168*a_21*a_32*a_43*a_54*b_5*(a_51 + a_52 + a_53 + a_54)^2 + 168*b_6*(a_21*a_32*a_43*a_64 + a_65*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32))))*(a_61 + a_62 + a_63 + a_64 + a_65)^2 + 168*b_7*(a_21*a_32*a_43*a_74 + a_75*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32))) + a_76*(a_21*a_32*a_63 + a_64*(a_21*a_42 + a_43*(a_31 + a_32)) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))))*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2 + 168*b_8*(a_21*a_32*a_43*a_84 + a_85*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32))) + a_86*(a_21*a_32*a_63 + a_64*(a_21*a_42 + a_43*(a_31 + a_32)) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))) + a_87*(a_21*a_32*a_73 + a_74*(a_21*a_42 + a_43*(a_31 + a_32)) + a_75*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)) + a_76*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))))*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^2 - 1, - 210*a_21^4*a_32*a_43*b_4 + 210*b_5*(a_21^4*a_32*a_53 + a_54*(a_21^4*a_42 + a_43*(a_31 + a_32)^4)) + 210*b_6*(a_21^4*a_32*a_63 + a_64*(a_21^4*a_42 + a_43*(a_31 + a_32)^4) + a_65*(a_21^4*a_52 + a_53*(a_31 + a_32)^4 + a_54*(a_41 + a_42 + a_43)^4)) + 210*b_7*(a_21^4*a_32*a_73 + a_74*(a_21^4*a_42 + a_43*(a_31 + a_32)^4) + a_75*(a_21^4*a_52 + a_53*(a_31 + a_32)^4 + a_54*(a_41 + a_42 + a_43)^4) + a_76*(a_21^4*a_62 + a_63*(a_31 + a_32)^4 + a_64*(a_41 + a_42 + a_43)^4 + a_65*(a_51 + a_52 + a_53 + a_54)^4)) + 210*b_8*(a_21^4*a_32*a_83 + a_84*(a_21^4*a_42 + a_43*(a_31 + a_32)^4) + a_85*(a_21^4*a_52 + a_53*(a_31 + a_32)^4 + a_54*(a_41 + a_42 + a_43)^4) + a_86*(a_21^4*a_62 + a_63*(a_31 + a_32)^4 + a_64*(a_41 + a_42 + a_43)^4 + a_65*(a_51 + a_52 + a_53 + a_54)^4) + a_87*(a_21^4*a_72 + a_73*(a_31 + a_32)^4 + a_74*(a_41 + a_42 + a_43)^4 + a_75*(a_51 + a_52 + a_53 + a_54)^4 + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)^4)) - 1, - 168*a_21^3*a_32*a_43*b_4*(a_31 + a_32) + 168*b_5*(a_21^3*a_32*a_53*(a_31 + a_32) + a_54*(a_21^3*a_42 + a_43*(a_31 + a_32)^3)*(a_41 + a_42 + a_43)) + 168*b_6*(a_21^3*a_32*a_63*(a_31 + a_32) + a_64*(a_21^3*a_42 + a_43*(a_31 + a_32)^3)*(a_41 + a_42 + a_43) + a_65*(a_21^3*a_52 + a_53*(a_31 + a_32)^3 + a_54*(a_41 + a_42 + a_43)^3)*(a_51 + a_52 + a_53 + a_54)) + 168*b_7*(a_21^3*a_32*a_73*(a_31 + a_32) + a_74*(a_21^3*a_42 + a_43*(a_31 + a_32)^3)*(a_41 + a_42 + a_43) + a_75*(a_21^3*a_52 + a_53*(a_31 + a_32)^3 + a_54*(a_41 + a_42 + a_43)^3)*(a_51 + a_52 + a_53 + a_54) + a_76*(a_21^3*a_62 + a_63*(a_31 + a_32)^3 + a_64*(a_41 + a_42 + a_43)^3 + a_65*(a_51 + a_52 + a_53 + a_54)^3)*(a_61 + a_62 + a_63 + a_64 + a_65)) + 168*b_8*(a_21^3*a_32*a_83*(a_31 + a_32) + a_84*(a_21^3*a_42 + a_43*(a_31 + a_32)^3)*(a_41 + a_42 + a_43) + a_85*(a_21^3*a_52 + a_53*(a_31 + a_32)^3 + a_54*(a_41 + a_42 + a_43)^3)*(a_51 + a_52 + a_53 + a_54) + a_86*(a_21^3*a_62 + a_63*(a_31 + a_32)^3 + a_64*(a_41 + a_42 + a_43)^3 + a_65*(a_51 + a_52 + a_53 + a_54)^3)*(a_61 + a_62 + a_63 + a_64 + a_65) + a_87*(a_21^3*a_72 + a_73*(a_31 + a_32)^3 + a_74*(a_41 + a_42 + a_43)^3 + a_75*(a_51 + a_52 + a_53 + a_54)^3 + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)^3)*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)) - 1, - 140*a_21^3*a_32*a_43*b_4*(a_41 + a_42 + a_43) + 140*b_5*(a_21^3*a_32*a_53 + a_54*(a_21^3*a_42 + a_43*(a_31 + a_32)^3))*(a_51 + a_52 + a_53 + a_54) + 140*b_6*(a_21^3*a_32*a_63 + a_64*(a_21^3*a_42 + a_43*(a_31 + a_32)^3) + a_65*(a_21^3*a_52 + a_53*(a_31 + a_32)^3 + a_54*(a_41 + a_42 + a_43)^3))*(a_61 + a_62 + a_63 + a_64 + a_65) + 140*b_7*(a_21^3*a_32*a_73 + a_74*(a_21^3*a_42 + a_43*(a_31 + a_32)^3) + a_75*(a_21^3*a_52 + a_53*(a_31 + a_32)^3 + a_54*(a_41 + a_42 + a_43)^3) + a_76*(a_21^3*a_62 + a_63*(a_31 + a_32)^3 + a_64*(a_41 + a_42 + a_43)^3 + a_65*(a_51 + a_52 + a_53 + a_54)^3))*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76) + 140*b_8*(a_21^3*a_32*a_83 + a_84*(a_21^3*a_42 + a_43*(a_31 + a_32)^3) + a_85*(a_21^3*a_52 + a_53*(a_31 + a_32)^3 + a_54*(a_41 + a_42 + a_43)^3) + a_86*(a_21^3*a_62 + a_63*(a_31 + a_32)^3 + a_64*(a_41 + a_42 + a_43)^3 + a_65*(a_51 + a_52 + a_53 + a_54)^3) + a_87*(a_21^3*a_72 + a_73*(a_31 + a_32)^3 + a_74*(a_41 + a_42 + a_43)^3 + a_75*(a_51 + a_52 + a_53 + a_54)^3 + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)^3))*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87) - 1, - 252*a_21^3*a_32^2*a_43*b_4 + 252*b_5*(a_21^3*a_32^2*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32))*(a_21^2*a_42 + a_43*(a_31 + a_32)^2)) + 252*b_6*(a_21^3*a_32^2*a_63 + a_64*(a_21*a_42 + a_43*(a_31 + a_32))*(a_21^2*a_42 + a_43*(a_31 + a_32)^2) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2)) + 252*b_7*(a_21^3*a_32^2*a_73 + a_74*(a_21*a_42 + a_43*(a_31 + a_32))*(a_21^2*a_42 + a_43*(a_31 + a_32)^2) + a_75*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2) + a_76*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))*(a_21^2*a_62 + a_63*(a_31 + a_32)^2 + a_64*(a_41 + a_42 + a_43)^2 + a_65*(a_51 + a_52 + a_53 + a_54)^2)) + 252*b_8*(a_21^3*a_32^2*a_83 + a_84*(a_21*a_42 + a_43*(a_31 + a_32))*(a_21^2*a_42 + a_43*(a_31 + a_32)^2) + a_85*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2) + a_86*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))*(a_21^2*a_62 + a_63*(a_31 + a_32)^2 + a_64*(a_41 + a_42 + a_43)^2 + a_65*(a_51 + a_52 + a_53 + a_54)^2) + a_87*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65))*(a_21^2*a_72 + a_73*(a_31 + a_32)^2 + a_74*(a_41 + a_42 + a_43)^2 + a_75*(a_51 + a_52 + a_53 + a_54)^2 + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)^2)) - 1, - 126*a_21^2*a_32*a_43*b_4*(a_31 + a_32)^2 + 126*b_5*(a_21^2*a_32*a_53*(a_31 + a_32)^2 + a_54*(a_21^2*a_42 + a_43*(a_31 + a_32)^2)*(a_41 + a_42 + a_43)^2) + 126*b_6*(a_21^2*a_32*a_63*(a_31 + a_32)^2 + a_64*(a_21^2*a_42 + a_43*(a_31 + a_32)^2)*(a_41 + a_42 + a_43)^2 + a_65*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2)*(a_51 + a_52 + a_53 + a_54)^2) + 126*b_7*(a_21^2*a_32*a_73*(a_31 + a_32)^2 + a_74*(a_21^2*a_42 + a_43*(a_31 + a_32)^2)*(a_41 + a_42 + a_43)^2 + a_75*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2)*(a_51 + a_52 + a_53 + a_54)^2 + a_76*(a_21^2*a_62 + a_63*(a_31 + a_32)^2 + a_64*(a_41 + a_42 + a_43)^2 + a_65*(a_51 + a_52 + a_53 + a_54)^2)*(a_61 + a_62 + a_63 + a_64 + a_65)^2) + 126*b_8*(a_21^2*a_32*a_83*(a_31 + a_32)^2 + a_84*(a_21^2*a_42 + a_43*(a_31 + a_32)^2)*(a_41 + a_42 + a_43)^2 + a_85*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2)*(a_51 + a_52 + a_53 + a_54)^2 + a_86*(a_21^2*a_62 + a_63*(a_31 + a_32)^2 + a_64*(a_41 + a_42 + a_43)^2 + a_65*(a_51 + a_52 + a_53 + a_54)^2)*(a_61 + a_62 + a_63 + a_64 + a_65)^2 + a_87*(a_21^2*a_72 + a_73*(a_31 + a_32)^2 + a_74*(a_41 + a_42 + a_43)^2 + a_75*(a_51 + a_52 + a_53 + a_54)^2 + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)^2)*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2) - 1, - 105*a_21^2*a_32*a_43*b_4*(a_31 + a_32)*(a_41 + a_42 + a_43) + 105*b_5*(a_21^2*a_32*a_53*(a_31 + a_32) + a_54*(a_21^2*a_42 + a_43*(a_31 + a_32)^2)*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54) + 105*b_6*(a_21^2*a_32*a_63*(a_31 + a_32) + a_64*(a_21^2*a_42 + a_43*(a_31 + a_32)^2)*(a_41 + a_42 + a_43) + a_65*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2)*(a_51 + a_52 + a_53 + a_54))*(a_61 + a_62 + a_63 + a_64 + a_65) + 105*b_7*(a_21^2*a_32*a_73*(a_31 + a_32) + a_74*(a_21^2*a_42 + a_43*(a_31 + a_32)^2)*(a_41 + a_42 + a_43) + a_75*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2)*(a_51 + a_52 + a_53 + a_54) + a_76*(a_21^2*a_62 + a_63*(a_31 + a_32)^2 + a_64*(a_41 + a_42 + a_43)^2 + a_65*(a_51 + a_52 + a_53 + a_54)^2)*(a_61 + a_62 + a_63 + a_64 + a_65))*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76) + 105*b_8*(a_21^2*a_32*a_83*(a_31 + a_32) + a_84*(a_21^2*a_42 + a_43*(a_31 + a_32)^2)*(a_41 + a_42 + a_43) + a_85*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2)*(a_51 + a_52 + a_53 + a_54) + a_86*(a_21^2*a_62 + a_63*(a_31 + a_32)^2 + a_64*(a_41 + a_42 + a_43)^2 + a_65*(a_51 + a_52 + a_53 + a_54)^2)*(a_61 + a_62 + a_63 + a_64 + a_65) + a_87*(a_21^2*a_72 + a_73*(a_31 + a_32)^2 + a_74*(a_41 + a_42 + a_43)^2 + a_75*(a_51 + a_52 + a_53 + a_54)^2 + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)^2)*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76))*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87) - 1, - 168*a_21^2*a_32*a_43*b_4*(a_21*a_42 + a_43*(a_31 + a_32)) + 168*b_5*(a_21^2*a_32*a_53 + a_54*(a_21^2*a_42 + a_43*(a_31 + a_32)^2))*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)) + 168*b_6*(a_21^2*a_32*a_63 + a_64*(a_21^2*a_42 + a_43*(a_31 + a_32)^2) + a_65*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2))*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54)) + 168*b_7*(a_21^2*a_32*a_73 + a_74*(a_21^2*a_42 + a_43*(a_31 + a_32)^2) + a_75*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2) + a_76*(a_21^2*a_62 + a_63*(a_31 + a_32)^2 + a_64*(a_41 + a_42 + a_43)^2 + a_65*(a_51 + a_52 + a_53 + a_54)^2))*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)) + 168*b_8*(a_21^2*a_32*a_83 + a_84*(a_21^2*a_42 + a_43*(a_31 + a_32)^2) + a_85*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2) + a_86*(a_21^2*a_62 + a_63*(a_31 + a_32)^2 + a_64*(a_41 + a_42 + a_43)^2 + a_65*(a_51 + a_52 + a_53 + a_54)^2) + a_87*(a_21^2*a_72 + a_73*(a_31 + a_32)^2 + a_74*(a_41 + a_42 + a_43)^2 + a_75*(a_51 + a_52 + a_53 + a_54)^2 + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)^2))*(a_21*a_82 + a_83*(a_31 + a_32) + a_84*(a_41 + a_42 + a_43) + a_85*(a_51 + a_52 + a_53 + a_54) + a_86*(a_61 + a_62 + a_63 + a_64 + a_65) + a_87*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)) - 1, - 84*a_21^2*a_32*a_43*b_4*(a_41 + a_42 + a_43)^2 + 84*b_5*(a_21^2*a_32*a_53 + a_54*(a_21^2*a_42 + a_43*(a_31 + a_32)^2))*(a_51 + a_52 + a_53 + a_54)^2 + 84*b_6*(a_21^2*a_32*a_63 + a_64*(a_21^2*a_42 + a_43*(a_31 + a_32)^2) + a_65*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2))*(a_61 + a_62 + a_63 + a_64 + a_65)^2 + 84*b_7*(a_21^2*a_32*a_73 + a_74*(a_21^2*a_42 + a_43*(a_31 + a_32)^2) + a_75*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2) + a_76*(a_21^2*a_62 + a_63*(a_31 + a_32)^2 + a_64*(a_41 + a_42 + a_43)^2 + a_65*(a_51 + a_52 + a_53 + a_54)^2))*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2 + 84*b_8*(a_21^2*a_32*a_83 + a_84*(a_21^2*a_42 + a_43*(a_31 + a_32)^2) + a_85*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2) + a_86*(a_21^2*a_62 + a_63*(a_31 + a_32)^2 + a_64*(a_41 + a_42 + a_43)^2 + a_65*(a_51 + a_52 + a_53 + a_54)^2) + a_87*(a_21^2*a_72 + a_73*(a_31 + a_32)^2 + a_74*(a_41 + a_42 + a_43)^2 + a_75*(a_51 + a_52 + a_53 + a_54)^2 + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)^2))*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^2 - 1, - 168*a_21^2*a_32^2*a_43*b_4*(a_31 + a_32) + 168*b_5*(a_21^2*a_32^2*a_53*(a_31 + a_32) + a_54*(a_21*a_42 + a_43*(a_31 + a_32))^2*(a_41 + a_42 + a_43)) + 168*b_6*(a_21^2*a_32^2*a_63*(a_31 + a_32) + a_64*(a_21*a_42 + a_43*(a_31 + a_32))^2*(a_41 + a_42 + a_43) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))^2*(a_51 + a_52 + a_53 + a_54)) + 168*b_7*(a_21^2*a_32^2*a_73*(a_31 + a_32) + a_74*(a_21*a_42 + a_43*(a_31 + a_32))^2*(a_41 + a_42 + a_43) + a_75*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))^2*(a_51 + a_52 + a_53 + a_54) + a_76*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))^2*(a_61 + a_62 + a_63 + a_64 + a_65)) + 168*b_8*(a_21^2*a_32^2*a_83*(a_31 + a_32) + a_84*(a_21*a_42 + a_43*(a_31 + a_32))^2*(a_41 + a_42 + a_43) + a_85*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))^2*(a_51 + a_52 + a_53 + a_54) + a_86*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))^2*(a_61 + a_62 + a_63 + a_64 + a_65) + a_87*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65))^2*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)) - 1, - 140*a_21^2*a_32^2*a_43*b_4*(a_41 + a_42 + a_43) + 140*b_5*(a_21^2*a_32^2*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32))^2)*(a_51 + a_52 + a_53 + a_54) + 140*b_6*(a_21^2*a_32^2*a_63 + a_64*(a_21*a_42 + a_43*(a_31 + a_32))^2 + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))^2)*(a_61 + a_62 + a_63 + a_64 + a_65) + 140*b_7*(a_21^2*a_32^2*a_73 + a_74*(a_21*a_42 + a_43*(a_31 + a_32))^2 + a_75*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))^2 + a_76*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))^2)*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76) + 140*b_8*(a_21^2*a_32^2*a_83 + a_84*(a_21*a_42 + a_43*(a_31 + a_32))^2 + a_85*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))^2 + a_86*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))^2 + a_87*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65))^2)*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87) - 1, - 84*a_21*a_32*a_43*b_4*(a_31 + a_32)^3 + 84*b_5*(a_21*a_32*a_53*(a_31 + a_32)^3 + a_54*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43)^3) + 84*b_6*(a_21*a_32*a_63*(a_31 + a_32)^3 + a_64*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43)^3 + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54)^3) + 84*b_7*(a_21*a_32*a_73*(a_31 + a_32)^3 + a_74*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43)^3 + a_75*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54)^3 + a_76*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))*(a_61 + a_62 + a_63 + a_64 + a_65)^3) + 84*b_8*(a_21*a_32*a_83*(a_31 + a_32)^3 + a_84*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43)^3 + a_85*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54)^3 + a_86*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))*(a_61 + a_62 + a_63 + a_64 + a_65)^3 + a_87*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65))*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^3) - 1, - 70*a_21*a_32*a_43*b_4*(a_31 + a_32)^2*(a_41 + a_42 + a_43) + 70*b_5*(a_21*a_32*a_53*(a_31 + a_32)^2 + a_54*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43)^2)*(a_51 + a_52 + a_53 + a_54) + 70*b_6*(a_21*a_32*a_63*(a_31 + a_32)^2 + a_64*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43)^2 + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54)^2)*(a_61 + a_62 + a_63 + a_64 + a_65) + 70*b_7*(a_21*a_32*a_73*(a_31 + a_32)^2 + a_74*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43)^2 + a_75*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54)^2 + a_76*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))*(a_61 + a_62 + a_63 + a_64 + a_65)^2)*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76) + 70*b_8*(a_21*a_32*a_83*(a_31 + a_32)^2 + a_84*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43)^2 + a_85*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54)^2 + a_86*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))*(a_61 + a_62 + a_63 + a_64 + a_65)^2 + a_87*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65))*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2)*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87) - 1, - 112*a_21*a_32*a_43*b_4*(a_31 + a_32)*(a_21*a_42 + a_43*(a_31 + a_32)) + 112*b_5*(a_21*a_32*a_53*(a_31 + a_32) + a_54*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43))*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)) + 112*b_6*(a_21*a_32*a_63*(a_31 + a_32) + a_64*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54))*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54)) + 112*b_7*(a_21*a_32*a_73*(a_31 + a_32) + a_74*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43) + a_75*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54) + a_76*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))*(a_61 + a_62 + a_63 + a_64 + a_65))*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)) + 112*b_8*(a_21*a_32*a_83*(a_31 + a_32) + a_84*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43) + a_85*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54) + a_86*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))*(a_61 + a_62 + a_63 + a_64 + a_65) + a_87*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65))*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76))*(a_21*a_82 + a_83*(a_31 + a_32) + a_84*(a_41 + a_42 + a_43) + a_85*(a_51 + a_52 + a_53 + a_54) + a_86*(a_61 + a_62 + a_63 + a_64 + a_65) + a_87*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)) - 1, - 56*a_21*a_32*a_43*b_4*(a_31 + a_32)*(a_41 + a_42 + a_43)^2 + 56*b_5*(a_21*a_32*a_53*(a_31 + a_32) + a_54*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54)^2 + 56*b_6*(a_21*a_32*a_63*(a_31 + a_32) + a_64*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54))*(a_61 + a_62 + a_63 + a_64 + a_65)^2 + 56*b_7*(a_21*a_32*a_73*(a_31 + a_32) + a_74*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43) + a_75*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54) + a_76*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))*(a_61 + a_62 + a_63 + a_64 + a_65))*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2 + 56*b_8*(a_21*a_32*a_83*(a_31 + a_32) + a_84*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43) + a_85*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54) + a_86*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))*(a_61 + a_62 + a_63 + a_64 + a_65) + a_87*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65))*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76))*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^2 - 1, - 252*a_21^2*a_32^2*a_43^2*b_4 + 252*b_5*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32)))^2 + 252*b_6*(a_21*a_32*a_63 + a_64*(a_21*a_42 + a_43*(a_31 + a_32)) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)))^2 + 252*b_7*(a_21*a_32*a_73 + a_74*(a_21*a_42 + a_43*(a_31 + a_32)) + a_75*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)) + a_76*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54)))^2 + 252*b_8*(a_21*a_32*a_83 + a_84*(a_21*a_42 + a_43*(a_31 + a_32)) + a_85*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)) + a_86*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54)) + a_87*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)))^2 - 1, - 126*a_21*a_32*a_43*b_4*(a_21^2*a_42 + a_43*(a_31 + a_32)^2) + 126*b_5*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32)))*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2) + 126*b_6*(a_21*a_32*a_63 + a_64*(a_21*a_42 + a_43*(a_31 + a_32)) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)))*(a_21^2*a_62 + a_63*(a_31 + a_32)^2 + a_64*(a_41 + a_42 + a_43)^2 + a_65*(a_51 + a_52 + a_53 + a_54)^2) + 126*b_7*(a_21*a_32*a_73 + a_74*(a_21*a_42 + a_43*(a_31 + a_32)) + a_75*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)) + a_76*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54)))*(a_21^2*a_72 + a_73*(a_31 + a_32)^2 + a_74*(a_41 + a_42 + a_43)^2 + a_75*(a_51 + a_52 + a_53 + a_54)^2 + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)^2) + 126*b_8*(a_21*a_32*a_83 + a_84*(a_21*a_42 + a_43*(a_31 + a_32)) + a_85*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)) + a_86*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54)) + a_87*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)))*(a_21^2*a_82 + a_83*(a_31 + a_32)^2 + a_84*(a_41 + a_42 + a_43)^2 + a_85*(a_51 + a_52 + a_53 + a_54)^2 + a_86*(a_61 + a_62 + a_63 + a_64 + a_65)^2 + a_87*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2) - 1, - 84*a_21*a_32*a_43*b_4*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43) + 84*b_5*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32)))*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54) + 84*b_6*(a_21*a_32*a_63 + a_64*(a_21*a_42 + a_43*(a_31 + a_32)) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)))*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))*(a_61 + a_62 + a_63 + a_64 + a_65) + 84*b_7*(a_21*a_32*a_73 + a_74*(a_21*a_42 + a_43*(a_31 + a_32)) + a_75*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)) + a_76*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54)))*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65))*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76) + 84*b_8*(a_21*a_32*a_83 + a_84*(a_21*a_42 + a_43*(a_31 + a_32)) + a_85*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)) + a_86*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54)) + a_87*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)))*(a_21*a_82 + a_83*(a_31 + a_32) + a_84*(a_41 + a_42 + a_43) + a_85*(a_51 + a_52 + a_53 + a_54) + a_86*(a_61 + a_62 + a_63 + a_64 + a_65) + a_87*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76))*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87) - 1, - 42*a_21*a_32*a_43*b_4*(a_41 + a_42 + a_43)^3 + 42*b_5*(a_21*a_32*a_53 + a_54*(a_21*a_42 + a_43*(a_31 + a_32)))*(a_51 + a_52 + a_53 + a_54)^3 + 42*b_6*(a_21*a_32*a_63 + a_64*(a_21*a_42 + a_43*(a_31 + a_32)) + a_65*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)))*(a_61 + a_62 + a_63 + a_64 + a_65)^3 + 42*b_7*(a_21*a_32*a_73 + a_74*(a_21*a_42 + a_43*(a_31 + a_32)) + a_75*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)) + a_76*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54)))*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^3 + 42*b_8*(a_21*a_32*a_83 + a_84*(a_21*a_42 + a_43*(a_31 + a_32)) + a_85*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43)) + a_86*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54)) + a_87*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)))*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^3 - 1, - 42*a_21^5*a_32*b_3 + 42*b_4*(a_21^5*a_42 + a_43*(a_31 + a_32)^5) + 42*b_5*(a_21^5*a_52 + a_53*(a_31 + a_32)^5 + a_54*(a_41 + a_42 + a_43)^5) + 42*b_6*(a_21^5*a_62 + a_63*(a_31 + a_32)^5 + a_64*(a_41 + a_42 + a_43)^5 + a_65*(a_51 + a_52 + a_53 + a_54)^5) + 42*b_7*(a_21^5*a_72 + a_73*(a_31 + a_32)^5 + a_74*(a_41 + a_42 + a_43)^5 + a_75*(a_51 + a_52 + a_53 + a_54)^5 + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)^5) + 42*b_8*(a_21^5*a_82 + a_83*(a_31 + a_32)^5 + a_84*(a_41 + a_42 + a_43)^5 + a_85*(a_51 + a_52 + a_53 + a_54)^5 + a_86*(a_61 + a_62 + a_63 + a_64 + a_65)^5 + a_87*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^5) - 1, - 35*a_21^4*a_32*b_3*(a_31 + a_32) + 35*b_4*(a_21^4*a_42 + a_43*(a_31 + a_32)^4)*(a_41 + a_42 + a_43) + 35*b_5*(a_21^4*a_52 + a_53*(a_31 + a_32)^4 + a_54*(a_41 + a_42 + a_43)^4)*(a_51 + a_52 + a_53 + a_54) + 35*b_6*(a_21^4*a_62 + a_63*(a_31 + a_32)^4 + a_64*(a_41 + a_42 + a_43)^4 + a_65*(a_51 + a_52 + a_53 + a_54)^4)*(a_61 + a_62 + a_63 + a_64 + a_65) + 35*b_7*(a_21^4*a_72 + a_73*(a_31 + a_32)^4 + a_74*(a_41 + a_42 + a_43)^4 + a_75*(a_51 + a_52 + a_53 + a_54)^4 + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)^4)*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76) + 35*b_8*(a_21^4*a_82 + a_83*(a_31 + a_32)^4 + a_84*(a_41 + a_42 + a_43)^4 + a_85*(a_51 + a_52 + a_53 + a_54)^4 + a_86*(a_61 + a_62 + a_63 + a_64 + a_65)^4 + a_87*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^4)*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87) - 1, - 56*a_21^4*a_32^2*b_3 + 56*b_4*(a_21*a_42 + a_43*(a_31 + a_32))*(a_21^3*a_42 + a_43*(a_31 + a_32)^3) + 56*b_5*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_21^3*a_52 + a_53*(a_31 + a_32)^3 + a_54*(a_41 + a_42 + a_43)^3) + 56*b_6*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))*(a_21^3*a_62 + a_63*(a_31 + a_32)^3 + a_64*(a_41 + a_42 + a_43)^3 + a_65*(a_51 + a_52 + a_53 + a_54)^3) + 56*b_7*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65))*(a_21^3*a_72 + a_73*(a_31 + a_32)^3 + a_74*(a_41 + a_42 + a_43)^3 + a_75*(a_51 + a_52 + a_53 + a_54)^3 + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)^3) + 56*b_8*(a_21*a_82 + a_83*(a_31 + a_32) + a_84*(a_41 + a_42 + a_43) + a_85*(a_51 + a_52 + a_53 + a_54) + a_86*(a_61 + a_62 + a_63 + a_64 + a_65) + a_87*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76))*(a_21^3*a_82 + a_83*(a_31 + a_32)^3 + a_84*(a_41 + a_42 + a_43)^3 + a_85*(a_51 + a_52 + a_53 + a_54)^3 + a_86*(a_61 + a_62 + a_63 + a_64 + a_65)^3 + a_87*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^3) - 1, - 28*a_21^3*a_32*b_3*(a_31 + a_32)^2 + 28*b_4*(a_21^3*a_42 + a_43*(a_31 + a_32)^3)*(a_41 + a_42 + a_43)^2 + 28*b_5*(a_21^3*a_52 + a_53*(a_31 + a_32)^3 + a_54*(a_41 + a_42 + a_43)^3)*(a_51 + a_52 + a_53 + a_54)^2 + 28*b_6*(a_21^3*a_62 + a_63*(a_31 + a_32)^3 + a_64*(a_41 + a_42 + a_43)^3 + a_65*(a_51 + a_52 + a_53 + a_54)^3)*(a_61 + a_62 + a_63 + a_64 + a_65)^2 + 28*b_7*(a_21^3*a_72 + a_73*(a_31 + a_32)^3 + a_74*(a_41 + a_42 + a_43)^3 + a_75*(a_51 + a_52 + a_53 + a_54)^3 + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)^3)*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2 + 28*b_8*(a_21^3*a_82 + a_83*(a_31 + a_32)^3 + a_84*(a_41 + a_42 + a_43)^3 + a_85*(a_51 + a_52 + a_53 + a_54)^3 + a_86*(a_61 + a_62 + a_63 + a_64 + a_65)^3 + a_87*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^3)*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^2 - 1, - 63*a_21^4*a_32^2*b_3 + 63*b_4*(a_21^2*a_42 + a_43*(a_31 + a_32)^2)^2 + 63*b_5*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2)^2 + 63*b_6*(a_21^2*a_62 + a_63*(a_31 + a_32)^2 + a_64*(a_41 + a_42 + a_43)^2 + a_65*(a_51 + a_52 + a_53 + a_54)^2)^2 + 63*b_7*(a_21^2*a_72 + a_73*(a_31 + a_32)^2 + a_74*(a_41 + a_42 + a_43)^2 + a_75*(a_51 + a_52 + a_53 + a_54)^2 + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)^2)^2 + 63*b_8*(a_21^2*a_82 + a_83*(a_31 + a_32)^2 + a_84*(a_41 + a_42 + a_43)^2 + a_85*(a_51 + a_52 + a_53 + a_54)^2 + a_86*(a_61 + a_62 + a_63 + a_64 + a_65)^2 + a_87*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2)^2 - 1, - 42*a_21^3*a_32^2*b_3*(a_31 + a_32) + 42*b_4*(a_21*a_42 + a_43*(a_31 + a_32))*(a_21^2*a_42 + a_43*(a_31 + a_32)^2)*(a_41 + a_42 + a_43) + 42*b_5*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2)*(a_51 + a_52 + a_53 + a_54) + 42*b_6*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))*(a_21^2*a_62 + a_63*(a_31 + a_32)^2 + a_64*(a_41 + a_42 + a_43)^2 + a_65*(a_51 + a_52 + a_53 + a_54)^2)*(a_61 + a_62 + a_63 + a_64 + a_65) + 42*b_7*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65))*(a_21^2*a_72 + a_73*(a_31 + a_32)^2 + a_74*(a_41 + a_42 + a_43)^2 + a_75*(a_51 + a_52 + a_53 + a_54)^2 + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)^2)*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76) + 42*b_8*(a_21*a_82 + a_83*(a_31 + a_32) + a_84*(a_41 + a_42 + a_43) + a_85*(a_51 + a_52 + a_53 + a_54) + a_86*(a_61 + a_62 + a_63 + a_64 + a_65) + a_87*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76))*(a_21^2*a_82 + a_83*(a_31 + a_32)^2 + a_84*(a_41 + a_42 + a_43)^2 + a_85*(a_51 + a_52 + a_53 + a_54)^2 + a_86*(a_61 + a_62 + a_63 + a_64 + a_65)^2 + a_87*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2)*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87) - 1, - 21*a_21^2*a_32*b_3*(a_31 + a_32)^3 + 21*b_4*(a_21^2*a_42 + a_43*(a_31 + a_32)^2)*(a_41 + a_42 + a_43)^3 + 21*b_5*(a_21^2*a_52 + a_53*(a_31 + a_32)^2 + a_54*(a_41 + a_42 + a_43)^2)*(a_51 + a_52 + a_53 + a_54)^3 + 21*b_6*(a_21^2*a_62 + a_63*(a_31 + a_32)^2 + a_64*(a_41 + a_42 + a_43)^2 + a_65*(a_51 + a_52 + a_53 + a_54)^2)*(a_61 + a_62 + a_63 + a_64 + a_65)^3 + 21*b_7*(a_21^2*a_72 + a_73*(a_31 + a_32)^2 + a_74*(a_41 + a_42 + a_43)^2 + a_75*(a_51 + a_52 + a_53 + a_54)^2 + a_76*(a_61 + a_62 + a_63 + a_64 + a_65)^2)*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^3 + 21*b_8*(a_21^2*a_82 + a_83*(a_31 + a_32)^2 + a_84*(a_41 + a_42 + a_43)^2 + a_85*(a_51 + a_52 + a_53 + a_54)^2 + a_86*(a_61 + a_62 + a_63 + a_64 + a_65)^2 + a_87*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2)*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^3 - 1, - 56*a_21^3*a_32^3*b_3 + 56*b_4*(a_21*a_42 + a_43*(a_31 + a_32))^3 + 56*b_5*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))^3 + 56*b_6*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))^3 + 56*b_7*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65))^3 + 56*b_8*(a_21*a_82 + a_83*(a_31 + a_32) + a_84*(a_41 + a_42 + a_43) + a_85*(a_51 + a_52 + a_53 + a_54) + a_86*(a_61 + a_62 + a_63 + a_64 + a_65) + a_87*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76))^3 - 1, - 28*a_21^2*a_32^2*b_3*(a_31 + a_32)^2 + 28*b_4*(a_21*a_42 + a_43*(a_31 + a_32))^2*(a_41 + a_42 + a_43)^2 + 28*b_5*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))^2*(a_51 + a_52 + a_53 + a_54)^2 + 28*b_6*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))^2*(a_61 + a_62 + a_63 + a_64 + a_65)^2 + 28*b_7*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65))^2*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2 + 28*b_8*(a_21*a_82 + a_83*(a_31 + a_32) + a_84*(a_41 + a_42 + a_43) + a_85*(a_51 + a_52 + a_53 + a_54) + a_86*(a_61 + a_62 + a_63 + a_64 + a_65) + a_87*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76))^2*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^2 - 1, - 14*a_21*a_32*b_3*(a_31 + a_32)^4 + 14*b_4*(a_21*a_42 + a_43*(a_31 + a_32))*(a_41 + a_42 + a_43)^4 + 14*b_5*(a_21*a_52 + a_53*(a_31 + a_32) + a_54*(a_41 + a_42 + a_43))*(a_51 + a_52 + a_53 + a_54)^4 + 14*b_6*(a_21*a_62 + a_63*(a_31 + a_32) + a_64*(a_41 + a_42 + a_43) + a_65*(a_51 + a_52 + a_53 + a_54))*(a_61 + a_62 + a_63 + a_64 + a_65)^4 + 14*b_7*(a_21*a_72 + a_73*(a_31 + a_32) + a_74*(a_41 + a_42 + a_43) + a_75*(a_51 + a_52 + a_53 + a_54) + a_76*(a_61 + a_62 + a_63 + a_64 + a_65))*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^4 + 14*b_8*(a_21*a_82 + a_83*(a_31 + a_32) + a_84*(a_41 + a_42 + a_43) + a_85*(a_51 + a_52 + a_53 + a_54) + a_86*(a_61 + a_62 + a_63 + a_64 + a_65) + a_87*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76))*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^4 - 1, - 7*a_21^6*b_2 + 7*b_3*(a_31 + a_32)^6 + 7*b_4*(a_41 + a_42 + a_43)^6 + 7*b_5*(a_51 + a_52 + a_53 + a_54)^6 + 7*b_6*(a_61 + a_62 + a_63 + a_64 + a_65)^6 + 7*b_7*(a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^6 + 7*b_8*(a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^6 - 1 -]: - -print("Running RK(8,7)"); -kernelopts(bytesalloc) / (1024 * 1024.0); -st := time[real](): -gb := Groebner[Basis](J, tdeg(a_21, a_31, a_32, a_41, a_42, a_43, a_51, a_52, a_53, a_54, a_61, a_62, a_63, a_64, a_65, a_71, a_72, a_73, a_74, a_75, a_76, a_81, a_82, a_83, a_84, a_85, a_86, a_87, b_1, b_2, b_3, b_4, b_5, b_6, b_7, b_8), method=fgb, characteristic=2^31-1): - -print("RK(8,7): ", time[real]() - st); -kernelopts(bytesalloc) / (1024 * 1024.0); diff --git a/benchmark/scripts/runge-kutta/aa-runge-kutta-4-4.jl b/benchmark/scripts/runge-kutta/aa-runge-kutta-4-4.jl deleted file mode 100644 index 35daaaa3..00000000 --- a/benchmark/scripts/runge-kutta/aa-runge-kutta-4-4.jl +++ /dev/null @@ -1,57 +0,0 @@ -R, (a_21, a_31, a_32, a_41, a_42, a_43, b_1, b_2, b_3, b_4) = polynomial_ring( - QQ, - ["a_21", "a_31", "a_32", "a_41", "a_42", "a_43", "b_1", "b_2", "b_3", "b_4"] -) - -system = [ - b_1 + b_2 + b_3 + b_4 - 1, - 2 * a_21 * b_2 + - 2 * a_31 * b_3 + - 2 * a_32 * b_3 + - 2 * a_41 * b_4 + - 2 * a_42 * b_4 + - 2 * a_43 * b_4 - 1, - 6 * a_21 * a_32 * b_3 + 6 * a_21 * a_42 * b_4 + 6 * a_31 * a_43 * b_4 + 6 * a_32 * a_43 * b_4 - 1, - 3 * a_21^2 * b_2 + - 3 * a_31^2 * b_3 + - 6 * a_31 * a_32 * b_3 + - 3 * a_32^2 * b_3 + - 3 * a_41^2 * b_4 + - 6 * a_41 * a_42 * b_4 + - 6 * a_41 * a_43 * b_4 + - 3 * a_42^2 * b_4 + - 6 * a_42 * a_43 * b_4 + - 3 * a_43^2 * b_4 - 1, - 24 * a_21 * a_32 * a_43 * b_4 - 1, - 12 * a_21^2 * a_32 * b_3 + - 12 * a_21^2 * a_42 * b_4 + - 12 * a_31^2 * a_43 * b_4 + - 24 * a_31 * a_32 * a_43 * b_4 + - 12 * a_32^2 * a_43 * b_4 - 1, - 8 * a_21 * a_31 * a_32 * b_3 + - 8 * a_21 * a_32^2 * b_3 + - 8 * a_21 * a_41 * a_42 * b_4 + - 8 * a_21 * a_42^2 * b_4 + - 8 * a_21 * a_42 * a_43 * b_4 + - 8 * a_31 * a_41 * a_43 * b_4 + - 8 * a_31 * a_42 * a_43 * b_4 + - 8 * a_31 * a_43^2 * b_4 + - 8 * a_32 * a_41 * a_43 * b_4 + - 8 * a_32 * a_42 * a_43 * b_4 + - 8 * a_32 * a_43^2 * b_4 - 1, - 4 * a_21^3 * b_2 + - 4 * a_31^3 * b_3 + - 12 * a_31^2 * a_32 * b_3 + - 12 * a_31 * a_32^2 * b_3 + - 4 * a_32^3 * b_3 + - 4 * a_41^3 * b_4 + - 12 * a_41^2 * a_42 * b_4 + - 12 * a_41^2 * a_43 * b_4 + - 12 * a_41 * a_42^2 * b_4 + - 24 * a_41 * a_42 * a_43 * b_4 + - 12 * a_41 * a_43^2 * b_4 + - 4 * a_42^3 * b_4 + - 12 * a_42^2 * a_43 * b_4 + - 12 * a_42 * a_43^2 * b_4 + - 4 * a_43^3 * b_4 - 1 -] diff --git a/benchmark/scripts/runge-kutta/aa-runge-kutta-6-6.jl b/benchmark/scripts/runge-kutta/aa-runge-kutta-6-6.jl deleted file mode 100644 index accb2bde..00000000 --- a/benchmark/scripts/runge-kutta/aa-runge-kutta-6-6.jl +++ /dev/null @@ -1,4156 +0,0 @@ -R, -( - a_21, - a_31, - a_32, - a_41, - a_42, - a_43, - a_51, - a_52, - a_53, - a_54, - a_61, - a_62, - a_63, - a_64, - a_65, - b_1, - b_2, - b_3, - b_4, - b_5, - b_6 -) = polynomial_ring( - QQ, - [ - "a_21", - "a_31", - "a_32", - "a_41", - "a_42", - "a_43", - "a_51", - "a_52", - "a_53", - "a_54", - "a_61", - "a_62", - "a_63", - "a_64", - "a_65", - "b_1", - "b_2", - "b_3", - "b_4", - "b_5", - "b_6" - ] -) - -system = [ - b_1 + b_2 + b_3 + b_4 + b_5 + b_6 - 1, - 2 * a_21 * b_2 + - 2 * a_31 * b_3 + - 2 * a_32 * b_3 + - 2 * a_41 * b_4 + - 2 * a_42 * b_4 + - 2 * a_43 * b_4 + - 2 * a_51 * b_5 + - 2 * a_52 * b_5 + - 2 * a_53 * b_5 + - 2 * a_54 * b_5 + - 2 * a_61 * b_6 + - 2 * a_62 * b_6 + - 2 * a_63 * b_6 + - 2 * a_64 * b_6 + - 2 * a_65 * b_6 - 1, - 6 * a_21 * a_32 * b_3 + - 6 * a_21 * a_42 * b_4 + - 6 * a_21 * a_52 * b_5 + - 6 * a_21 * a_62 * b_6 + - 6 * a_31 * a_43 * b_4 + - 6 * a_31 * a_53 * b_5 + - 6 * a_31 * a_63 * b_6 + - 6 * a_32 * a_43 * b_4 + - 6 * a_32 * a_53 * b_5 + - 6 * a_32 * a_63 * b_6 + - 6 * a_41 * a_54 * b_5 + - 6 * a_41 * a_64 * b_6 + - 6 * a_42 * a_54 * b_5 + - 6 * a_42 * a_64 * b_6 + - 6 * a_43 * a_54 * b_5 + - 6 * a_43 * a_64 * b_6 + - 6 * a_51 * a_65 * b_6 + - 6 * a_52 * a_65 * b_6 + - 6 * a_53 * a_65 * b_6 + - 6 * a_54 * a_65 * b_6 - 1, - 3 * a_21^2 * b_2 + - 3 * a_31^2 * b_3 + - 6 * a_31 * a_32 * b_3 + - 3 * a_32^2 * b_3 + - 3 * a_41^2 * b_4 + - 6 * a_41 * a_42 * b_4 + - 6 * a_41 * a_43 * b_4 + - 3 * a_42^2 * b_4 + - 6 * a_42 * a_43 * b_4 + - 3 * a_43^2 * b_4 + - 3 * a_51^2 * b_5 + - 6 * a_51 * a_52 * b_5 + - 6 * a_51 * a_53 * b_5 + - 6 * a_51 * a_54 * b_5 + - 3 * a_52^2 * b_5 + - 6 * a_52 * a_53 * b_5 + - 6 * a_52 * a_54 * b_5 + - 3 * a_53^2 * b_5 + - 6 * a_53 * a_54 * b_5 + - 3 * a_54^2 * b_5 + - 3 * a_61^2 * b_6 + - 6 * a_61 * a_62 * b_6 + - 6 * a_61 * a_63 * b_6 + - 6 * a_61 * a_64 * b_6 + - 6 * a_61 * a_65 * b_6 + - 3 * a_62^2 * b_6 + - 6 * a_62 * a_63 * b_6 + - 6 * a_62 * a_64 * b_6 + - 6 * a_62 * a_65 * b_6 + - 3 * a_63^2 * b_6 + - 6 * a_63 * a_64 * b_6 + - 6 * a_63 * a_65 * b_6 + - 3 * a_64^2 * b_6 + - 6 * a_64 * a_65 * b_6 + - 3 * a_65^2 * b_6 - 1, - 24 * a_21 * a_32 * a_43 * b_4 + - 24 * a_21 * a_32 * a_53 * b_5 + - 24 * a_21 * a_32 * a_63 * b_6 + - 24 * a_21 * a_42 * a_54 * b_5 + - 24 * a_21 * a_42 * a_64 * b_6 + - 24 * a_21 * a_52 * a_65 * b_6 + - 24 * a_31 * a_43 * a_54 * b_5 + - 24 * a_31 * a_43 * a_64 * b_6 + - 24 * a_31 * a_53 * a_65 * b_6 + - 24 * a_32 * a_43 * a_54 * b_5 + - 24 * a_32 * a_43 * a_64 * b_6 + - 24 * a_32 * a_53 * a_65 * b_6 + - 24 * a_41 * a_54 * a_65 * b_6 + - 24 * a_42 * a_54 * a_65 * b_6 + - 24 * a_43 * a_54 * a_65 * b_6 - 1, - 12 * a_21^2 * a_32 * b_3 + - 12 * a_21^2 * a_42 * b_4 + - 12 * a_21^2 * a_52 * b_5 + - 12 * a_21^2 * a_62 * b_6 + - 12 * a_31^2 * a_43 * b_4 + - 12 * a_31^2 * a_53 * b_5 + - 12 * a_31^2 * a_63 * b_6 + - 24 * a_31 * a_32 * a_43 * b_4 + - 24 * a_31 * a_32 * a_53 * b_5 + - 24 * a_31 * a_32 * a_63 * b_6 + - 12 * a_32^2 * a_43 * b_4 + - 12 * a_32^2 * a_53 * b_5 + - 12 * a_32^2 * a_63 * b_6 + - 12 * a_41^2 * a_54 * b_5 + - 12 * a_41^2 * a_64 * b_6 + - 24 * a_41 * a_42 * a_54 * b_5 + - 24 * a_41 * a_42 * a_64 * b_6 + - 24 * a_41 * a_43 * a_54 * b_5 + - 24 * a_41 * a_43 * a_64 * b_6 + - 12 * a_42^2 * a_54 * b_5 + - 12 * a_42^2 * a_64 * b_6 + - 24 * a_42 * a_43 * a_54 * b_5 + - 24 * a_42 * a_43 * a_64 * b_6 + - 12 * a_43^2 * a_54 * b_5 + - 12 * a_43^2 * a_64 * b_6 + - 12 * a_51^2 * a_65 * b_6 + - 24 * a_51 * a_52 * a_65 * b_6 + - 24 * a_51 * a_53 * a_65 * b_6 + - 24 * a_51 * a_54 * a_65 * b_6 + - 12 * a_52^2 * a_65 * b_6 + - 24 * a_52 * a_53 * a_65 * b_6 + - 24 * a_52 * a_54 * a_65 * b_6 + - 12 * a_53^2 * a_65 * b_6 + - 24 * a_53 * a_54 * a_65 * b_6 + - 12 * a_54^2 * a_65 * b_6 - 1, - 8 * a_21 * a_31 * a_32 * b_3 + - 8 * a_21 * a_32^2 * b_3 + - 8 * a_21 * a_41 * a_42 * b_4 + - 8 * a_21 * a_42^2 * b_4 + - 8 * a_21 * a_42 * a_43 * b_4 + - 8 * a_21 * a_51 * a_52 * b_5 + - 8 * a_21 * a_52^2 * b_5 + - 8 * a_21 * a_52 * a_53 * b_5 + - 8 * a_21 * a_52 * a_54 * b_5 + - 8 * a_21 * a_61 * a_62 * b_6 + - 8 * a_21 * a_62^2 * b_6 + - 8 * a_21 * a_62 * a_63 * b_6 + - 8 * a_21 * a_62 * a_64 * b_6 + - 8 * a_21 * a_62 * a_65 * b_6 + - 8 * a_31 * a_41 * a_43 * b_4 + - 8 * a_31 * a_42 * a_43 * b_4 + - 8 * a_31 * a_43^2 * b_4 + - 8 * a_31 * a_51 * a_53 * b_5 + - 8 * a_31 * a_52 * a_53 * b_5 + - 8 * a_31 * a_53^2 * b_5 + - 8 * a_31 * a_53 * a_54 * b_5 + - 8 * a_31 * a_61 * a_63 * b_6 + - 8 * a_31 * a_62 * a_63 * b_6 + - 8 * a_31 * a_63^2 * b_6 + - 8 * a_31 * a_63 * a_64 * b_6 + - 8 * a_31 * a_63 * a_65 * b_6 + - 8 * a_32 * a_41 * a_43 * b_4 + - 8 * a_32 * a_42 * a_43 * b_4 + - 8 * a_32 * a_43^2 * b_4 + - 8 * a_32 * a_51 * a_53 * b_5 + - 8 * a_32 * a_52 * a_53 * b_5 + - 8 * a_32 * a_53^2 * b_5 + - 8 * a_32 * a_53 * a_54 * b_5 + - 8 * a_32 * a_61 * a_63 * b_6 + - 8 * a_32 * a_62 * a_63 * b_6 + - 8 * a_32 * a_63^2 * b_6 + - 8 * a_32 * a_63 * a_64 * b_6 + - 8 * a_32 * a_63 * a_65 * b_6 + - 8 * a_41 * a_51 * a_54 * b_5 + - 8 * a_41 * a_52 * a_54 * b_5 + - 8 * a_41 * a_53 * a_54 * b_5 + - 8 * a_41 * a_54^2 * b_5 + - 8 * a_41 * a_61 * a_64 * b_6 + - 8 * a_41 * a_62 * a_64 * b_6 + - 8 * a_41 * a_63 * a_64 * b_6 + - 8 * a_41 * a_64^2 * b_6 + - 8 * a_41 * a_64 * a_65 * b_6 + - 8 * a_42 * a_51 * a_54 * b_5 + - 8 * a_42 * a_52 * a_54 * b_5 + - 8 * a_42 * a_53 * a_54 * b_5 + - 8 * a_42 * a_54^2 * b_5 + - 8 * a_42 * a_61 * a_64 * b_6 + - 8 * a_42 * a_62 * a_64 * b_6 + - 8 * a_42 * a_63 * a_64 * b_6 + - 8 * a_42 * a_64^2 * b_6 + - 8 * a_42 * a_64 * a_65 * b_6 + - 8 * a_43 * a_51 * a_54 * b_5 + - 8 * a_43 * a_52 * a_54 * b_5 + - 8 * a_43 * a_53 * a_54 * b_5 + - 8 * a_43 * a_54^2 * b_5 + - 8 * a_43 * a_61 * a_64 * b_6 + - 8 * a_43 * a_62 * a_64 * b_6 + - 8 * a_43 * a_63 * a_64 * b_6 + - 8 * a_43 * a_64^2 * b_6 + - 8 * a_43 * a_64 * a_65 * b_6 + - 8 * a_51 * a_61 * a_65 * b_6 + - 8 * a_51 * a_62 * a_65 * b_6 + - 8 * a_51 * a_63 * a_65 * b_6 + - 8 * a_51 * a_64 * a_65 * b_6 + - 8 * a_51 * a_65^2 * b_6 + - 8 * a_52 * a_61 * a_65 * b_6 + - 8 * a_52 * a_62 * a_65 * b_6 + - 8 * a_52 * a_63 * a_65 * b_6 + - 8 * a_52 * a_64 * a_65 * b_6 + - 8 * a_52 * a_65^2 * b_6 + - 8 * a_53 * a_61 * a_65 * b_6 + - 8 * a_53 * a_62 * a_65 * b_6 + - 8 * a_53 * a_63 * a_65 * b_6 + - 8 * a_53 * a_64 * a_65 * b_6 + - 8 * a_53 * a_65^2 * b_6 + - 8 * a_54 * a_61 * a_65 * b_6 + - 8 * a_54 * a_62 * a_65 * b_6 + - 8 * a_54 * a_63 * a_65 * b_6 + - 8 * a_54 * a_64 * a_65 * b_6 + - 8 * a_54 * a_65^2 * b_6 - 1, - 4 * a_21^3 * b_2 + - 4 * a_31^3 * b_3 + - 12 * a_31^2 * a_32 * b_3 + - 12 * a_31 * a_32^2 * b_3 + - 4 * a_32^3 * b_3 + - 4 * a_41^3 * b_4 + - 12 * a_41^2 * a_42 * b_4 + - 12 * a_41^2 * a_43 * b_4 + - 12 * a_41 * a_42^2 * b_4 + - 24 * a_41 * a_42 * a_43 * b_4 + - 12 * a_41 * a_43^2 * b_4 + - 4 * a_42^3 * b_4 + - 12 * a_42^2 * a_43 * b_4 + - 12 * a_42 * a_43^2 * b_4 + - 4 * a_43^3 * b_4 + - 4 * a_51^3 * b_5 + - 12 * a_51^2 * a_52 * b_5 + - 12 * a_51^2 * a_53 * b_5 + - 12 * a_51^2 * a_54 * b_5 + - 12 * a_51 * a_52^2 * b_5 + - 24 * a_51 * a_52 * a_53 * b_5 + - 24 * a_51 * a_52 * a_54 * b_5 + - 12 * a_51 * a_53^2 * b_5 + - 24 * a_51 * a_53 * a_54 * b_5 + - 12 * a_51 * a_54^2 * b_5 + - 4 * a_52^3 * b_5 + - 12 * a_52^2 * a_53 * b_5 + - 12 * a_52^2 * a_54 * b_5 + - 12 * a_52 * a_53^2 * b_5 + - 24 * a_52 * a_53 * a_54 * b_5 + - 12 * a_52 * a_54^2 * b_5 + - 4 * a_53^3 * b_5 + - 12 * a_53^2 * a_54 * b_5 + - 12 * a_53 * a_54^2 * b_5 + - 4 * a_54^3 * b_5 + - 4 * a_61^3 * b_6 + - 12 * a_61^2 * a_62 * b_6 + - 12 * a_61^2 * a_63 * b_6 + - 12 * a_61^2 * a_64 * b_6 + - 12 * a_61^2 * a_65 * b_6 + - 12 * a_61 * a_62^2 * b_6 + - 24 * a_61 * a_62 * a_63 * b_6 + - 24 * a_61 * a_62 * a_64 * b_6 + - 24 * a_61 * a_62 * a_65 * b_6 + - 12 * a_61 * a_63^2 * b_6 + - 24 * a_61 * a_63 * a_64 * b_6 + - 24 * a_61 * a_63 * a_65 * b_6 + - 12 * a_61 * a_64^2 * b_6 + - 24 * a_61 * a_64 * a_65 * b_6 + - 12 * a_61 * a_65^2 * b_6 + - 4 * a_62^3 * b_6 + - 12 * a_62^2 * a_63 * b_6 + - 12 * a_62^2 * a_64 * b_6 + - 12 * a_62^2 * a_65 * b_6 + - 12 * a_62 * a_63^2 * b_6 + - 24 * a_62 * a_63 * a_64 * b_6 + - 24 * a_62 * a_63 * a_65 * b_6 + - 12 * a_62 * a_64^2 * b_6 + - 24 * a_62 * a_64 * a_65 * b_6 + - 12 * a_62 * a_65^2 * b_6 + - 4 * a_63^3 * b_6 + - 12 * a_63^2 * a_64 * b_6 + - 12 * a_63^2 * a_65 * b_6 + - 12 * a_63 * a_64^2 * b_6 + - 24 * a_63 * a_64 * a_65 * b_6 + - 12 * a_63 * a_65^2 * b_6 + - 4 * a_64^3 * b_6 + - 12 * a_64^2 * a_65 * b_6 + - 12 * a_64 * a_65^2 * b_6 + - 4 * a_65^3 * b_6 - 1, - 120 * a_21 * a_32 * a_43 * a_54 * b_5 + - 120 * a_21 * a_32 * a_43 * a_64 * b_6 + - 120 * a_21 * a_32 * a_53 * a_65 * b_6 + - 120 * a_21 * a_42 * a_54 * a_65 * b_6 + - 120 * a_31 * a_43 * a_54 * a_65 * b_6 + - 120 * a_32 * a_43 * a_54 * a_65 * b_6 - 1, - 60 * a_21^2 * a_32 * a_43 * b_4 + - 60 * a_21^2 * a_32 * a_53 * b_5 + - 60 * a_21^2 * a_32 * a_63 * b_6 + - 60 * a_21^2 * a_42 * a_54 * b_5 + - 60 * a_21^2 * a_42 * a_64 * b_6 + - 60 * a_21^2 * a_52 * a_65 * b_6 + - 60 * a_31^2 * a_43 * a_54 * b_5 + - 60 * a_31^2 * a_43 * a_64 * b_6 + - 60 * a_31^2 * a_53 * a_65 * b_6 + - 120 * a_31 * a_32 * a_43 * a_54 * b_5 + - 120 * a_31 * a_32 * a_43 * a_64 * b_6 + - 120 * a_31 * a_32 * a_53 * a_65 * b_6 + - 60 * a_32^2 * a_43 * a_54 * b_5 + - 60 * a_32^2 * a_43 * a_64 * b_6 + - 60 * a_32^2 * a_53 * a_65 * b_6 + - 60 * a_41^2 * a_54 * a_65 * b_6 + - 120 * a_41 * a_42 * a_54 * a_65 * b_6 + - 120 * a_41 * a_43 * a_54 * a_65 * b_6 + - 60 * a_42^2 * a_54 * a_65 * b_6 + - 120 * a_42 * a_43 * a_54 * a_65 * b_6 + - 60 * a_43^2 * a_54 * a_65 * b_6 - 1, - 40 * a_21 * a_31 * a_32 * a_43 * b_4 + - 40 * a_21 * a_31 * a_32 * a_53 * b_5 + - 40 * a_21 * a_31 * a_32 * a_63 * b_6 + - 40 * a_21 * a_32^2 * a_43 * b_4 + - 40 * a_21 * a_32^2 * a_53 * b_5 + - 40 * a_21 * a_32^2 * a_63 * b_6 + - 40 * a_21 * a_41 * a_42 * a_54 * b_5 + - 40 * a_21 * a_41 * a_42 * a_64 * b_6 + - 40 * a_21 * a_42^2 * a_54 * b_5 + - 40 * a_21 * a_42^2 * a_64 * b_6 + - 40 * a_21 * a_42 * a_43 * a_54 * b_5 + - 40 * a_21 * a_42 * a_43 * a_64 * b_6 + - 40 * a_21 * a_51 * a_52 * a_65 * b_6 + - 40 * a_21 * a_52^2 * a_65 * b_6 + - 40 * a_21 * a_52 * a_53 * a_65 * b_6 + - 40 * a_21 * a_52 * a_54 * a_65 * b_6 + - 40 * a_31 * a_41 * a_43 * a_54 * b_5 + - 40 * a_31 * a_41 * a_43 * a_64 * b_6 + - 40 * a_31 * a_42 * a_43 * a_54 * b_5 + - 40 * a_31 * a_42 * a_43 * a_64 * b_6 + - 40 * a_31 * a_43^2 * a_54 * b_5 + - 40 * a_31 * a_43^2 * a_64 * b_6 + - 40 * a_31 * a_51 * a_53 * a_65 * b_6 + - 40 * a_31 * a_52 * a_53 * a_65 * b_6 + - 40 * a_31 * a_53^2 * a_65 * b_6 + - 40 * a_31 * a_53 * a_54 * a_65 * b_6 + - 40 * a_32 * a_41 * a_43 * a_54 * b_5 + - 40 * a_32 * a_41 * a_43 * a_64 * b_6 + - 40 * a_32 * a_42 * a_43 * a_54 * b_5 + - 40 * a_32 * a_42 * a_43 * a_64 * b_6 + - 40 * a_32 * a_43^2 * a_54 * b_5 + - 40 * a_32 * a_43^2 * a_64 * b_6 + - 40 * a_32 * a_51 * a_53 * a_65 * b_6 + - 40 * a_32 * a_52 * a_53 * a_65 * b_6 + - 40 * a_32 * a_53^2 * a_65 * b_6 + - 40 * a_32 * a_53 * a_54 * a_65 * b_6 + - 40 * a_41 * a_51 * a_54 * a_65 * b_6 + - 40 * a_41 * a_52 * a_54 * a_65 * b_6 + - 40 * a_41 * a_53 * a_54 * a_65 * b_6 + - 40 * a_41 * a_54^2 * a_65 * b_6 + - 40 * a_42 * a_51 * a_54 * a_65 * b_6 + - 40 * a_42 * a_52 * a_54 * a_65 * b_6 + - 40 * a_42 * a_53 * a_54 * a_65 * b_6 + - 40 * a_42 * a_54^2 * a_65 * b_6 + - 40 * a_43 * a_51 * a_54 * a_65 * b_6 + - 40 * a_43 * a_52 * a_54 * a_65 * b_6 + - 40 * a_43 * a_53 * a_54 * a_65 * b_6 + - 40 * a_43 * a_54^2 * a_65 * b_6 - 1, - 30 * a_21 * a_32 * a_41 * a_43 * b_4 + - 30 * a_21 * a_32 * a_42 * a_43 * b_4 + - 30 * a_21 * a_32 * a_43^2 * b_4 + - 30 * a_21 * a_32 * a_51 * a_53 * b_5 + - 30 * a_21 * a_32 * a_52 * a_53 * b_5 + - 30 * a_21 * a_32 * a_53^2 * b_5 + - 30 * a_21 * a_32 * a_53 * a_54 * b_5 + - 30 * a_21 * a_32 * a_61 * a_63 * b_6 + - 30 * a_21 * a_32 * a_62 * a_63 * b_6 + - 30 * a_21 * a_32 * a_63^2 * b_6 + - 30 * a_21 * a_32 * a_63 * a_64 * b_6 + - 30 * a_21 * a_32 * a_63 * a_65 * b_6 + - 30 * a_21 * a_42 * a_51 * a_54 * b_5 + - 30 * a_21 * a_42 * a_52 * a_54 * b_5 + - 30 * a_21 * a_42 * a_53 * a_54 * b_5 + - 30 * a_21 * a_42 * a_54^2 * b_5 + - 30 * a_21 * a_42 * a_61 * a_64 * b_6 + - 30 * a_21 * a_42 * a_62 * a_64 * b_6 + - 30 * a_21 * a_42 * a_63 * a_64 * b_6 + - 30 * a_21 * a_42 * a_64^2 * b_6 + - 30 * a_21 * a_42 * a_64 * a_65 * b_6 + - 30 * a_21 * a_52 * a_61 * a_65 * b_6 + - 30 * a_21 * a_52 * a_62 * a_65 * b_6 + - 30 * a_21 * a_52 * a_63 * a_65 * b_6 + - 30 * a_21 * a_52 * a_64 * a_65 * b_6 + - 30 * a_21 * a_52 * a_65^2 * b_6 + - 30 * a_31 * a_43 * a_51 * a_54 * b_5 + - 30 * a_31 * a_43 * a_52 * a_54 * b_5 + - 30 * a_31 * a_43 * a_53 * a_54 * b_5 + - 30 * a_31 * a_43 * a_54^2 * b_5 + - 30 * a_31 * a_43 * a_61 * a_64 * b_6 + - 30 * a_31 * a_43 * a_62 * a_64 * b_6 + - 30 * a_31 * a_43 * a_63 * a_64 * b_6 + - 30 * a_31 * a_43 * a_64^2 * b_6 + - 30 * a_31 * a_43 * a_64 * a_65 * b_6 + - 30 * a_31 * a_53 * a_61 * a_65 * b_6 + - 30 * a_31 * a_53 * a_62 * a_65 * b_6 + - 30 * a_31 * a_53 * a_63 * a_65 * b_6 + - 30 * a_31 * a_53 * a_64 * a_65 * b_6 + - 30 * a_31 * a_53 * a_65^2 * b_6 + - 30 * a_32 * a_43 * a_51 * a_54 * b_5 + - 30 * a_32 * a_43 * a_52 * a_54 * b_5 + - 30 * a_32 * a_43 * a_53 * a_54 * b_5 + - 30 * a_32 * a_43 * a_54^2 * b_5 + - 30 * a_32 * a_43 * a_61 * a_64 * b_6 + - 30 * a_32 * a_43 * a_62 * a_64 * b_6 + - 30 * a_32 * a_43 * a_63 * a_64 * b_6 + - 30 * a_32 * a_43 * a_64^2 * b_6 + - 30 * a_32 * a_43 * a_64 * a_65 * b_6 + - 30 * a_32 * a_53 * a_61 * a_65 * b_6 + - 30 * a_32 * a_53 * a_62 * a_65 * b_6 + - 30 * a_32 * a_53 * a_63 * a_65 * b_6 + - 30 * a_32 * a_53 * a_64 * a_65 * b_6 + - 30 * a_32 * a_53 * a_65^2 * b_6 + - 30 * a_41 * a_54 * a_61 * a_65 * b_6 + - 30 * a_41 * a_54 * a_62 * a_65 * b_6 + - 30 * a_41 * a_54 * a_63 * a_65 * b_6 + - 30 * a_41 * a_54 * a_64 * a_65 * b_6 + - 30 * a_41 * a_54 * a_65^2 * b_6 + - 30 * a_42 * a_54 * a_61 * a_65 * b_6 + - 30 * a_42 * a_54 * a_62 * a_65 * b_6 + - 30 * a_42 * a_54 * a_63 * a_65 * b_6 + - 30 * a_42 * a_54 * a_64 * a_65 * b_6 + - 30 * a_42 * a_54 * a_65^2 * b_6 + - 30 * a_43 * a_54 * a_61 * a_65 * b_6 + - 30 * a_43 * a_54 * a_62 * a_65 * b_6 + - 30 * a_43 * a_54 * a_63 * a_65 * b_6 + - 30 * a_43 * a_54 * a_64 * a_65 * b_6 + - 30 * a_43 * a_54 * a_65^2 * b_6 - 1, - 20 * a_21^3 * a_32 * b_3 + - 20 * a_21^3 * a_42 * b_4 + - 20 * a_21^3 * a_52 * b_5 + - 20 * a_21^3 * a_62 * b_6 + - 20 * a_31^3 * a_43 * b_4 + - 20 * a_31^3 * a_53 * b_5 + - 20 * a_31^3 * a_63 * b_6 + - 60 * a_31^2 * a_32 * a_43 * b_4 + - 60 * a_31^2 * a_32 * a_53 * b_5 + - 60 * a_31^2 * a_32 * a_63 * b_6 + - 60 * a_31 * a_32^2 * a_43 * b_4 + - 60 * a_31 * a_32^2 * a_53 * b_5 + - 60 * a_31 * a_32^2 * a_63 * b_6 + - 20 * a_32^3 * a_43 * b_4 + - 20 * a_32^3 * a_53 * b_5 + - 20 * a_32^3 * a_63 * b_6 + - 20 * a_41^3 * a_54 * b_5 + - 20 * a_41^3 * a_64 * b_6 + - 60 * a_41^2 * a_42 * a_54 * b_5 + - 60 * a_41^2 * a_42 * a_64 * b_6 + - 60 * a_41^2 * a_43 * a_54 * b_5 + - 60 * a_41^2 * a_43 * a_64 * b_6 + - 60 * a_41 * a_42^2 * a_54 * b_5 + - 60 * a_41 * a_42^2 * a_64 * b_6 + - 120 * a_41 * a_42 * a_43 * a_54 * b_5 + - 120 * a_41 * a_42 * a_43 * a_64 * b_6 + - 60 * a_41 * a_43^2 * a_54 * b_5 + - 60 * a_41 * a_43^2 * a_64 * b_6 + - 20 * a_42^3 * a_54 * b_5 + - 20 * a_42^3 * a_64 * b_6 + - 60 * a_42^2 * a_43 * a_54 * b_5 + - 60 * a_42^2 * a_43 * a_64 * b_6 + - 60 * a_42 * a_43^2 * a_54 * b_5 + - 60 * a_42 * a_43^2 * a_64 * b_6 + - 20 * a_43^3 * a_54 * b_5 + - 20 * a_43^3 * a_64 * b_6 + - 20 * a_51^3 * a_65 * b_6 + - 60 * a_51^2 * a_52 * a_65 * b_6 + - 60 * a_51^2 * a_53 * a_65 * b_6 + - 60 * a_51^2 * a_54 * a_65 * b_6 + - 60 * a_51 * a_52^2 * a_65 * b_6 + - 120 * a_51 * a_52 * a_53 * a_65 * b_6 + - 120 * a_51 * a_52 * a_54 * a_65 * b_6 + - 60 * a_51 * a_53^2 * a_65 * b_6 + - 120 * a_51 * a_53 * a_54 * a_65 * b_6 + - 60 * a_51 * a_54^2 * a_65 * b_6 + - 20 * a_52^3 * a_65 * b_6 + - 60 * a_52^2 * a_53 * a_65 * b_6 + - 60 * a_52^2 * a_54 * a_65 * b_6 + - 60 * a_52 * a_53^2 * a_65 * b_6 + - 120 * a_52 * a_53 * a_54 * a_65 * b_6 + - 60 * a_52 * a_54^2 * a_65 * b_6 + - 20 * a_53^3 * a_65 * b_6 + - 60 * a_53^2 * a_54 * a_65 * b_6 + - 60 * a_53 * a_54^2 * a_65 * b_6 + - 20 * a_54^3 * a_65 * b_6 - 1, - 15 * a_21^2 * a_31 * a_32 * b_3 + - 15 * a_21^2 * a_32^2 * b_3 + - 15 * a_21^2 * a_41 * a_42 * b_4 + - 15 * a_21^2 * a_42^2 * b_4 + - 15 * a_21^2 * a_42 * a_43 * b_4 + - 15 * a_21^2 * a_51 * a_52 * b_5 + - 15 * a_21^2 * a_52^2 * b_5 + - 15 * a_21^2 * a_52 * a_53 * b_5 + - 15 * a_21^2 * a_52 * a_54 * b_5 + - 15 * a_21^2 * a_61 * a_62 * b_6 + - 15 * a_21^2 * a_62^2 * b_6 + - 15 * a_21^2 * a_62 * a_63 * b_6 + - 15 * a_21^2 * a_62 * a_64 * b_6 + - 15 * a_21^2 * a_62 * a_65 * b_6 + - 15 * a_31^2 * a_41 * a_43 * b_4 + - 15 * a_31^2 * a_42 * a_43 * b_4 + - 15 * a_31^2 * a_43^2 * b_4 + - 15 * a_31^2 * a_51 * a_53 * b_5 + - 15 * a_31^2 * a_52 * a_53 * b_5 + - 15 * a_31^2 * a_53^2 * b_5 + - 15 * a_31^2 * a_53 * a_54 * b_5 + - 15 * a_31^2 * a_61 * a_63 * b_6 + - 15 * a_31^2 * a_62 * a_63 * b_6 + - 15 * a_31^2 * a_63^2 * b_6 + - 15 * a_31^2 * a_63 * a_64 * b_6 + - 15 * a_31^2 * a_63 * a_65 * b_6 + - 30 * a_31 * a_32 * a_41 * a_43 * b_4 + - 30 * a_31 * a_32 * a_42 * a_43 * b_4 + - 30 * a_31 * a_32 * a_43^2 * b_4 + - 30 * a_31 * a_32 * a_51 * a_53 * b_5 + - 30 * a_31 * a_32 * a_52 * a_53 * b_5 + - 30 * a_31 * a_32 * a_53^2 * b_5 + - 30 * a_31 * a_32 * a_53 * a_54 * b_5 + - 30 * a_31 * a_32 * a_61 * a_63 * b_6 + - 30 * a_31 * a_32 * a_62 * a_63 * b_6 + - 30 * a_31 * a_32 * a_63^2 * b_6 + - 30 * a_31 * a_32 * a_63 * a_64 * b_6 + - 30 * a_31 * a_32 * a_63 * a_65 * b_6 + - 15 * a_32^2 * a_41 * a_43 * b_4 + - 15 * a_32^2 * a_42 * a_43 * b_4 + - 15 * a_32^2 * a_43^2 * b_4 + - 15 * a_32^2 * a_51 * a_53 * b_5 + - 15 * a_32^2 * a_52 * a_53 * b_5 + - 15 * a_32^2 * a_53^2 * b_5 + - 15 * a_32^2 * a_53 * a_54 * b_5 + - 15 * a_32^2 * a_61 * a_63 * b_6 + - 15 * a_32^2 * a_62 * a_63 * b_6 + - 15 * a_32^2 * a_63^2 * b_6 + - 15 * a_32^2 * a_63 * a_64 * b_6 + - 15 * a_32^2 * a_63 * a_65 * b_6 + - 15 * a_41^2 * a_51 * a_54 * b_5 + - 15 * a_41^2 * a_52 * a_54 * b_5 + - 15 * a_41^2 * a_53 * a_54 * b_5 + - 15 * a_41^2 * a_54^2 * b_5 + - 15 * a_41^2 * a_61 * a_64 * b_6 + - 15 * a_41^2 * a_62 * a_64 * b_6 + - 15 * a_41^2 * a_63 * a_64 * b_6 + - 15 * a_41^2 * a_64^2 * b_6 + - 15 * a_41^2 * a_64 * a_65 * b_6 + - 30 * a_41 * a_42 * a_51 * a_54 * b_5 + - 30 * a_41 * a_42 * a_52 * a_54 * b_5 + - 30 * a_41 * a_42 * a_53 * a_54 * b_5 + - 30 * a_41 * a_42 * a_54^2 * b_5 + - 30 * a_41 * a_42 * a_61 * a_64 * b_6 + - 30 * a_41 * a_42 * a_62 * a_64 * b_6 + - 30 * a_41 * a_42 * a_63 * a_64 * b_6 + - 30 * a_41 * a_42 * a_64^2 * b_6 + - 30 * a_41 * a_42 * a_64 * a_65 * b_6 + - 30 * a_41 * a_43 * a_51 * a_54 * b_5 + - 30 * a_41 * a_43 * a_52 * a_54 * b_5 + - 30 * a_41 * a_43 * a_53 * a_54 * b_5 + - 30 * a_41 * a_43 * a_54^2 * b_5 + - 30 * a_41 * a_43 * a_61 * a_64 * b_6 + - 30 * a_41 * a_43 * a_62 * a_64 * b_6 + - 30 * a_41 * a_43 * a_63 * a_64 * b_6 + - 30 * a_41 * a_43 * a_64^2 * b_6 + - 30 * a_41 * a_43 * a_64 * a_65 * b_6 + - 15 * a_42^2 * a_51 * a_54 * b_5 + - 15 * a_42^2 * a_52 * a_54 * b_5 + - 15 * a_42^2 * a_53 * a_54 * b_5 + - 15 * a_42^2 * a_54^2 * b_5 + - 15 * a_42^2 * a_61 * a_64 * b_6 + - 15 * a_42^2 * a_62 * a_64 * b_6 + - 15 * a_42^2 * a_63 * a_64 * b_6 + - 15 * a_42^2 * a_64^2 * b_6 + - 15 * a_42^2 * a_64 * a_65 * b_6 + - 30 * a_42 * a_43 * a_51 * a_54 * b_5 + - 30 * a_42 * a_43 * a_52 * a_54 * b_5 + - 30 * a_42 * a_43 * a_53 * a_54 * b_5 + - 30 * a_42 * a_43 * a_54^2 * b_5 + - 30 * a_42 * a_43 * a_61 * a_64 * b_6 + - 30 * a_42 * a_43 * a_62 * a_64 * b_6 + - 30 * a_42 * a_43 * a_63 * a_64 * b_6 + - 30 * a_42 * a_43 * a_64^2 * b_6 + - 30 * a_42 * a_43 * a_64 * a_65 * b_6 + - 15 * a_43^2 * a_51 * a_54 * b_5 + - 15 * a_43^2 * a_52 * a_54 * b_5 + - 15 * a_43^2 * a_53 * a_54 * b_5 + - 15 * a_43^2 * a_54^2 * b_5 + - 15 * a_43^2 * a_61 * a_64 * b_6 + - 15 * a_43^2 * a_62 * a_64 * b_6 + - 15 * a_43^2 * a_63 * a_64 * b_6 + - 15 * a_43^2 * a_64^2 * b_6 + - 15 * a_43^2 * a_64 * a_65 * b_6 + - 15 * a_51^2 * a_61 * a_65 * b_6 + - 15 * a_51^2 * a_62 * a_65 * b_6 + - 15 * a_51^2 * a_63 * a_65 * b_6 + - 15 * a_51^2 * a_64 * a_65 * b_6 + - 15 * a_51^2 * a_65^2 * b_6 + - 30 * a_51 * a_52 * a_61 * a_65 * b_6 + - 30 * a_51 * a_52 * a_62 * a_65 * b_6 + - 30 * a_51 * a_52 * a_63 * a_65 * b_6 + - 30 * a_51 * a_52 * a_64 * a_65 * b_6 + - 30 * a_51 * a_52 * a_65^2 * b_6 + - 30 * a_51 * a_53 * a_61 * a_65 * b_6 + - 30 * a_51 * a_53 * a_62 * a_65 * b_6 + - 30 * a_51 * a_53 * a_63 * a_65 * b_6 + - 30 * a_51 * a_53 * a_64 * a_65 * b_6 + - 30 * a_51 * a_53 * a_65^2 * b_6 + - 30 * a_51 * a_54 * a_61 * a_65 * b_6 + - 30 * a_51 * a_54 * a_62 * a_65 * b_6 + - 30 * a_51 * a_54 * a_63 * a_65 * b_6 + - 30 * a_51 * a_54 * a_64 * a_65 * b_6 + - 30 * a_51 * a_54 * a_65^2 * b_6 + - 15 * a_52^2 * a_61 * a_65 * b_6 + - 15 * a_52^2 * a_62 * a_65 * b_6 + - 15 * a_52^2 * a_63 * a_65 * b_6 + - 15 * a_52^2 * a_64 * a_65 * b_6 + - 15 * a_52^2 * a_65^2 * b_6 + - 30 * a_52 * a_53 * a_61 * a_65 * b_6 + - 30 * a_52 * a_53 * a_62 * a_65 * b_6 + - 30 * a_52 * a_53 * a_63 * a_65 * b_6 + - 30 * a_52 * a_53 * a_64 * a_65 * b_6 + - 30 * a_52 * a_53 * a_65^2 * b_6 + - 30 * a_52 * a_54 * a_61 * a_65 * b_6 + - 30 * a_52 * a_54 * a_62 * a_65 * b_6 + - 30 * a_52 * a_54 * a_63 * a_65 * b_6 + - 30 * a_52 * a_54 * a_64 * a_65 * b_6 + - 30 * a_52 * a_54 * a_65^2 * b_6 + - 15 * a_53^2 * a_61 * a_65 * b_6 + - 15 * a_53^2 * a_62 * a_65 * b_6 + - 15 * a_53^2 * a_63 * a_65 * b_6 + - 15 * a_53^2 * a_64 * a_65 * b_6 + - 15 * a_53^2 * a_65^2 * b_6 + - 30 * a_53 * a_54 * a_61 * a_65 * b_6 + - 30 * a_53 * a_54 * a_62 * a_65 * b_6 + - 30 * a_53 * a_54 * a_63 * a_65 * b_6 + - 30 * a_53 * a_54 * a_64 * a_65 * b_6 + - 30 * a_53 * a_54 * a_65^2 * b_6 + - 15 * a_54^2 * a_61 * a_65 * b_6 + - 15 * a_54^2 * a_62 * a_65 * b_6 + - 15 * a_54^2 * a_63 * a_65 * b_6 + - 15 * a_54^2 * a_64 * a_65 * b_6 + - 15 * a_54^2 * a_65^2 * b_6 - 1, - 20 * a_21^2 * a_32^2 * b_3 + - 20 * a_21^2 * a_42^2 * b_4 + - 20 * a_21^2 * a_52^2 * b_5 + - 20 * a_21^2 * a_62^2 * b_6 + - 40 * a_21 * a_31 * a_42 * a_43 * b_4 + - 40 * a_21 * a_31 * a_52 * a_53 * b_5 + - 40 * a_21 * a_31 * a_62 * a_63 * b_6 + - 40 * a_21 * a_32 * a_42 * a_43 * b_4 + - 40 * a_21 * a_32 * a_52 * a_53 * b_5 + - 40 * a_21 * a_32 * a_62 * a_63 * b_6 + - 40 * a_21 * a_41 * a_52 * a_54 * b_5 + - 40 * a_21 * a_41 * a_62 * a_64 * b_6 + - 40 * a_21 * a_42 * a_52 * a_54 * b_5 + - 40 * a_21 * a_42 * a_62 * a_64 * b_6 + - 40 * a_21 * a_43 * a_52 * a_54 * b_5 + - 40 * a_21 * a_43 * a_62 * a_64 * b_6 + - 40 * a_21 * a_51 * a_62 * a_65 * b_6 + - 40 * a_21 * a_52 * a_62 * a_65 * b_6 + - 40 * a_21 * a_53 * a_62 * a_65 * b_6 + - 40 * a_21 * a_54 * a_62 * a_65 * b_6 + - 20 * a_31^2 * a_43^2 * b_4 + - 20 * a_31^2 * a_53^2 * b_5 + - 20 * a_31^2 * a_63^2 * b_6 + - 40 * a_31 * a_32 * a_43^2 * b_4 + - 40 * a_31 * a_32 * a_53^2 * b_5 + - 40 * a_31 * a_32 * a_63^2 * b_6 + - 40 * a_31 * a_41 * a_53 * a_54 * b_5 + - 40 * a_31 * a_41 * a_63 * a_64 * b_6 + - 40 * a_31 * a_42 * a_53 * a_54 * b_5 + - 40 * a_31 * a_42 * a_63 * a_64 * b_6 + - 40 * a_31 * a_43 * a_53 * a_54 * b_5 + - 40 * a_31 * a_43 * a_63 * a_64 * b_6 + - 40 * a_31 * a_51 * a_63 * a_65 * b_6 + - 40 * a_31 * a_52 * a_63 * a_65 * b_6 + - 40 * a_31 * a_53 * a_63 * a_65 * b_6 + - 40 * a_31 * a_54 * a_63 * a_65 * b_6 + - 20 * a_32^2 * a_43^2 * b_4 + - 20 * a_32^2 * a_53^2 * b_5 + - 20 * a_32^2 * a_63^2 * b_6 + - 40 * a_32 * a_41 * a_53 * a_54 * b_5 + - 40 * a_32 * a_41 * a_63 * a_64 * b_6 + - 40 * a_32 * a_42 * a_53 * a_54 * b_5 + - 40 * a_32 * a_42 * a_63 * a_64 * b_6 + - 40 * a_32 * a_43 * a_53 * a_54 * b_5 + - 40 * a_32 * a_43 * a_63 * a_64 * b_6 + - 40 * a_32 * a_51 * a_63 * a_65 * b_6 + - 40 * a_32 * a_52 * a_63 * a_65 * b_6 + - 40 * a_32 * a_53 * a_63 * a_65 * b_6 + - 40 * a_32 * a_54 * a_63 * a_65 * b_6 + - 20 * a_41^2 * a_54^2 * b_5 + - 20 * a_41^2 * a_64^2 * b_6 + - 40 * a_41 * a_42 * a_54^2 * b_5 + - 40 * a_41 * a_42 * a_64^2 * b_6 + - 40 * a_41 * a_43 * a_54^2 * b_5 + - 40 * a_41 * a_43 * a_64^2 * b_6 + - 40 * a_41 * a_51 * a_64 * a_65 * b_6 + - 40 * a_41 * a_52 * a_64 * a_65 * b_6 + - 40 * a_41 * a_53 * a_64 * a_65 * b_6 + - 40 * a_41 * a_54 * a_64 * a_65 * b_6 + - 20 * a_42^2 * a_54^2 * b_5 + - 20 * a_42^2 * a_64^2 * b_6 + - 40 * a_42 * a_43 * a_54^2 * b_5 + - 40 * a_42 * a_43 * a_64^2 * b_6 + - 40 * a_42 * a_51 * a_64 * a_65 * b_6 + - 40 * a_42 * a_52 * a_64 * a_65 * b_6 + - 40 * a_42 * a_53 * a_64 * a_65 * b_6 + - 40 * a_42 * a_54 * a_64 * a_65 * b_6 + - 20 * a_43^2 * a_54^2 * b_5 + - 20 * a_43^2 * a_64^2 * b_6 + - 40 * a_43 * a_51 * a_64 * a_65 * b_6 + - 40 * a_43 * a_52 * a_64 * a_65 * b_6 + - 40 * a_43 * a_53 * a_64 * a_65 * b_6 + - 40 * a_43 * a_54 * a_64 * a_65 * b_6 + - 20 * a_51^2 * a_65^2 * b_6 + - 40 * a_51 * a_52 * a_65^2 * b_6 + - 40 * a_51 * a_53 * a_65^2 * b_6 + - 40 * a_51 * a_54 * a_65^2 * b_6 + - 20 * a_52^2 * a_65^2 * b_6 + - 40 * a_52 * a_53 * a_65^2 * b_6 + - 40 * a_52 * a_54 * a_65^2 * b_6 + - 20 * a_53^2 * a_65^2 * b_6 + - 40 * a_53 * a_54 * a_65^2 * b_6 + - 20 * a_54^2 * a_65^2 * b_6 - 1, - 10 * a_21 * a_31^2 * a_32 * b_3 + - 20 * a_21 * a_31 * a_32^2 * b_3 + - 10 * a_21 * a_32^3 * b_3 + - 10 * a_21 * a_41^2 * a_42 * b_4 + - 20 * a_21 * a_41 * a_42^2 * b_4 + - 20 * a_21 * a_41 * a_42 * a_43 * b_4 + - 10 * a_21 * a_42^3 * b_4 + - 20 * a_21 * a_42^2 * a_43 * b_4 + - 10 * a_21 * a_42 * a_43^2 * b_4 + - 10 * a_21 * a_51^2 * a_52 * b_5 + - 20 * a_21 * a_51 * a_52^2 * b_5 + - 20 * a_21 * 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20 * a_54 * a_63 * a_64 * a_65 * b_6 + - 20 * a_54 * a_63 * a_65^2 * b_6 + - 10 * a_54 * a_64^2 * a_65 * b_6 + - 20 * a_54 * a_64 * a_65^2 * b_6 + - 10 * a_54 * a_65^3 * b_6 - 1, - 5 * a_21^4 * b_2 + - 5 * a_31^4 * b_3 + - 20 * a_31^3 * a_32 * b_3 + - 30 * a_31^2 * a_32^2 * b_3 + - 20 * a_31 * a_32^3 * b_3 + - 5 * a_32^4 * b_3 + - 5 * a_41^4 * b_4 + - 20 * a_41^3 * a_42 * b_4 + - 20 * a_41^3 * a_43 * b_4 + - 30 * a_41^2 * a_42^2 * b_4 + - 60 * a_41^2 * a_42 * a_43 * b_4 + - 30 * a_41^2 * a_43^2 * b_4 + - 20 * a_41 * a_42^3 * b_4 + - 60 * a_41 * a_42^2 * a_43 * b_4 + - 60 * a_41 * a_42 * a_43^2 * b_4 + - 20 * a_41 * a_43^3 * b_4 + - 5 * a_42^4 * b_4 + - 20 * a_42^3 * a_43 * b_4 + - 30 * a_42^2 * a_43^2 * b_4 + - 20 * a_42 * a_43^3 * b_4 + - 5 * a_43^4 * b_4 + - 5 * a_51^4 * b_5 + - 20 * a_51^3 * a_52 * b_5 + - 20 * a_51^3 * a_53 * b_5 + - 20 * a_51^3 * a_54 * b_5 + - 30 * a_51^2 * a_52^2 * b_5 + - 60 * a_51^2 * a_52 * a_53 * b_5 + - 60 * a_51^2 * a_52 * a_54 * b_5 + - 30 * a_51^2 * a_53^2 * b_5 + - 60 * a_51^2 * a_53 * a_54 * b_5 + - 30 * a_51^2 * a_54^2 * b_5 + - 20 * a_51 * a_52^3 * b_5 + - 60 * a_51 * a_52^2 * a_53 * b_5 + - 60 * a_51 * a_52^2 * a_54 * b_5 + - 60 * a_51 * a_52 * a_53^2 * b_5 + - 120 * a_51 * a_52 * a_53 * a_54 * b_5 + - 60 * a_51 * a_52 * a_54^2 * b_5 + - 20 * a_51 * a_53^3 * b_5 + - 60 * a_51 * a_53^2 * a_54 * b_5 + - 60 * a_51 * a_53 * a_54^2 * b_5 + - 20 * a_51 * a_54^3 * b_5 + - 5 * a_52^4 * b_5 + - 20 * a_52^3 * a_53 * b_5 + - 20 * a_52^3 * a_54 * b_5 + - 30 * a_52^2 * a_53^2 * b_5 + - 60 * a_52^2 * a_53 * a_54 * b_5 + - 30 * a_52^2 * a_54^2 * b_5 + - 20 * a_52 * a_53^3 * b_5 + - 60 * a_52 * a_53^2 * a_54 * b_5 + - 60 * a_52 * a_53 * a_54^2 * b_5 + - 20 * a_52 * a_54^3 * b_5 + - 5 * a_53^4 * b_5 + - 20 * a_53^3 * a_54 * b_5 + - 30 * a_53^2 * a_54^2 * b_5 + - 20 * a_53 * a_54^3 * b_5 + - 5 * a_54^4 * b_5 + - 5 * a_61^4 * b_6 + - 20 * a_61^3 * a_62 * b_6 + - 20 * a_61^3 * a_63 * b_6 + - 20 * a_61^3 * a_64 * b_6 + - 20 * a_61^3 * a_65 * b_6 + - 30 * a_61^2 * a_62^2 * b_6 + - 60 * a_61^2 * a_62 * a_63 * b_6 + - 60 * a_61^2 * a_62 * a_64 * b_6 + - 60 * a_61^2 * a_62 * a_65 * b_6 + - 30 * a_61^2 * a_63^2 * b_6 + - 60 * a_61^2 * a_63 * a_64 * b_6 + - 60 * a_61^2 * a_63 * a_65 * b_6 + - 30 * a_61^2 * a_64^2 * b_6 + - 60 * a_61^2 * a_64 * a_65 * b_6 + - 30 * a_61^2 * a_65^2 * b_6 + - 20 * a_61 * a_62^3 * b_6 + - 60 * a_61 * a_62^2 * a_63 * b_6 + - 60 * a_61 * a_62^2 * a_64 * b_6 + - 60 * a_61 * a_62^2 * a_65 * b_6 + - 60 * a_61 * a_62 * a_63^2 * b_6 + - 120 * a_61 * a_62 * a_63 * a_64 * b_6 + - 120 * a_61 * a_62 * a_63 * a_65 * b_6 + - 60 * a_61 * a_62 * a_64^2 * b_6 + - 120 * a_61 * a_62 * a_64 * a_65 * b_6 + - 60 * a_61 * a_62 * a_65^2 * b_6 + - 20 * a_61 * a_63^3 * b_6 + - 60 * a_61 * a_63^2 * a_64 * b_6 + - 60 * a_61 * a_63^2 * a_65 * b_6 + - 60 * a_61 * a_63 * a_64^2 * b_6 + - 120 * a_61 * a_63 * a_64 * a_65 * b_6 + - 60 * a_61 * a_63 * a_65^2 * b_6 + - 20 * a_61 * a_64^3 * b_6 + - 60 * a_61 * a_64^2 * a_65 * b_6 + - 60 * a_61 * a_64 * a_65^2 * b_6 + - 20 * a_61 * a_65^3 * b_6 + - 5 * a_62^4 * b_6 + - 20 * a_62^3 * a_63 * b_6 + - 20 * a_62^3 * a_64 * b_6 + - 20 * a_62^3 * a_65 * b_6 + - 30 * a_62^2 * a_63^2 * b_6 + - 60 * a_62^2 * a_63 * a_64 * b_6 + - 60 * a_62^2 * a_63 * a_65 * b_6 + - 30 * a_62^2 * a_64^2 * b_6 + - 60 * a_62^2 * a_64 * a_65 * b_6 + - 30 * a_62^2 * a_65^2 * b_6 + - 20 * a_62 * a_63^3 * b_6 + - 60 * a_62 * a_63^2 * a_64 * b_6 + - 60 * a_62 * a_63^2 * a_65 * b_6 + - 60 * a_62 * a_63 * a_64^2 * b_6 + - 120 * a_62 * a_63 * a_64 * a_65 * b_6 + - 60 * a_62 * a_63 * a_65^2 * b_6 + - 20 * a_62 * a_64^3 * b_6 + - 60 * a_62 * a_64^2 * a_65 * b_6 + - 60 * a_62 * a_64 * a_65^2 * b_6 + - 20 * a_62 * a_65^3 * b_6 + - 5 * a_63^4 * b_6 + - 20 * a_63^3 * a_64 * b_6 + - 20 * a_63^3 * a_65 * b_6 + - 30 * a_63^2 * a_64^2 * b_6 + - 60 * a_63^2 * a_64 * a_65 * b_6 + - 30 * a_63^2 * a_65^2 * b_6 + - 20 * a_63 * a_64^3 * b_6 + - 60 * a_63 * a_64^2 * a_65 * b_6 + - 60 * a_63 * a_64 * a_65^2 * b_6 + - 20 * a_63 * a_65^3 * b_6 + - 5 * a_64^4 * b_6 + - 20 * a_64^3 * a_65 * b_6 + - 30 * a_64^2 * a_65^2 * b_6 + - 20 * a_64 * a_65^3 * b_6 + - 5 * a_65^4 * b_6 - 1, - 720 * a_21 * a_32 * a_43 * a_54 * a_65 * b_6 - 1, - 360 * a_21^2 * a_32 * a_43 * a_54 * b_5 + - 360 * a_21^2 * a_32 * a_43 * a_64 * b_6 + - 360 * a_21^2 * a_32 * a_53 * a_65 * b_6 + - 360 * a_21^2 * a_42 * a_54 * a_65 * b_6 + - 360 * a_31^2 * a_43 * a_54 * a_65 * b_6 + - 720 * a_31 * a_32 * a_43 * a_54 * a_65 * b_6 + - 360 * a_32^2 * a_43 * a_54 * a_65 * b_6 - 1, - 240 * a_21 * a_31 * a_32 * a_43 * a_54 * b_5 + - 240 * a_21 * a_31 * a_32 * a_43 * a_64 * b_6 + - 240 * a_21 * a_31 * a_32 * a_53 * a_65 * b_6 + - 240 * a_21 * a_32^2 * a_43 * a_54 * b_5 + - 240 * a_21 * a_32^2 * a_43 * a_64 * b_6 + - 240 * a_21 * a_32^2 * a_53 * a_65 * b_6 + - 240 * a_21 * a_41 * a_42 * a_54 * a_65 * b_6 + - 240 * a_21 * a_42^2 * a_54 * a_65 * b_6 + - 240 * a_21 * a_42 * a_43 * a_54 * a_65 * b_6 + - 240 * a_31 * a_41 * a_43 * a_54 * a_65 * b_6 + - 240 * a_31 * a_42 * a_43 * a_54 * a_65 * b_6 + - 240 * a_31 * a_43^2 * a_54 * a_65 * b_6 + - 240 * a_32 * a_41 * a_43 * a_54 * a_65 * b_6 + - 240 * a_32 * a_42 * a_43 * a_54 * a_65 * b_6 + - 240 * a_32 * a_43^2 * a_54 * a_65 * b_6 - 1, - 180 * a_21 * a_32 * a_41 * a_43 * a_54 * b_5 + - 180 * a_21 * a_32 * a_41 * a_43 * a_64 * b_6 + - 180 * a_21 * a_32 * a_42 * a_43 * a_54 * b_5 + - 180 * a_21 * a_32 * a_42 * a_43 * a_64 * b_6 + - 180 * a_21 * a_32 * a_43^2 * a_54 * b_5 + - 180 * a_21 * a_32 * a_43^2 * a_64 * b_6 + - 180 * a_21 * a_32 * a_51 * a_53 * a_65 * b_6 + - 180 * a_21 * a_32 * a_52 * a_53 * a_65 * b_6 + - 180 * a_21 * a_32 * a_53^2 * a_65 * b_6 + - 180 * a_21 * a_32 * a_53 * a_54 * a_65 * b_6 + - 180 * a_21 * a_42 * a_51 * a_54 * a_65 * b_6 + - 180 * a_21 * a_42 * a_52 * a_54 * a_65 * b_6 + - 180 * a_21 * a_42 * a_53 * a_54 * a_65 * b_6 + - 180 * a_21 * a_42 * a_54^2 * a_65 * b_6 + - 180 * a_31 * a_43 * a_51 * a_54 * a_65 * b_6 + - 180 * a_31 * a_43 * a_52 * a_54 * a_65 * b_6 + - 180 * a_31 * a_43 * a_53 * a_54 * a_65 * b_6 + - 180 * a_31 * a_43 * a_54^2 * a_65 * b_6 + - 180 * a_32 * a_43 * a_51 * a_54 * a_65 * b_6 + - 180 * a_32 * a_43 * a_52 * a_54 * a_65 * b_6 + - 180 * a_32 * a_43 * a_53 * a_54 * a_65 * b_6 + - 180 * a_32 * a_43 * a_54^2 * a_65 * b_6 - 1, - 144 * a_21 * a_32 * a_43 * a_51 * a_54 * b_5 + - 144 * a_21 * a_32 * a_43 * a_52 * a_54 * b_5 + - 144 * a_21 * a_32 * a_43 * a_53 * a_54 * b_5 + - 144 * a_21 * a_32 * a_43 * a_54^2 * b_5 + - 144 * a_21 * a_32 * a_43 * a_61 * a_64 * b_6 + - 144 * a_21 * a_32 * a_43 * a_62 * a_64 * b_6 + - 144 * a_21 * a_32 * a_43 * a_63 * a_64 * b_6 + - 144 * a_21 * a_32 * a_43 * a_64^2 * b_6 + - 144 * a_21 * a_32 * a_43 * a_64 * a_65 * b_6 + - 144 * a_21 * a_32 * a_53 * a_61 * a_65 * b_6 + - 144 * a_21 * a_32 * a_53 * a_62 * a_65 * b_6 + - 144 * a_21 * a_32 * a_53 * a_63 * a_65 * b_6 + - 144 * a_21 * a_32 * a_53 * a_64 * a_65 * b_6 + - 144 * a_21 * a_32 * a_53 * a_65^2 * b_6 + - 144 * a_21 * a_42 * a_54 * a_61 * a_65 * b_6 + - 144 * a_21 * a_42 * a_54 * a_62 * a_65 * b_6 + - 144 * a_21 * a_42 * a_54 * a_63 * a_65 * b_6 + - 144 * a_21 * a_42 * a_54 * a_64 * a_65 * b_6 + - 144 * a_21 * a_42 * a_54 * a_65^2 * b_6 + - 144 * a_31 * a_43 * a_54 * a_61 * a_65 * b_6 + - 144 * a_31 * a_43 * a_54 * a_62 * a_65 * b_6 + - 144 * a_31 * a_43 * a_54 * a_63 * a_65 * b_6 + - 144 * a_31 * a_43 * a_54 * a_64 * a_65 * b_6 + - 144 * a_31 * a_43 * a_54 * a_65^2 * b_6 + - 144 * a_32 * a_43 * a_54 * a_61 * a_65 * b_6 + - 144 * a_32 * a_43 * a_54 * a_62 * a_65 * b_6 + - 144 * a_32 * a_43 * a_54 * a_63 * a_65 * b_6 + - 144 * a_32 * a_43 * a_54 * a_64 * a_65 * b_6 + - 144 * a_32 * a_43 * a_54 * a_65^2 * b_6 - 1, - 120 * a_21^3 * a_32 * a_43 * b_4 + - 120 * a_21^3 * a_32 * a_53 * b_5 + - 120 * a_21^3 * a_32 * a_63 * b_6 + - 120 * a_21^3 * a_42 * a_54 * b_5 + - 120 * a_21^3 * a_42 * a_64 * b_6 + - 120 * a_21^3 * a_52 * a_65 * b_6 + - 120 * a_31^3 * a_43 * a_54 * b_5 + - 120 * a_31^3 * a_43 * a_64 * b_6 + - 120 * a_31^3 * a_53 * a_65 * b_6 + - 360 * a_31^2 * a_32 * a_43 * a_54 * b_5 + - 360 * a_31^2 * a_32 * a_43 * a_64 * b_6 + - 360 * a_31^2 * a_32 * a_53 * a_65 * b_6 + - 360 * a_31 * a_32^2 * a_43 * a_54 * b_5 + - 360 * a_31 * a_32^2 * a_43 * a_64 * b_6 + - 360 * a_31 * a_32^2 * a_53 * a_65 * b_6 + - 120 * a_32^3 * a_43 * a_54 * b_5 + - 120 * a_32^3 * a_43 * a_64 * b_6 + - 120 * a_32^3 * a_53 * a_65 * b_6 + - 120 * a_41^3 * a_54 * a_65 * b_6 + - 360 * a_41^2 * a_42 * a_54 * a_65 * b_6 + - 360 * a_41^2 * a_43 * a_54 * a_65 * b_6 + - 360 * a_41 * a_42^2 * a_54 * a_65 * b_6 + - 720 * a_41 * a_42 * a_43 * a_54 * a_65 * b_6 + - 360 * a_41 * a_43^2 * a_54 * a_65 * b_6 + - 120 * a_42^3 * a_54 * a_65 * b_6 + - 360 * a_42^2 * a_43 * a_54 * a_65 * b_6 + - 360 * a_42 * a_43^2 * a_54 * a_65 * b_6 + - 120 * a_43^3 * a_54 * a_65 * b_6 - 1, - 90 * a_21^2 * a_31 * a_32 * a_43 * b_4 + - 90 * a_21^2 * a_31 * a_32 * a_53 * b_5 + - 90 * a_21^2 * a_31 * a_32 * a_63 * b_6 + - 90 * a_21^2 * a_32^2 * a_43 * b_4 + - 90 * a_21^2 * a_32^2 * a_53 * b_5 + - 90 * a_21^2 * a_32^2 * a_63 * b_6 + - 90 * a_21^2 * a_41 * a_42 * a_54 * b_5 + - 90 * a_21^2 * a_41 * a_42 * a_64 * b_6 + - 90 * a_21^2 * a_42^2 * a_54 * b_5 + - 90 * a_21^2 * a_42^2 * a_64 * b_6 + - 90 * a_21^2 * a_42 * a_43 * a_54 * b_5 + - 90 * a_21^2 * a_42 * a_43 * a_64 * b_6 + - 90 * a_21^2 * a_51 * a_52 * a_65 * b_6 + - 90 * a_21^2 * a_52^2 * a_65 * b_6 + - 90 * a_21^2 * a_52 * a_53 * a_65 * b_6 + - 90 * a_21^2 * a_52 * a_54 * a_65 * b_6 + - 90 * a_31^2 * a_41 * a_43 * a_54 * b_5 + - 90 * a_31^2 * a_41 * a_43 * a_64 * b_6 + - 90 * a_31^2 * a_42 * a_43 * a_54 * b_5 + - 90 * a_31^2 * a_42 * a_43 * a_64 * b_6 + - 90 * a_31^2 * a_43^2 * a_54 * b_5 + - 90 * a_31^2 * a_43^2 * a_64 * b_6 + - 90 * a_31^2 * a_51 * a_53 * a_65 * b_6 + - 90 * a_31^2 * a_52 * a_53 * a_65 * b_6 + - 90 * a_31^2 * a_53^2 * a_65 * b_6 + - 90 * a_31^2 * a_53 * a_54 * a_65 * b_6 + - 180 * a_31 * a_32 * a_41 * a_43 * a_54 * b_5 + - 180 * a_31 * a_32 * a_41 * a_43 * a_64 * b_6 + - 180 * a_31 * a_32 * a_42 * a_43 * a_54 * b_5 + - 180 * a_31 * a_32 * a_42 * a_43 * a_64 * b_6 + - 180 * a_31 * a_32 * a_43^2 * a_54 * b_5 + - 180 * a_31 * a_32 * a_43^2 * a_64 * b_6 + - 180 * a_31 * a_32 * a_51 * a_53 * a_65 * b_6 + - 180 * a_31 * a_32 * a_52 * a_53 * a_65 * b_6 + - 180 * a_31 * a_32 * a_53^2 * a_65 * b_6 + - 180 * a_31 * a_32 * a_53 * a_54 * a_65 * b_6 + - 90 * a_32^2 * a_41 * a_43 * a_54 * b_5 + - 90 * a_32^2 * a_41 * a_43 * a_64 * b_6 + - 90 * a_32^2 * a_42 * a_43 * a_54 * b_5 + - 90 * a_32^2 * a_42 * a_43 * a_64 * b_6 + - 90 * a_32^2 * a_43^2 * a_54 * b_5 + - 90 * a_32^2 * a_43^2 * a_64 * b_6 + - 90 * a_32^2 * a_51 * a_53 * a_65 * b_6 + - 90 * a_32^2 * a_52 * a_53 * a_65 * b_6 + - 90 * a_32^2 * a_53^2 * a_65 * b_6 + - 90 * a_32^2 * a_53 * a_54 * a_65 * b_6 + - 90 * a_41^2 * a_51 * a_54 * a_65 * b_6 + - 90 * a_41^2 * a_52 * a_54 * a_65 * b_6 + - 90 * a_41^2 * a_53 * a_54 * a_65 * b_6 + - 90 * a_41^2 * a_54^2 * a_65 * b_6 + - 180 * a_41 * a_42 * a_51 * a_54 * a_65 * b_6 + - 180 * a_41 * a_42 * a_52 * a_54 * a_65 * b_6 + - 180 * a_41 * a_42 * a_53 * a_54 * a_65 * b_6 + - 180 * a_41 * a_42 * a_54^2 * a_65 * b_6 + - 180 * a_41 * a_43 * a_51 * a_54 * a_65 * b_6 + - 180 * a_41 * a_43 * a_52 * a_54 * a_65 * b_6 + - 180 * a_41 * a_43 * a_53 * a_54 * a_65 * b_6 + - 180 * a_41 * a_43 * a_54^2 * a_65 * b_6 + - 90 * a_42^2 * a_51 * a_54 * a_65 * b_6 + - 90 * a_42^2 * a_52 * a_54 * a_65 * b_6 + - 90 * a_42^2 * a_53 * a_54 * a_65 * b_6 + - 90 * a_42^2 * a_54^2 * a_65 * b_6 + - 180 * a_42 * a_43 * a_51 * a_54 * a_65 * b_6 + - 180 * a_42 * a_43 * a_52 * a_54 * a_65 * b_6 + - 180 * a_42 * a_43 * a_53 * a_54 * a_65 * b_6 + - 180 * a_42 * a_43 * a_54^2 * a_65 * b_6 + - 90 * a_43^2 * a_51 * a_54 * a_65 * b_6 + - 90 * a_43^2 * a_52 * a_54 * a_65 * b_6 + - 90 * a_43^2 * a_53 * a_54 * a_65 * b_6 + - 90 * a_43^2 * a_54^2 * a_65 * b_6 - 1, - 72 * a_21^2 * a_32 * a_41 * a_43 * b_4 + - 72 * a_21^2 * a_32 * a_42 * a_43 * b_4 + - 72 * a_21^2 * a_32 * a_43^2 * b_4 + - 72 * a_21^2 * a_32 * a_51 * a_53 * b_5 + - 72 * a_21^2 * a_32 * a_52 * a_53 * b_5 + - 72 * a_21^2 * a_32 * a_53^2 * b_5 + - 72 * a_21^2 * a_32 * a_53 * a_54 * b_5 + - 72 * a_21^2 * a_32 * a_61 * a_63 * b_6 + - 72 * a_21^2 * a_32 * a_62 * a_63 * b_6 + - 72 * a_21^2 * a_32 * a_63^2 * b_6 + - 72 * a_21^2 * a_32 * a_63 * a_64 * b_6 + - 72 * a_21^2 * a_32 * a_63 * a_65 * b_6 + - 72 * a_21^2 * a_42 * a_51 * a_54 * b_5 + - 72 * a_21^2 * a_42 * a_52 * a_54 * b_5 + - 72 * a_21^2 * a_42 * a_53 * a_54 * b_5 + - 72 * a_21^2 * a_42 * a_54^2 * b_5 + - 72 * a_21^2 * a_42 * a_61 * a_64 * b_6 + - 72 * a_21^2 * a_42 * a_62 * a_64 * b_6 + - 72 * a_21^2 * a_42 * a_63 * a_64 * b_6 + - 72 * a_21^2 * a_42 * a_64^2 * b_6 + - 72 * a_21^2 * a_42 * a_64 * a_65 * b_6 + - 72 * a_21^2 * a_52 * a_61 * a_65 * b_6 + - 72 * a_21^2 * a_52 * a_62 * a_65 * b_6 + - 72 * a_21^2 * a_52 * a_63 * a_65 * b_6 + - 72 * a_21^2 * a_52 * a_64 * a_65 * b_6 + - 72 * a_21^2 * a_52 * a_65^2 * b_6 + - 72 * a_31^2 * a_43 * a_51 * a_54 * b_5 + - 72 * a_31^2 * a_43 * a_52 * a_54 * b_5 + - 72 * a_31^2 * a_43 * a_53 * a_54 * b_5 + - 72 * a_31^2 * a_43 * a_54^2 * b_5 + - 72 * a_31^2 * a_43 * a_61 * a_64 * b_6 + - 72 * a_31^2 * a_43 * a_62 * a_64 * b_6 + - 72 * a_31^2 * a_43 * a_63 * a_64 * b_6 + - 72 * a_31^2 * a_43 * a_64^2 * b_6 + - 72 * a_31^2 * a_43 * a_64 * a_65 * b_6 + - 72 * a_31^2 * a_53 * a_61 * a_65 * b_6 + - 72 * a_31^2 * a_53 * a_62 * a_65 * b_6 + - 72 * a_31^2 * a_53 * a_63 * a_65 * b_6 + - 72 * a_31^2 * a_53 * a_64 * a_65 * b_6 + - 72 * a_31^2 * a_53 * a_65^2 * b_6 + - 144 * a_31 * a_32 * a_43 * a_51 * a_54 * b_5 + - 144 * a_31 * a_32 * a_43 * a_52 * a_54 * b_5 + - 144 * a_31 * a_32 * a_43 * a_53 * a_54 * b_5 + - 144 * a_31 * a_32 * a_43 * a_54^2 * b_5 + - 144 * a_31 * a_32 * a_43 * a_61 * a_64 * b_6 + - 144 * a_31 * a_32 * a_43 * a_62 * a_64 * b_6 + - 144 * a_31 * a_32 * a_43 * a_63 * a_64 * b_6 + - 144 * a_31 * a_32 * a_43 * a_64^2 * b_6 + - 144 * a_31 * a_32 * a_43 * a_64 * a_65 * b_6 + - 144 * a_31 * a_32 * a_53 * a_61 * a_65 * b_6 + - 144 * a_31 * a_32 * a_53 * a_62 * a_65 * b_6 + - 144 * a_31 * a_32 * a_53 * a_63 * a_65 * b_6 + - 144 * a_31 * a_32 * a_53 * a_64 * a_65 * b_6 + - 144 * a_31 * a_32 * a_53 * a_65^2 * b_6 + - 72 * a_32^2 * a_43 * a_51 * a_54 * b_5 + - 72 * a_32^2 * a_43 * a_52 * a_54 * b_5 + - 72 * a_32^2 * a_43 * a_53 * a_54 * b_5 + - 72 * a_32^2 * a_43 * a_54^2 * b_5 + - 72 * a_32^2 * a_43 * a_61 * a_64 * b_6 + - 72 * a_32^2 * a_43 * a_62 * a_64 * b_6 + - 72 * a_32^2 * a_43 * a_63 * a_64 * b_6 + - 72 * a_32^2 * a_43 * a_64^2 * b_6 + - 72 * a_32^2 * a_43 * a_64 * a_65 * b_6 + - 72 * a_32^2 * a_53 * a_61 * a_65 * b_6 + - 72 * a_32^2 * a_53 * a_62 * a_65 * b_6 + - 72 * a_32^2 * a_53 * a_63 * a_65 * b_6 + - 72 * a_32^2 * a_53 * a_64 * a_65 * b_6 + - 72 * a_32^2 * a_53 * a_65^2 * b_6 + - 72 * a_41^2 * a_54 * a_61 * a_65 * b_6 + - 72 * a_41^2 * a_54 * a_62 * a_65 * b_6 + - 72 * a_41^2 * a_54 * a_63 * a_65 * b_6 + - 72 * a_41^2 * a_54 * a_64 * a_65 * b_6 + - 72 * a_41^2 * a_54 * a_65^2 * b_6 + - 144 * a_41 * a_42 * a_54 * a_61 * a_65 * b_6 + - 144 * a_41 * a_42 * a_54 * a_62 * a_65 * b_6 + - 144 * a_41 * a_42 * a_54 * a_63 * a_65 * b_6 + - 144 * a_41 * a_42 * a_54 * a_64 * a_65 * b_6 + - 144 * a_41 * a_42 * a_54 * a_65^2 * b_6 + - 144 * a_41 * a_43 * a_54 * a_61 * a_65 * b_6 + - 144 * a_41 * a_43 * a_54 * a_62 * a_65 * b_6 + - 144 * a_41 * a_43 * a_54 * a_63 * a_65 * b_6 + - 144 * a_41 * a_43 * a_54 * a_64 * a_65 * b_6 + - 144 * a_41 * a_43 * a_54 * a_65^2 * b_6 + - 72 * a_42^2 * a_54 * a_61 * a_65 * b_6 + - 72 * a_42^2 * a_54 * a_62 * a_65 * b_6 + - 72 * a_42^2 * a_54 * a_63 * a_65 * b_6 + - 72 * a_42^2 * a_54 * a_64 * a_65 * b_6 + - 72 * a_42^2 * a_54 * a_65^2 * b_6 + - 144 * a_42 * a_43 * a_54 * a_61 * a_65 * b_6 + - 144 * a_42 * a_43 * a_54 * a_62 * a_65 * b_6 + - 144 * a_42 * a_43 * a_54 * a_63 * a_65 * b_6 + - 144 * a_42 * a_43 * a_54 * a_64 * a_65 * b_6 + - 144 * a_42 * a_43 * a_54 * a_65^2 * b_6 + - 72 * a_43^2 * a_54 * a_61 * a_65 * b_6 + - 72 * a_43^2 * a_54 * a_62 * a_65 * b_6 + - 72 * a_43^2 * a_54 * a_63 * a_65 * b_6 + - 72 * a_43^2 * a_54 * a_64 * a_65 * b_6 + - 72 * a_43^2 * a_54 * a_65^2 * b_6 - 1, - 120 * a_21^2 * a_32^2 * a_43 * b_4 + - 120 * a_21^2 * a_32^2 * a_53 * b_5 + - 120 * a_21^2 * a_32^2 * a_63 * b_6 + - 120 * a_21^2 * a_42^2 * a_54 * b_5 + - 120 * a_21^2 * a_42^2 * a_64 * b_6 + - 120 * a_21^2 * a_52^2 * a_65 * b_6 + - 240 * a_21 * a_31 * a_42 * a_43 * a_54 * b_5 + - 240 * a_21 * a_31 * a_42 * a_43 * a_64 * b_6 + - 240 * a_21 * a_31 * a_52 * a_53 * a_65 * b_6 + - 240 * a_21 * a_32 * a_42 * a_43 * a_54 * b_5 + - 240 * a_21 * a_32 * a_42 * a_43 * a_64 * b_6 + - 240 * a_21 * a_32 * a_52 * a_53 * a_65 * b_6 + - 240 * a_21 * a_41 * a_52 * a_54 * a_65 * b_6 + - 240 * a_21 * a_42 * a_52 * a_54 * a_65 * b_6 + - 240 * a_21 * a_43 * a_52 * a_54 * a_65 * b_6 + - 120 * a_31^2 * a_43^2 * a_54 * b_5 + - 120 * a_31^2 * a_43^2 * a_64 * b_6 + - 120 * a_31^2 * a_53^2 * a_65 * b_6 + - 240 * a_31 * a_32 * a_43^2 * a_54 * b_5 + - 240 * a_31 * a_32 * a_43^2 * a_64 * b_6 + - 240 * a_31 * a_32 * a_53^2 * a_65 * b_6 + - 240 * a_31 * a_41 * a_53 * a_54 * a_65 * b_6 + - 240 * a_31 * a_42 * a_53 * a_54 * a_65 * b_6 + - 240 * a_31 * a_43 * a_53 * a_54 * a_65 * b_6 + - 120 * a_32^2 * a_43^2 * a_54 * b_5 + - 120 * a_32^2 * a_43^2 * a_64 * b_6 + - 120 * a_32^2 * a_53^2 * a_65 * b_6 + - 240 * a_32 * a_41 * a_53 * a_54 * a_65 * b_6 + - 240 * a_32 * a_42 * a_53 * a_54 * a_65 * b_6 + - 240 * a_32 * a_43 * a_53 * a_54 * a_65 * b_6 + - 120 * a_41^2 * a_54^2 * a_65 * b_6 + - 240 * a_41 * a_42 * a_54^2 * a_65 * b_6 + - 240 * a_41 * a_43 * a_54^2 * a_65 * b_6 + - 120 * a_42^2 * a_54^2 * a_65 * b_6 + - 240 * a_42 * a_43 * a_54^2 * a_65 * b_6 + - 120 * a_43^2 * a_54^2 * a_65 * b_6 - 1, - 60 * a_21 * a_31^2 * a_32 * a_43 * b_4 + - 60 * a_21 * a_31^2 * a_32 * a_53 * b_5 + - 60 * a_21 * a_31^2 * a_32 * a_63 * b_6 + - 120 * a_21 * a_31 * a_32^2 * a_43 * b_4 + - 120 * a_21 * a_31 * a_32^2 * a_53 * b_5 + - 120 * a_21 * a_31 * a_32^2 * a_63 * b_6 + - 60 * a_21 * a_32^3 * a_43 * b_4 + - 60 * a_21 * a_32^3 * a_53 * b_5 + - 60 * a_21 * a_32^3 * a_63 * b_6 + - 60 * a_21 * a_41^2 * a_42 * a_54 * b_5 + - 60 * a_21 * a_41^2 * a_42 * a_64 * b_6 + - 120 * a_21 * a_41 * a_42^2 * a_54 * b_5 + - 120 * a_21 * a_41 * a_42^2 * a_64 * b_6 + - 120 * a_21 * a_41 * a_42 * a_43 * a_54 * b_5 + - 120 * a_21 * a_41 * a_42 * a_43 * a_64 * b_6 + - 60 * a_21 * a_42^3 * a_54 * b_5 + - 60 * a_21 * a_42^3 * a_64 * b_6 + - 120 * a_21 * a_42^2 * a_43 * a_54 * b_5 + - 120 * a_21 * a_42^2 * a_43 * a_64 * b_6 + - 60 * a_21 * a_42 * a_43^2 * a_54 * b_5 + - 60 * a_21 * a_42 * a_43^2 * a_64 * b_6 + - 60 * a_21 * a_51^2 * a_52 * a_65 * b_6 + - 120 * a_21 * a_51 * a_52^2 * a_65 * b_6 + - 120 * a_21 * a_51 * a_52 * a_53 * a_65 * b_6 + - 120 * a_21 * a_51 * a_52 * a_54 * a_65 * b_6 + - 60 * a_21 * a_52^3 * a_65 * b_6 + - 120 * a_21 * a_52^2 * a_53 * a_65 * b_6 + - 120 * a_21 * a_52^2 * a_54 * a_65 * b_6 + - 60 * a_21 * a_52 * a_53^2 * a_65 * b_6 + - 120 * a_21 * a_52 * a_53 * a_54 * a_65 * b_6 + - 60 * a_21 * a_52 * a_54^2 * a_65 * b_6 + - 60 * a_31 * a_41^2 * a_43 * a_54 * b_5 + - 60 * a_31 * a_41^2 * a_43 * a_64 * b_6 + - 120 * a_31 * a_41 * a_42 * a_43 * a_54 * b_5 + - 120 * a_31 * a_41 * a_42 * a_43 * a_64 * b_6 + - 120 * a_31 * a_41 * a_43^2 * a_54 * b_5 + - 120 * a_31 * a_41 * a_43^2 * a_64 * b_6 + - 60 * a_31 * a_42^2 * a_43 * a_54 * b_5 + - 60 * a_31 * a_42^2 * a_43 * a_64 * b_6 + - 120 * a_31 * a_42 * a_43^2 * a_54 * b_5 + - 120 * a_31 * a_42 * a_43^2 * a_64 * b_6 + - 60 * a_31 * a_43^3 * a_54 * b_5 + - 60 * a_31 * a_43^3 * a_64 * b_6 + - 60 * a_31 * a_51^2 * a_53 * a_65 * b_6 + - 120 * a_31 * a_51 * a_52 * a_53 * a_65 * b_6 + - 120 * a_31 * a_51 * a_53^2 * a_65 * b_6 + - 120 * a_31 * a_51 * a_53 * a_54 * a_65 * b_6 + - 60 * a_31 * a_52^2 * a_53 * a_65 * b_6 + - 120 * a_31 * a_52 * a_53^2 * a_65 * b_6 + - 120 * a_31 * a_52 * a_53 * a_54 * a_65 * b_6 + - 60 * a_31 * a_53^3 * a_65 * b_6 + - 120 * a_31 * a_53^2 * a_54 * a_65 * b_6 + - 60 * a_31 * a_53 * a_54^2 * a_65 * b_6 + - 60 * a_32 * a_41^2 * a_43 * a_54 * b_5 + - 60 * a_32 * a_41^2 * a_43 * a_64 * b_6 + - 120 * a_32 * a_41 * a_42 * a_43 * a_54 * b_5 + - 120 * a_32 * a_41 * a_42 * a_43 * a_64 * b_6 + - 120 * a_32 * a_41 * a_43^2 * a_54 * b_5 + - 120 * a_32 * a_41 * a_43^2 * a_64 * b_6 + - 60 * a_32 * a_42^2 * a_43 * a_54 * b_5 + - 60 * a_32 * a_42^2 * a_43 * a_64 * b_6 + - 120 * a_32 * a_42 * a_43^2 * a_54 * b_5 + - 120 * a_32 * a_42 * a_43^2 * a_64 * b_6 + - 60 * a_32 * a_43^3 * a_54 * b_5 + - 60 * a_32 * a_43^3 * a_64 * b_6 + - 60 * a_32 * a_51^2 * a_53 * a_65 * b_6 + - 120 * a_32 * a_51 * a_52 * a_53 * a_65 * b_6 + - 120 * a_32 * a_51 * a_53^2 * a_65 * b_6 + - 120 * a_32 * a_51 * a_53 * a_54 * a_65 * b_6 + - 60 * a_32 * a_52^2 * a_53 * a_65 * b_6 + - 120 * a_32 * a_52 * a_53^2 * a_65 * b_6 + - 120 * a_32 * a_52 * a_53 * a_54 * a_65 * b_6 + - 60 * a_32 * a_53^3 * a_65 * b_6 + - 120 * a_32 * a_53^2 * a_54 * a_65 * b_6 + - 60 * a_32 * a_53 * a_54^2 * a_65 * b_6 + - 60 * a_41 * a_51^2 * a_54 * a_65 * b_6 + - 120 * a_41 * a_51 * a_52 * a_54 * a_65 * b_6 + - 120 * a_41 * a_51 * a_53 * a_54 * a_65 * b_6 + - 120 * a_41 * a_51 * a_54^2 * a_65 * b_6 + - 60 * a_41 * a_52^2 * a_54 * a_65 * b_6 + - 120 * a_41 * a_52 * a_53 * a_54 * a_65 * b_6 + - 120 * a_41 * a_52 * a_54^2 * a_65 * b_6 + - 60 * a_41 * a_53^2 * a_54 * a_65 * b_6 + - 120 * a_41 * a_53 * a_54^2 * a_65 * b_6 + - 60 * a_41 * a_54^3 * a_65 * b_6 + - 60 * a_42 * a_51^2 * a_54 * a_65 * b_6 + - 120 * a_42 * a_51 * a_52 * a_54 * a_65 * b_6 + - 120 * a_42 * a_51 * a_53 * a_54 * a_65 * b_6 + - 120 * a_42 * a_51 * a_54^2 * a_65 * b_6 + - 60 * a_42 * a_52^2 * a_54 * a_65 * b_6 + - 120 * a_42 * a_52 * a_53 * a_54 * a_65 * b_6 + - 120 * a_42 * a_52 * a_54^2 * a_65 * b_6 + - 60 * a_42 * a_53^2 * a_54 * a_65 * b_6 + - 120 * a_42 * a_53 * a_54^2 * a_65 * b_6 + - 60 * a_42 * a_54^3 * a_65 * b_6 + - 60 * a_43 * a_51^2 * a_54 * a_65 * b_6 + - 120 * a_43 * a_51 * a_52 * a_54 * a_65 * b_6 + - 120 * a_43 * a_51 * a_53 * a_54 * a_65 * b_6 + - 120 * a_43 * a_51 * a_54^2 * a_65 * b_6 + - 60 * a_43 * a_52^2 * a_54 * a_65 * b_6 + - 120 * a_43 * a_52 * a_53 * a_54 * a_65 * b_6 + - 120 * a_43 * a_52 * a_54^2 * a_65 * b_6 + - 60 * a_43 * a_53^2 * a_54 * a_65 * b_6 + - 120 * a_43 * a_53 * a_54^2 * a_65 * b_6 + - 60 * a_43 * a_54^3 * a_65 * b_6 - 1, - 48 * a_21 * a_31 * a_32 * a_41 * a_43 * b_4 + - 48 * a_21 * a_31 * a_32 * a_42 * a_43 * b_4 + - 48 * a_21 * a_31 * a_32 * a_43^2 * b_4 + - 48 * a_21 * a_31 * a_32 * a_51 * a_53 * b_5 + - 48 * a_21 * a_31 * a_32 * a_52 * a_53 * b_5 + - 48 * a_21 * a_31 * a_32 * a_53^2 * b_5 + - 48 * a_21 * a_31 * a_32 * a_53 * a_54 * b_5 + - 48 * a_21 * a_31 * a_32 * a_61 * a_63 * b_6 + - 48 * a_21 * a_31 * a_32 * a_62 * a_63 * b_6 + - 48 * a_21 * a_31 * a_32 * a_63^2 * b_6 + - 48 * a_21 * a_31 * a_32 * a_63 * a_64 * b_6 + - 48 * a_21 * a_31 * a_32 * a_63 * a_65 * b_6 + - 48 * a_21 * a_32^2 * a_41 * a_43 * b_4 + - 48 * a_21 * a_32^2 * a_42 * a_43 * b_4 + - 48 * a_21 * a_32^2 * a_43^2 * b_4 + - 48 * a_21 * a_32^2 * a_51 * a_53 * b_5 + - 48 * a_21 * a_32^2 * a_52 * a_53 * b_5 + - 48 * a_21 * a_32^2 * a_53^2 * b_5 + - 48 * a_21 * a_32^2 * a_53 * a_54 * b_5 + - 48 * a_21 * a_32^2 * a_61 * a_63 * b_6 + - 48 * a_21 * a_32^2 * a_62 * a_63 * b_6 + - 48 * a_21 * a_32^2 * a_63^2 * b_6 + - 48 * a_21 * a_32^2 * a_63 * a_64 * b_6 + - 48 * a_21 * a_32^2 * a_63 * a_65 * b_6 + - 48 * a_21 * a_41 * a_42 * a_51 * a_54 * b_5 + - 48 * a_21 * a_41 * a_42 * a_52 * a_54 * b_5 + - 48 * a_21 * a_41 * a_42 * a_53 * a_54 * b_5 + - 48 * a_21 * a_41 * a_42 * a_54^2 * b_5 + - 48 * a_21 * a_41 * a_42 * a_61 * a_64 * b_6 + - 48 * a_21 * a_41 * a_42 * a_62 * a_64 * b_6 + - 48 * a_21 * a_41 * a_42 * a_63 * a_64 * b_6 + - 48 * a_21 * a_41 * a_42 * a_64^2 * b_6 + - 48 * a_21 * a_41 * a_42 * a_64 * a_65 * b_6 + - 48 * a_21 * a_42^2 * a_51 * a_54 * b_5 + - 48 * a_21 * a_42^2 * a_52 * a_54 * b_5 + - 48 * a_21 * a_42^2 * a_53 * a_54 * b_5 + - 48 * a_21 * a_42^2 * a_54^2 * b_5 + - 48 * a_21 * a_42^2 * a_61 * a_64 * b_6 + - 48 * a_21 * a_42^2 * a_62 * a_64 * b_6 + - 48 * a_21 * a_42^2 * a_63 * a_64 * b_6 + - 48 * a_21 * a_42^2 * a_64^2 * b_6 + - 48 * a_21 * a_42^2 * a_64 * a_65 * b_6 + - 48 * a_21 * a_42 * a_43 * a_51 * a_54 * b_5 + - 48 * a_21 * a_42 * a_43 * a_52 * a_54 * b_5 + - 48 * a_21 * a_42 * a_43 * a_53 * a_54 * b_5 + - 48 * a_21 * a_42 * a_43 * a_54^2 * b_5 + - 48 * a_21 * a_42 * a_43 * a_61 * a_64 * b_6 + - 48 * a_21 * a_42 * a_43 * a_62 * a_64 * b_6 + - 48 * a_21 * a_42 * a_43 * a_63 * a_64 * b_6 + - 48 * a_21 * a_42 * a_43 * a_64^2 * b_6 + - 48 * a_21 * a_42 * a_43 * a_64 * a_65 * b_6 + - 48 * a_21 * a_51 * a_52 * a_61 * a_65 * b_6 + - 48 * a_21 * a_51 * a_52 * a_62 * a_65 * b_6 + - 48 * a_21 * a_51 * a_52 * a_63 * a_65 * b_6 + - 48 * a_21 * a_51 * a_52 * a_64 * a_65 * b_6 + - 48 * a_21 * a_51 * a_52 * a_65^2 * b_6 + - 48 * a_21 * a_52^2 * a_61 * a_65 * b_6 + - 48 * a_21 * a_52^2 * a_62 * a_65 * b_6 + - 48 * a_21 * a_52^2 * a_63 * a_65 * b_6 + - 48 * a_21 * a_52^2 * a_64 * a_65 * b_6 + - 48 * a_21 * a_52^2 * a_65^2 * b_6 + - 48 * a_21 * a_52 * a_53 * a_61 * a_65 * b_6 + - 48 * a_21 * a_52 * a_53 * a_62 * a_65 * b_6 + - 48 * a_21 * a_52 * a_53 * a_63 * a_65 * b_6 + - 48 * a_21 * a_52 * a_53 * a_64 * a_65 * b_6 + - 48 * a_21 * a_52 * a_53 * a_65^2 * b_6 + - 48 * a_21 * a_52 * a_54 * a_61 * a_65 * b_6 + - 48 * a_21 * a_52 * a_54 * a_62 * a_65 * b_6 + - 48 * a_21 * a_52 * a_54 * a_63 * a_65 * b_6 + - 48 * a_21 * a_52 * a_54 * a_64 * a_65 * b_6 + - 48 * a_21 * a_52 * a_54 * a_65^2 * b_6 + - 48 * a_31 * a_41 * a_43 * a_51 * a_54 * b_5 + - 48 * a_31 * a_41 * a_43 * a_52 * a_54 * b_5 + - 48 * a_31 * a_41 * a_43 * a_53 * a_54 * b_5 + - 48 * a_31 * a_41 * a_43 * a_54^2 * b_5 + - 48 * a_31 * a_41 * a_43 * a_61 * a_64 * b_6 + - 48 * a_31 * a_41 * a_43 * a_62 * a_64 * b_6 + - 48 * a_31 * a_41 * a_43 * a_63 * a_64 * b_6 + - 48 * a_31 * a_41 * a_43 * a_64^2 * b_6 + - 48 * a_31 * a_41 * a_43 * a_64 * a_65 * b_6 + - 48 * a_31 * a_42 * a_43 * a_51 * a_54 * b_5 + - 48 * a_31 * a_42 * a_43 * a_52 * a_54 * b_5 + - 48 * a_31 * a_42 * a_43 * a_53 * a_54 * b_5 + - 48 * a_31 * a_42 * a_43 * a_54^2 * b_5 + - 48 * a_31 * a_42 * a_43 * a_61 * a_64 * b_6 + - 48 * a_31 * a_42 * a_43 * a_62 * a_64 * b_6 + - 48 * a_31 * a_42 * a_43 * a_63 * a_64 * b_6 + - 48 * a_31 * a_42 * a_43 * a_64^2 * b_6 + - 48 * a_31 * a_42 * a_43 * a_64 * a_65 * b_6 + - 48 * a_31 * a_43^2 * a_51 * a_54 * b_5 + - 48 * a_31 * a_43^2 * a_52 * a_54 * b_5 + - 48 * a_31 * a_43^2 * a_53 * a_54 * b_5 + - 48 * a_31 * a_43^2 * a_54^2 * b_5 + - 48 * a_31 * a_43^2 * a_61 * a_64 * b_6 + - 48 * a_31 * a_43^2 * a_62 * a_64 * b_6 + - 48 * a_31 * a_43^2 * a_63 * a_64 * b_6 + - 48 * a_31 * a_43^2 * a_64^2 * b_6 + - 48 * a_31 * a_43^2 * a_64 * a_65 * b_6 + - 48 * a_31 * a_51 * a_53 * a_61 * a_65 * b_6 + - 48 * a_31 * a_51 * a_53 * a_62 * a_65 * b_6 + - 48 * a_31 * a_51 * a_53 * a_63 * a_65 * b_6 + - 48 * a_31 * a_51 * a_53 * a_64 * a_65 * b_6 + - 48 * a_31 * a_51 * a_53 * a_65^2 * b_6 + - 48 * a_31 * a_52 * a_53 * a_61 * a_65 * b_6 + - 48 * a_31 * a_52 * a_53 * a_62 * a_65 * b_6 + - 48 * a_31 * a_52 * a_53 * a_63 * a_65 * b_6 + - 48 * a_31 * a_52 * a_53 * a_64 * a_65 * b_6 + - 48 * a_31 * a_52 * a_53 * a_65^2 * b_6 + - 48 * a_31 * a_53^2 * a_61 * a_65 * b_6 + - 48 * a_31 * a_53^2 * a_62 * a_65 * b_6 + - 48 * a_31 * a_53^2 * a_63 * a_65 * b_6 + - 48 * a_31 * a_53^2 * a_64 * a_65 * b_6 + - 48 * a_31 * a_53^2 * a_65^2 * b_6 + - 48 * a_31 * a_53 * a_54 * a_61 * a_65 * b_6 + - 48 * a_31 * a_53 * a_54 * a_62 * a_65 * b_6 + - 48 * a_31 * a_53 * a_54 * a_63 * a_65 * b_6 + - 48 * a_31 * a_53 * a_54 * a_64 * a_65 * b_6 + - 48 * a_31 * a_53 * a_54 * a_65^2 * b_6 + - 48 * a_32 * a_41 * a_43 * a_51 * a_54 * b_5 + - 48 * a_32 * a_41 * a_43 * a_52 * a_54 * b_5 + - 48 * a_32 * a_41 * a_43 * a_53 * a_54 * b_5 + - 48 * a_32 * a_41 * a_43 * a_54^2 * b_5 + - 48 * a_32 * a_41 * a_43 * a_61 * a_64 * b_6 + - 48 * a_32 * a_41 * a_43 * a_62 * a_64 * b_6 + - 48 * a_32 * a_41 * a_43 * a_63 * a_64 * b_6 + - 48 * a_32 * a_41 * a_43 * a_64^2 * b_6 + - 48 * a_32 * a_41 * a_43 * a_64 * a_65 * b_6 + - 48 * a_32 * a_42 * a_43 * a_51 * a_54 * b_5 + - 48 * a_32 * a_42 * a_43 * a_52 * a_54 * b_5 + - 48 * a_32 * a_42 * a_43 * a_53 * a_54 * b_5 + - 48 * a_32 * a_42 * a_43 * a_54^2 * b_5 + - 48 * a_32 * a_42 * a_43 * a_61 * a_64 * b_6 + - 48 * a_32 * a_42 * a_43 * a_62 * a_64 * b_6 + - 48 * a_32 * a_42 * a_43 * a_63 * a_64 * b_6 + - 48 * a_32 * a_42 * a_43 * a_64^2 * b_6 + - 48 * a_32 * a_42 * a_43 * a_64 * a_65 * b_6 + - 48 * a_32 * a_43^2 * a_51 * a_54 * b_5 + - 48 * a_32 * a_43^2 * a_52 * a_54 * b_5 + - 48 * a_32 * a_43^2 * a_53 * a_54 * b_5 + - 48 * a_32 * a_43^2 * a_54^2 * b_5 + - 48 * a_32 * a_43^2 * a_61 * a_64 * b_6 + - 48 * a_32 * a_43^2 * a_62 * a_64 * b_6 + - 48 * a_32 * a_43^2 * a_63 * a_64 * b_6 + - 48 * a_32 * a_43^2 * a_64^2 * b_6 + - 48 * a_32 * a_43^2 * a_64 * a_65 * b_6 + - 48 * a_32 * a_51 * a_53 * a_61 * a_65 * b_6 + - 48 * a_32 * a_51 * a_53 * a_62 * a_65 * b_6 + - 48 * a_32 * a_51 * a_53 * a_63 * a_65 * b_6 + - 48 * a_32 * a_51 * a_53 * a_64 * a_65 * b_6 + - 48 * a_32 * a_51 * a_53 * a_65^2 * b_6 + - 48 * a_32 * a_52 * a_53 * a_61 * a_65 * b_6 + - 48 * a_32 * a_52 * a_53 * a_62 * a_65 * b_6 + - 48 * a_32 * a_52 * a_53 * a_63 * a_65 * b_6 + - 48 * a_32 * a_52 * a_53 * a_64 * a_65 * b_6 + - 48 * a_32 * a_52 * a_53 * a_65^2 * b_6 + - 48 * a_32 * a_53^2 * a_61 * a_65 * b_6 + - 48 * a_32 * a_53^2 * a_62 * a_65 * b_6 + - 48 * a_32 * a_53^2 * a_63 * a_65 * b_6 + - 48 * a_32 * a_53^2 * a_64 * a_65 * b_6 + - 48 * a_32 * a_53^2 * a_65^2 * b_6 + - 48 * a_32 * a_53 * a_54 * a_61 * a_65 * b_6 + - 48 * a_32 * a_53 * a_54 * a_62 * a_65 * b_6 + - 48 * a_32 * a_53 * a_54 * a_63 * a_65 * b_6 + - 48 * a_32 * a_53 * a_54 * a_64 * a_65 * b_6 + - 48 * a_32 * a_53 * a_54 * a_65^2 * b_6 + - 48 * a_41 * a_51 * a_54 * a_61 * a_65 * b_6 + - 48 * a_41 * a_51 * a_54 * a_62 * a_65 * b_6 + - 48 * a_41 * a_51 * a_54 * a_63 * a_65 * b_6 + - 48 * a_41 * a_51 * a_54 * a_64 * a_65 * b_6 + - 48 * a_41 * a_51 * a_54 * a_65^2 * b_6 + - 48 * a_41 * a_52 * a_54 * a_61 * a_65 * b_6 + - 48 * a_41 * a_52 * a_54 * a_62 * a_65 * b_6 + - 48 * a_41 * a_52 * a_54 * a_63 * a_65 * b_6 + - 48 * a_41 * a_52 * a_54 * a_64 * a_65 * b_6 + - 48 * a_41 * a_52 * a_54 * a_65^2 * b_6 + - 48 * a_41 * a_53 * a_54 * a_61 * a_65 * b_6 + - 48 * a_41 * a_53 * a_54 * a_62 * a_65 * b_6 + - 48 * a_41 * a_53 * a_54 * a_63 * a_65 * b_6 + - 48 * a_41 * a_53 * a_54 * a_64 * a_65 * b_6 + - 48 * a_41 * a_53 * a_54 * a_65^2 * b_6 + - 48 * a_41 * a_54^2 * a_61 * a_65 * b_6 + - 48 * a_41 * a_54^2 * a_62 * a_65 * b_6 + - 48 * a_41 * a_54^2 * a_63 * a_65 * b_6 + - 48 * a_41 * a_54^2 * a_64 * a_65 * b_6 + - 48 * a_41 * a_54^2 * a_65^2 * b_6 + - 48 * a_42 * a_51 * a_54 * a_61 * a_65 * b_6 + - 48 * a_42 * a_51 * a_54 * a_62 * a_65 * b_6 + - 48 * a_42 * a_51 * a_54 * a_63 * a_65 * b_6 + - 48 * a_42 * a_51 * a_54 * a_64 * a_65 * b_6 + - 48 * a_42 * a_51 * a_54 * a_65^2 * b_6 + - 48 * a_42 * a_52 * a_54 * a_61 * a_65 * b_6 + - 48 * a_42 * a_52 * a_54 * a_62 * a_65 * b_6 + - 48 * a_42 * a_52 * a_54 * a_63 * a_65 * b_6 + - 48 * a_42 * a_52 * a_54 * a_64 * a_65 * b_6 + - 48 * a_42 * a_52 * a_54 * a_65^2 * b_6 + - 48 * a_42 * a_53 * a_54 * a_61 * a_65 * b_6 + - 48 * a_42 * a_53 * a_54 * a_62 * a_65 * b_6 + - 48 * a_42 * a_53 * a_54 * a_63 * a_65 * b_6 + - 48 * a_42 * a_53 * a_54 * a_64 * a_65 * b_6 + - 48 * a_42 * a_53 * a_54 * a_65^2 * b_6 + - 48 * a_42 * a_54^2 * a_61 * a_65 * b_6 + - 48 * a_42 * a_54^2 * a_62 * a_65 * b_6 + - 48 * a_42 * a_54^2 * a_63 * a_65 * b_6 + - 48 * a_42 * a_54^2 * a_64 * a_65 * b_6 + - 48 * a_42 * a_54^2 * a_65^2 * b_6 + - 48 * a_43 * a_51 * a_54 * a_61 * a_65 * b_6 + - 48 * a_43 * a_51 * a_54 * a_62 * a_65 * b_6 + - 48 * a_43 * a_51 * a_54 * a_63 * a_65 * b_6 + - 48 * a_43 * a_51 * a_54 * a_64 * a_65 * b_6 + - 48 * a_43 * a_51 * a_54 * a_65^2 * b_6 + - 48 * a_43 * a_52 * a_54 * a_61 * a_65 * b_6 + - 48 * a_43 * a_52 * a_54 * a_62 * a_65 * b_6 + - 48 * a_43 * a_52 * a_54 * a_63 * a_65 * b_6 + - 48 * a_43 * a_52 * a_54 * a_64 * a_65 * b_6 + - 48 * a_43 * a_52 * a_54 * a_65^2 * b_6 + - 48 * a_43 * a_53 * a_54 * a_61 * a_65 * b_6 + - 48 * a_43 * a_53 * a_54 * a_62 * a_65 * b_6 + - 48 * a_43 * a_53 * a_54 * a_63 * a_65 * b_6 + - 48 * a_43 * a_53 * a_54 * a_64 * a_65 * b_6 + - 48 * a_43 * a_53 * a_54 * a_65^2 * b_6 + - 48 * a_43 * a_54^2 * a_61 * a_65 * b_6 + - 48 * a_43 * a_54^2 * a_62 * a_65 * b_6 + - 48 * a_43 * a_54^2 * a_63 * a_65 * b_6 + - 48 * a_43 * a_54^2 * a_64 * a_65 * b_6 + - 48 * a_43 * a_54^2 * a_65^2 * b_6 - 1, - 72 * a_21^2 * a_32 * a_42 * a_43 * b_4 + - 72 * a_21^2 * a_32 * a_52 * a_53 * b_5 + - 72 * a_21^2 * a_32 * a_62 * a_63 * b_6 + - 72 * a_21^2 * a_42 * a_52 * a_54 * b_5 + - 72 * a_21^2 * a_42 * a_62 * a_64 * b_6 + - 72 * a_21^2 * a_52 * a_62 * a_65 * b_6 + - 72 * a_21 * a_31 * a_32 * a_43^2 * b_4 + - 72 * a_21 * a_31 * a_32 * a_53^2 * b_5 + - 72 * a_21 * a_31 * a_32 * a_63^2 * b_6 + - 72 * a_21 * a_31 * a_42 * a_53 * a_54 * b_5 + - 72 * a_21 * a_31 * a_42 * a_63 * a_64 * b_6 + - 72 * a_21 * a_31 * a_43 * a_52 * a_54 * b_5 + - 72 * a_21 * a_31 * a_43 * a_62 * a_64 * b_6 + - 72 * a_21 * a_31 * a_52 * a_63 * a_65 * b_6 + - 72 * a_21 * a_31 * a_53 * a_62 * a_65 * b_6 + - 72 * a_21 * a_32^2 * a_43^2 * b_4 + - 72 * a_21 * a_32^2 * a_53^2 * b_5 + - 72 * a_21 * a_32^2 * a_63^2 * b_6 + - 72 * a_21 * a_32 * a_41 * a_53 * a_54 * b_5 + - 72 * a_21 * a_32 * a_41 * a_63 * a_64 * b_6 + - 144 * a_21 * a_32 * a_42 * a_53 * a_54 * b_5 + - 144 * a_21 * a_32 * a_42 * a_63 * a_64 * b_6 + - 72 * a_21 * a_32 * a_43 * a_52 * a_54 * b_5 + - 72 * a_21 * a_32 * a_43 * a_53 * a_54 * b_5 + - 72 * a_21 * a_32 * a_43 * a_62 * a_64 * b_6 + - 72 * a_21 * a_32 * a_43 * a_63 * a_64 * b_6 + - 72 * a_21 * a_32 * a_51 * a_63 * a_65 * b_6 + - 144 * a_21 * a_32 * a_52 * a_63 * a_65 * b_6 + - 72 * a_21 * a_32 * a_53 * a_62 * a_65 * b_6 + - 72 * a_21 * a_32 * a_53 * a_63 * a_65 * b_6 + - 72 * a_21 * a_32 * a_54 * a_63 * a_65 * b_6 + - 72 * a_21 * a_41 * a_42 * a_54^2 * b_5 + - 72 * a_21 * a_41 * a_42 * a_64^2 * b_6 + - 72 * a_21 * a_41 * a_52 * a_64 * a_65 * b_6 + - 72 * a_21 * a_41 * a_54 * a_62 * a_65 * b_6 + - 72 * a_21 * a_42^2 * a_54^2 * b_5 + - 72 * a_21 * a_42^2 * a_64^2 * b_6 + - 72 * a_21 * a_42 * a_43 * a_54^2 * b_5 + - 72 * a_21 * a_42 * a_43 * a_64^2 * b_6 + - 72 * a_21 * a_42 * a_51 * a_64 * a_65 * b_6 + - 144 * a_21 * a_42 * a_52 * a_64 * a_65 * b_6 + - 72 * a_21 * a_42 * a_53 * a_64 * a_65 * b_6 + - 72 * a_21 * a_42 * a_54 * a_62 * a_65 * b_6 + - 72 * a_21 * a_42 * a_54 * a_64 * a_65 * b_6 + - 72 * a_21 * a_43 * a_52 * a_64 * a_65 * b_6 + - 72 * a_21 * a_43 * a_54 * a_62 * a_65 * b_6 + - 72 * a_21 * a_51 * a_52 * a_65^2 * b_6 + - 72 * a_21 * a_52^2 * a_65^2 * b_6 + - 72 * a_21 * a_52 * a_53 * a_65^2 * b_6 + - 72 * a_21 * a_52 * a_54 * a_65^2 * b_6 + - 72 * a_31^2 * a_43 * a_53 * a_54 * b_5 + - 72 * a_31^2 * a_43 * a_63 * a_64 * b_6 + - 72 * a_31^2 * a_53 * a_63 * a_65 * b_6 + - 144 * a_31 * a_32 * a_43 * a_53 * a_54 * b_5 + - 144 * a_31 * a_32 * a_43 * a_63 * a_64 * b_6 + - 144 * a_31 * a_32 * a_53 * a_63 * a_65 * b_6 + - 72 * a_31 * a_41 * a_43 * a_54^2 * b_5 + - 72 * a_31 * a_41 * a_43 * a_64^2 * b_6 + - 72 * a_31 * a_41 * a_53 * a_64 * a_65 * b_6 + - 72 * a_31 * a_41 * a_54 * a_63 * a_65 * b_6 + - 72 * a_31 * a_42 * a_43 * a_54^2 * b_5 + - 72 * a_31 * a_42 * a_43 * a_64^2 * b_6 + - 72 * a_31 * a_42 * a_53 * a_64 * a_65 * b_6 + - 72 * a_31 * a_42 * a_54 * a_63 * a_65 * b_6 + - 72 * a_31 * a_43^2 * a_54^2 * b_5 + - 72 * a_31 * a_43^2 * a_64^2 * b_6 + - 72 * a_31 * a_43 * a_51 * a_64 * a_65 * b_6 + - 72 * a_31 * a_43 * a_52 * a_64 * a_65 * b_6 + - 144 * a_31 * a_43 * a_53 * a_64 * a_65 * b_6 + - 72 * a_31 * a_43 * a_54 * a_63 * a_65 * b_6 + - 72 * a_31 * a_43 * a_54 * a_64 * a_65 * b_6 + - 72 * a_31 * a_51 * a_53 * a_65^2 * b_6 + - 72 * a_31 * a_52 * a_53 * a_65^2 * b_6 + - 72 * a_31 * a_53^2 * a_65^2 * b_6 + - 72 * a_31 * a_53 * a_54 * a_65^2 * b_6 + - 72 * a_32^2 * a_43 * a_53 * a_54 * b_5 + - 72 * a_32^2 * a_43 * a_63 * a_64 * b_6 + - 72 * a_32^2 * a_53 * a_63 * a_65 * b_6 + - 72 * a_32 * a_41 * a_43 * a_54^2 * b_5 + - 72 * a_32 * a_41 * a_43 * a_64^2 * b_6 + - 72 * a_32 * a_41 * a_53 * a_64 * a_65 * b_6 + - 72 * a_32 * a_41 * a_54 * a_63 * a_65 * b_6 + - 72 * a_32 * a_42 * a_43 * a_54^2 * b_5 + - 72 * a_32 * a_42 * a_43 * a_64^2 * b_6 + - 72 * a_32 * a_42 * a_53 * a_64 * a_65 * b_6 + - 72 * a_32 * a_42 * a_54 * a_63 * a_65 * b_6 + - 72 * a_32 * a_43^2 * a_54^2 * b_5 + - 72 * a_32 * a_43^2 * a_64^2 * b_6 + - 72 * a_32 * a_43 * a_51 * a_64 * a_65 * b_6 + - 72 * a_32 * a_43 * a_52 * a_64 * a_65 * b_6 + - 144 * a_32 * a_43 * a_53 * a_64 * a_65 * b_6 + - 72 * a_32 * a_43 * a_54 * a_63 * a_65 * b_6 + - 72 * a_32 * a_43 * a_54 * a_64 * a_65 * b_6 + - 72 * a_32 * a_51 * a_53 * a_65^2 * b_6 + - 72 * a_32 * a_52 * a_53 * a_65^2 * b_6 + - 72 * a_32 * a_53^2 * a_65^2 * b_6 + - 72 * a_32 * a_53 * a_54 * a_65^2 * b_6 + - 72 * a_41^2 * a_54 * a_64 * a_65 * b_6 + - 144 * a_41 * a_42 * a_54 * a_64 * a_65 * b_6 + - 144 * a_41 * a_43 * a_54 * a_64 * a_65 * b_6 + - 72 * a_41 * a_51 * a_54 * a_65^2 * b_6 + - 72 * a_41 * a_52 * a_54 * a_65^2 * b_6 + - 72 * a_41 * a_53 * a_54 * a_65^2 * b_6 + - 72 * a_41 * a_54^2 * a_65^2 * b_6 + - 72 * a_42^2 * a_54 * a_64 * a_65 * b_6 + - 144 * a_42 * a_43 * a_54 * a_64 * a_65 * b_6 + - 72 * a_42 * a_51 * a_54 * a_65^2 * b_6 + - 72 * a_42 * a_52 * a_54 * a_65^2 * b_6 + - 72 * a_42 * a_53 * a_54 * a_65^2 * b_6 + - 72 * a_42 * a_54^2 * a_65^2 * b_6 + - 72 * a_43^2 * a_54 * a_64 * a_65 * b_6 + - 72 * a_43 * a_51 * a_54 * a_65^2 * b_6 + - 72 * a_43 * a_52 * a_54 * a_65^2 * b_6 + - 72 * a_43 * a_53 * a_54 * a_65^2 * b_6 + - 72 * a_43 * a_54^2 * a_65^2 * b_6 - 1, - 36 * a_21 * a_32 * a_41^2 * a_43 * b_4 + - 72 * a_21 * a_32 * a_41 * a_42 * a_43 * b_4 + - 72 * a_21 * a_32 * a_41 * a_43^2 * b_4 + - 36 * a_21 * a_32 * a_42^2 * a_43 * b_4 + - 72 * a_21 * a_32 * a_42 * a_43^2 * b_4 + - 36 * a_21 * a_32 * a_43^3 * b_4 + - 36 * a_21 * a_32 * a_51^2 * a_53 * b_5 + - 72 * a_21 * a_32 * a_51 * a_52 * a_53 * b_5 + - 72 * a_21 * a_32 * a_51 * a_53^2 * b_5 + - 72 * a_21 * a_32 * a_51 * a_53 * a_54 * b_5 + - 36 * a_21 * a_32 * a_52^2 * a_53 * b_5 + - 72 * a_21 * a_32 * a_52 * a_53^2 * b_5 + - 72 * a_21 * a_32 * a_52 * a_53 * a_54 * b_5 + - 36 * a_21 * a_32 * a_53^3 * b_5 + - 72 * a_21 * a_32 * a_53^2 * a_54 * b_5 + - 36 * a_21 * a_32 * a_53 * a_54^2 * b_5 + - 36 * a_21 * a_32 * a_61^2 * a_63 * b_6 + - 72 * a_21 * a_32 * a_61 * a_62 * a_63 * b_6 + - 72 * a_21 * a_32 * a_61 * a_63^2 * b_6 + - 72 * a_21 * a_32 * a_61 * a_63 * a_64 * b_6 + - 72 * a_21 * a_32 * a_61 * a_63 * a_65 * b_6 + - 36 * a_21 * a_32 * a_62^2 * a_63 * b_6 + - 72 * a_21 * a_32 * a_62 * a_63^2 * b_6 + - 72 * a_21 * a_32 * a_62 * a_63 * a_64 * b_6 + - 72 * a_21 * a_32 * a_62 * a_63 * a_65 * b_6 + - 36 * a_21 * a_32 * a_63^3 * b_6 + - 72 * a_21 * a_32 * a_63^2 * a_64 * b_6 + - 72 * a_21 * a_32 * a_63^2 * a_65 * b_6 + - 36 * a_21 * a_32 * a_63 * a_64^2 * b_6 + - 72 * a_21 * a_32 * a_63 * a_64 * a_65 * b_6 + - 36 * a_21 * a_32 * a_63 * a_65^2 * b_6 + - 36 * a_21 * a_42 * a_51^2 * a_54 * b_5 + - 72 * a_21 * a_42 * a_51 * a_52 * a_54 * b_5 + - 72 * a_21 * a_42 * a_51 * a_53 * a_54 * b_5 + - 72 * a_21 * a_42 * a_51 * a_54^2 * b_5 + - 36 * a_21 * a_42 * a_52^2 * a_54 * b_5 + - 72 * a_21 * a_42 * a_52 * a_53 * a_54 * b_5 + - 72 * a_21 * a_42 * a_52 * a_54^2 * b_5 + - 36 * a_21 * a_42 * a_53^2 * a_54 * b_5 + - 72 * a_21 * a_42 * a_53 * a_54^2 * b_5 + - 36 * a_21 * a_42 * a_54^3 * b_5 + - 36 * a_21 * a_42 * a_61^2 * a_64 * b_6 + - 72 * a_21 * a_42 * a_61 * a_62 * a_64 * b_6 + - 72 * a_21 * a_42 * a_61 * a_63 * a_64 * b_6 + - 72 * a_21 * a_42 * a_61 * a_64^2 * b_6 + - 72 * a_21 * a_42 * a_61 * a_64 * a_65 * b_6 + - 36 * a_21 * a_42 * a_62^2 * a_64 * b_6 + - 72 * a_21 * a_42 * a_62 * a_63 * a_64 * b_6 + - 72 * a_21 * a_42 * a_62 * a_64^2 * b_6 + - 72 * a_21 * a_42 * a_62 * a_64 * a_65 * b_6 + - 36 * a_21 * a_42 * a_63^2 * a_64 * b_6 + - 72 * a_21 * a_42 * a_63 * a_64^2 * b_6 + - 72 * a_21 * a_42 * a_63 * a_64 * a_65 * b_6 + - 36 * a_21 * a_42 * a_64^3 * b_6 + - 72 * a_21 * a_42 * a_64^2 * a_65 * b_6 + - 36 * a_21 * a_42 * a_64 * a_65^2 * b_6 + - 36 * a_21 * a_52 * a_61^2 * a_65 * b_6 + - 72 * a_21 * a_52 * a_61 * a_62 * a_65 * b_6 + - 72 * a_21 * a_52 * a_61 * a_63 * a_65 * b_6 + - 72 * a_21 * a_52 * a_61 * a_64 * a_65 * b_6 + - 72 * a_21 * a_52 * a_61 * a_65^2 * b_6 + - 36 * a_21 * a_52 * a_62^2 * a_65 * b_6 + - 72 * a_21 * a_52 * a_62 * a_63 * a_65 * b_6 + - 72 * a_21 * a_52 * a_62 * a_64 * a_65 * b_6 + - 72 * a_21 * a_52 * a_62 * a_65^2 * b_6 + - 36 * a_21 * a_52 * a_63^2 * a_65 * b_6 + - 72 * a_21 * a_52 * a_63 * a_64 * a_65 * b_6 + - 72 * a_21 * a_52 * a_63 * a_65^2 * b_6 + - 36 * a_21 * a_52 * a_64^2 * a_65 * b_6 + - 72 * a_21 * a_52 * a_64 * a_65^2 * b_6 + - 36 * a_21 * a_52 * a_65^3 * b_6 + - 36 * a_31 * a_43 * a_51^2 * a_54 * b_5 + - 72 * a_31 * a_43 * a_51 * a_52 * a_54 * b_5 + - 72 * a_31 * a_43 * a_51 * a_53 * a_54 * b_5 + - 72 * a_31 * a_43 * a_51 * a_54^2 * b_5 + - 36 * a_31 * a_43 * a_52^2 * a_54 * b_5 + - 72 * a_31 * a_43 * a_52 * a_53 * a_54 * b_5 + - 72 * a_31 * a_43 * a_52 * a_54^2 * b_5 + - 36 * a_31 * a_43 * a_53^2 * a_54 * b_5 + - 72 * a_31 * a_43 * a_53 * a_54^2 * b_5 + - 36 * a_31 * a_43 * a_54^3 * b_5 + - 36 * a_31 * a_43 * a_61^2 * a_64 * b_6 + - 72 * a_31 * a_43 * a_61 * a_62 * a_64 * b_6 + - 72 * a_31 * a_43 * a_61 * a_63 * a_64 * b_6 + - 72 * a_31 * a_43 * a_61 * a_64^2 * b_6 + - 72 * a_31 * a_43 * a_61 * a_64 * a_65 * b_6 + - 36 * a_31 * a_43 * a_62^2 * a_64 * b_6 + - 72 * a_31 * a_43 * a_62 * a_63 * a_64 * b_6 + - 72 * a_31 * a_43 * a_62 * a_64^2 * b_6 + - 72 * a_31 * a_43 * a_62 * a_64 * a_65 * b_6 + - 36 * a_31 * a_43 * a_63^2 * a_64 * b_6 + - 72 * a_31 * a_43 * a_63 * a_64^2 * b_6 + - 72 * a_31 * a_43 * a_63 * a_64 * a_65 * b_6 + - 36 * a_31 * a_43 * a_64^3 * b_6 + - 72 * a_31 * a_43 * a_64^2 * a_65 * b_6 + - 36 * a_31 * a_43 * a_64 * a_65^2 * b_6 + - 36 * a_31 * a_53 * a_61^2 * a_65 * b_6 + - 72 * a_31 * a_53 * a_61 * a_62 * a_65 * b_6 + - 72 * a_31 * a_53 * a_61 * a_63 * a_65 * b_6 + - 72 * a_31 * a_53 * a_61 * a_64 * a_65 * b_6 + - 72 * a_31 * a_53 * a_61 * a_65^2 * b_6 + - 36 * a_31 * a_53 * a_62^2 * a_65 * b_6 + - 72 * a_31 * a_53 * a_62 * a_63 * a_65 * b_6 + - 72 * a_31 * a_53 * a_62 * a_64 * a_65 * b_6 + - 72 * a_31 * a_53 * a_62 * a_65^2 * b_6 + - 36 * a_31 * a_53 * a_63^2 * a_65 * b_6 + - 72 * a_31 * a_53 * a_63 * a_64 * a_65 * b_6 + - 72 * a_31 * a_53 * a_63 * a_65^2 * b_6 + - 36 * a_31 * a_53 * a_64^2 * a_65 * b_6 + - 72 * a_31 * a_53 * a_64 * a_65^2 * b_6 + - 36 * a_31 * a_53 * a_65^3 * b_6 + - 36 * a_32 * a_43 * a_51^2 * a_54 * b_5 + - 72 * a_32 * a_43 * a_51 * a_52 * a_54 * b_5 + - 72 * a_32 * a_43 * a_51 * a_53 * a_54 * b_5 + - 72 * a_32 * a_43 * a_51 * a_54^2 * b_5 + - 36 * a_32 * a_43 * a_52^2 * a_54 * b_5 + - 72 * a_32 * a_43 * a_52 * a_53 * a_54 * b_5 + - 72 * a_32 * a_43 * a_52 * a_54^2 * b_5 + - 36 * a_32 * a_43 * a_53^2 * a_54 * b_5 + - 72 * a_32 * a_43 * a_53 * a_54^2 * b_5 + - 36 * a_32 * a_43 * a_54^3 * b_5 + - 36 * a_32 * a_43 * a_61^2 * a_64 * b_6 + - 72 * a_32 * a_43 * a_61 * a_62 * a_64 * b_6 + - 72 * a_32 * a_43 * a_61 * a_63 * a_64 * b_6 + - 72 * a_32 * a_43 * a_61 * a_64^2 * b_6 + - 72 * a_32 * a_43 * a_61 * a_64 * a_65 * b_6 + - 36 * a_32 * a_43 * a_62^2 * a_64 * b_6 + - 72 * a_32 * a_43 * a_62 * a_63 * a_64 * b_6 + - 72 * a_32 * a_43 * a_62 * a_64^2 * b_6 + - 72 * a_32 * a_43 * a_62 * a_64 * a_65 * b_6 + - 36 * a_32 * a_43 * a_63^2 * a_64 * b_6 + - 72 * a_32 * a_43 * a_63 * a_64^2 * b_6 + - 72 * a_32 * a_43 * a_63 * a_64 * a_65 * b_6 + - 36 * a_32 * a_43 * a_64^3 * b_6 + - 72 * a_32 * a_43 * a_64^2 * a_65 * b_6 + - 36 * a_32 * a_43 * a_64 * a_65^2 * b_6 + - 36 * a_32 * a_53 * a_61^2 * a_65 * b_6 + - 72 * a_32 * a_53 * a_61 * a_62 * a_65 * b_6 + - 72 * a_32 * a_53 * a_61 * a_63 * a_65 * b_6 + - 72 * a_32 * a_53 * a_61 * a_64 * a_65 * b_6 + - 72 * a_32 * a_53 * a_61 * a_65^2 * b_6 + - 36 * a_32 * a_53 * a_62^2 * a_65 * b_6 + - 72 * a_32 * a_53 * a_62 * a_63 * a_65 * b_6 + - 72 * a_32 * a_53 * a_62 * a_64 * a_65 * b_6 + - 72 * a_32 * a_53 * a_62 * a_65^2 * b_6 + - 36 * a_32 * a_53 * a_63^2 * a_65 * b_6 + - 72 * a_32 * a_53 * a_63 * a_64 * a_65 * b_6 + - 72 * a_32 * a_53 * a_63 * a_65^2 * b_6 + - 36 * a_32 * a_53 * a_64^2 * a_65 * b_6 + - 72 * a_32 * a_53 * a_64 * a_65^2 * b_6 + - 36 * a_32 * a_53 * a_65^3 * b_6 + - 36 * a_41 * a_54 * a_61^2 * a_65 * b_6 + - 72 * a_41 * a_54 * a_61 * a_62 * a_65 * b_6 + - 72 * a_41 * a_54 * a_61 * a_63 * a_65 * b_6 + - 72 * a_41 * a_54 * a_61 * a_64 * a_65 * b_6 + - 72 * a_41 * a_54 * a_61 * a_65^2 * b_6 + - 36 * a_41 * a_54 * a_62^2 * a_65 * b_6 + - 72 * a_41 * a_54 * a_62 * a_63 * a_65 * b_6 + - 72 * a_41 * a_54 * a_62 * a_64 * a_65 * b_6 + - 72 * a_41 * a_54 * a_62 * a_65^2 * b_6 + - 36 * a_41 * a_54 * a_63^2 * a_65 * b_6 + - 72 * a_41 * a_54 * a_63 * a_64 * a_65 * b_6 + - 72 * a_41 * a_54 * a_63 * a_65^2 * b_6 + - 36 * a_41 * a_54 * a_64^2 * a_65 * b_6 + - 72 * a_41 * a_54 * a_64 * a_65^2 * b_6 + - 36 * a_41 * a_54 * a_65^3 * b_6 + - 36 * a_42 * a_54 * a_61^2 * a_65 * b_6 + - 72 * a_42 * a_54 * a_61 * a_62 * a_65 * b_6 + - 72 * a_42 * a_54 * a_61 * a_63 * a_65 * b_6 + - 72 * a_42 * a_54 * a_61 * a_64 * a_65 * b_6 + - 72 * a_42 * a_54 * a_61 * a_65^2 * b_6 + - 36 * a_42 * a_54 * a_62^2 * a_65 * b_6 + - 72 * a_42 * a_54 * a_62 * a_63 * a_65 * b_6 + - 72 * a_42 * a_54 * a_62 * a_64 * a_65 * b_6 + - 72 * a_42 * a_54 * a_62 * a_65^2 * b_6 + - 36 * a_42 * a_54 * a_63^2 * a_65 * b_6 + - 72 * a_42 * a_54 * a_63 * a_64 * a_65 * b_6 + - 72 * a_42 * a_54 * a_63 * a_65^2 * b_6 + - 36 * a_42 * a_54 * a_64^2 * a_65 * b_6 + - 72 * a_42 * a_54 * a_64 * a_65^2 * b_6 + - 36 * a_42 * a_54 * a_65^3 * b_6 + - 36 * a_43 * a_54 * a_61^2 * a_65 * b_6 + - 72 * a_43 * a_54 * a_61 * a_62 * a_65 * b_6 + - 72 * a_43 * a_54 * a_61 * a_63 * a_65 * b_6 + - 72 * a_43 * a_54 * a_61 * a_64 * a_65 * b_6 + - 72 * a_43 * a_54 * a_61 * a_65^2 * b_6 + - 36 * a_43 * a_54 * a_62^2 * a_65 * b_6 + - 72 * a_43 * a_54 * a_62 * a_63 * a_65 * b_6 + - 72 * a_43 * a_54 * a_62 * a_64 * a_65 * b_6 + - 72 * a_43 * a_54 * a_62 * a_65^2 * b_6 + - 36 * a_43 * a_54 * a_63^2 * a_65 * b_6 + - 72 * a_43 * a_54 * a_63 * a_64 * a_65 * b_6 + - 72 * a_43 * a_54 * a_63 * a_65^2 * b_6 + - 36 * a_43 * a_54 * a_64^2 * a_65 * b_6 + - 72 * a_43 * a_54 * a_64 * a_65^2 * b_6 + - 36 * a_43 * a_54 * a_65^3 * b_6 - 1, - 30 * a_21^4 * a_32 * b_3 + - 30 * a_21^4 * a_42 * b_4 + - 30 * a_21^4 * a_52 * b_5 + - 30 * a_21^4 * a_62 * b_6 + - 30 * a_31^4 * a_43 * b_4 + - 30 * a_31^4 * a_53 * b_5 + - 30 * a_31^4 * a_63 * b_6 + - 120 * a_31^3 * a_32 * a_43 * b_4 + - 120 * a_31^3 * a_32 * a_53 * b_5 + - 120 * a_31^3 * a_32 * a_63 * b_6 + - 180 * a_31^2 * a_32^2 * a_43 * b_4 + - 180 * a_31^2 * a_32^2 * a_53 * b_5 + - 180 * a_31^2 * a_32^2 * a_63 * b_6 + - 120 * a_31 * a_32^3 * a_43 * b_4 + - 120 * a_31 * a_32^3 * a_53 * b_5 + - 120 * a_31 * a_32^3 * a_63 * b_6 + - 30 * a_32^4 * a_43 * b_4 + - 30 * a_32^4 * a_53 * b_5 + - 30 * a_32^4 * a_63 * b_6 + - 30 * a_41^4 * a_54 * b_5 + - 30 * a_41^4 * a_64 * b_6 + - 120 * a_41^3 * a_42 * a_54 * b_5 + - 120 * a_41^3 * a_42 * a_64 * b_6 + - 120 * a_41^3 * a_43 * a_54 * b_5 + - 120 * a_41^3 * a_43 * a_64 * b_6 + - 180 * a_41^2 * a_42^2 * a_54 * b_5 + - 180 * a_41^2 * a_42^2 * a_64 * b_6 + - 360 * a_41^2 * a_42 * a_43 * a_54 * b_5 + - 360 * a_41^2 * a_42 * a_43 * a_64 * b_6 + - 180 * a_41^2 * a_43^2 * a_54 * b_5 + - 180 * a_41^2 * a_43^2 * a_64 * b_6 + - 120 * a_41 * a_42^3 * a_54 * b_5 + - 120 * a_41 * a_42^3 * a_64 * b_6 + - 360 * a_41 * a_42^2 * a_43 * a_54 * b_5 + - 360 * a_41 * a_42^2 * a_43 * a_64 * b_6 + - 360 * a_41 * a_42 * a_43^2 * a_54 * b_5 + - 360 * a_41 * a_42 * a_43^2 * a_64 * b_6 + - 120 * a_41 * a_43^3 * a_54 * b_5 + - 120 * a_41 * a_43^3 * a_64 * b_6 + - 30 * a_42^4 * a_54 * b_5 + - 30 * a_42^4 * a_64 * b_6 + - 120 * a_42^3 * a_43 * a_54 * b_5 + - 120 * a_42^3 * a_43 * a_64 * b_6 + - 180 * a_42^2 * a_43^2 * a_54 * b_5 + - 180 * a_42^2 * a_43^2 * a_64 * b_6 + - 120 * a_42 * a_43^3 * a_54 * b_5 + - 120 * a_42 * a_43^3 * a_64 * b_6 + - 30 * a_43^4 * a_54 * b_5 + - 30 * a_43^4 * a_64 * b_6 + - 30 * a_51^4 * a_65 * b_6 + - 120 * a_51^3 * a_52 * a_65 * b_6 + - 120 * a_51^3 * a_53 * a_65 * b_6 + - 120 * a_51^3 * a_54 * a_65 * b_6 + - 180 * a_51^2 * a_52^2 * a_65 * b_6 + - 360 * a_51^2 * a_52 * a_53 * a_65 * b_6 + - 360 * a_51^2 * a_52 * a_54 * a_65 * b_6 + - 180 * a_51^2 * a_53^2 * a_65 * b_6 + - 360 * a_51^2 * a_53 * a_54 * a_65 * b_6 + - 180 * a_51^2 * a_54^2 * a_65 * b_6 + - 120 * a_51 * a_52^3 * a_65 * b_6 + - 360 * a_51 * a_52^2 * a_53 * a_65 * b_6 + - 360 * a_51 * a_52^2 * a_54 * a_65 * b_6 + - 360 * a_51 * a_52 * a_53^2 * a_65 * b_6 + - 720 * a_51 * a_52 * a_53 * a_54 * a_65 * b_6 + - 360 * a_51 * a_52 * a_54^2 * a_65 * b_6 + - 120 * a_51 * a_53^3 * a_65 * b_6 + - 360 * a_51 * a_53^2 * a_54 * a_65 * b_6 + - 360 * a_51 * a_53 * a_54^2 * a_65 * b_6 + - 120 * a_51 * a_54^3 * a_65 * b_6 + - 30 * a_52^4 * a_65 * b_6 + - 120 * a_52^3 * a_53 * a_65 * b_6 + - 120 * a_52^3 * a_54 * a_65 * b_6 + - 180 * a_52^2 * a_53^2 * a_65 * b_6 + - 360 * a_52^2 * a_53 * a_54 * a_65 * b_6 + - 180 * a_52^2 * a_54^2 * a_65 * b_6 + - 120 * a_52 * a_53^3 * a_65 * b_6 + - 360 * a_52 * a_53^2 * a_54 * a_65 * b_6 + - 360 * a_52 * a_53 * a_54^2 * a_65 * b_6 + - 120 * a_52 * a_54^3 * a_65 * b_6 + - 30 * a_53^4 * a_65 * b_6 + - 120 * a_53^3 * a_54 * a_65 * b_6 + - 180 * a_53^2 * a_54^2 * a_65 * b_6 + - 120 * a_53 * a_54^3 * a_65 * b_6 + - 30 * a_54^4 * a_65 * b_6 - 1, - 24 * a_21^3 * a_31 * a_32 * b_3 + - 24 * a_21^3 * a_32^2 * b_3 + - 24 * a_21^3 * a_41 * a_42 * b_4 + - 24 * a_21^3 * a_42^2 * b_4 + - 24 * a_21^3 * a_42 * a_43 * b_4 + - 24 * a_21^3 * a_51 * a_52 * b_5 + - 24 * a_21^3 * a_52^2 * b_5 + - 24 * a_21^3 * a_52 * a_53 * b_5 + - 24 * a_21^3 * a_52 * a_54 * b_5 + - 24 * a_21^3 * a_61 * a_62 * b_6 + - 24 * a_21^3 * a_62^2 * b_6 + - 24 * a_21^3 * a_62 * a_63 * b_6 + - 24 * a_21^3 * a_62 * a_64 * b_6 + - 24 * a_21^3 * a_62 * a_65 * b_6 + - 24 * a_31^3 * a_41 * a_43 * b_4 + - 24 * a_31^3 * a_42 * a_43 * b_4 + - 24 * a_31^3 * a_43^2 * b_4 + - 24 * a_31^3 * a_51 * a_53 * b_5 + - 24 * a_31^3 * a_52 * a_53 * b_5 + - 24 * a_31^3 * a_53^2 * b_5 + - 24 * a_31^3 * a_53 * a_54 * b_5 + - 24 * a_31^3 * a_61 * a_63 * b_6 + - 24 * a_31^3 * a_62 * a_63 * b_6 + - 24 * a_31^3 * a_63^2 * b_6 + - 24 * a_31^3 * a_63 * a_64 * b_6 + - 24 * a_31^3 * a_63 * a_65 * b_6 + - 72 * a_31^2 * a_32 * a_41 * a_43 * b_4 + - 72 * a_31^2 * a_32 * a_42 * a_43 * b_4 + - 72 * a_31^2 * a_32 * a_43^2 * b_4 + - 72 * a_31^2 * a_32 * a_51 * a_53 * b_5 + - 72 * a_31^2 * a_32 * a_52 * a_53 * b_5 + - 72 * a_31^2 * a_32 * a_53^2 * b_5 + - 72 * a_31^2 * a_32 * a_53 * a_54 * b_5 + - 72 * a_31^2 * a_32 * a_61 * a_63 * b_6 + - 72 * a_31^2 * a_32 * a_62 * a_63 * b_6 + - 72 * a_31^2 * a_32 * a_63^2 * b_6 + - 72 * a_31^2 * a_32 * a_63 * a_64 * b_6 + - 72 * a_31^2 * a_32 * a_63 * a_65 * b_6 + - 72 * a_31 * a_32^2 * a_41 * a_43 * b_4 + - 72 * a_31 * a_32^2 * a_42 * a_43 * b_4 + - 72 * a_31 * a_32^2 * a_43^2 * b_4 + - 72 * a_31 * a_32^2 * a_51 * a_53 * b_5 + - 72 * a_31 * a_32^2 * a_52 * a_53 * b_5 + - 72 * a_31 * a_32^2 * a_53^2 * b_5 + - 72 * a_31 * a_32^2 * a_53 * a_54 * b_5 + - 72 * a_31 * a_32^2 * a_61 * a_63 * b_6 + - 72 * a_31 * a_32^2 * a_62 * a_63 * b_6 + - 72 * a_31 * a_32^2 * a_63^2 * b_6 + - 72 * a_31 * a_32^2 * a_63 * a_64 * b_6 + - 72 * a_31 * a_32^2 * a_63 * a_65 * b_6 + - 24 * a_32^3 * a_41 * a_43 * b_4 + - 24 * a_32^3 * a_42 * a_43 * b_4 + - 24 * a_32^3 * a_43^2 * b_4 + - 24 * a_32^3 * a_51 * a_53 * b_5 + - 24 * a_32^3 * a_52 * a_53 * b_5 + - 24 * a_32^3 * a_53^2 * b_5 + - 24 * a_32^3 * a_53 * a_54 * b_5 + - 24 * a_32^3 * a_61 * a_63 * b_6 + - 24 * a_32^3 * a_62 * a_63 * b_6 + - 24 * a_32^3 * a_63^2 * b_6 + - 24 * a_32^3 * a_63 * a_64 * b_6 + - 24 * a_32^3 * a_63 * a_65 * b_6 + - 24 * a_41^3 * a_51 * a_54 * b_5 + - 24 * a_41^3 * a_52 * a_54 * b_5 + - 24 * a_41^3 * a_53 * a_54 * b_5 + - 24 * a_41^3 * a_54^2 * b_5 + - 24 * a_41^3 * a_61 * a_64 * b_6 + - 24 * a_41^3 * a_62 * a_64 * b_6 + - 24 * a_41^3 * a_63 * a_64 * b_6 + - 24 * a_41^3 * a_64^2 * b_6 + - 24 * a_41^3 * a_64 * a_65 * b_6 + - 72 * a_41^2 * a_42 * a_51 * a_54 * b_5 + - 72 * a_41^2 * a_42 * a_52 * a_54 * b_5 + - 72 * a_41^2 * a_42 * a_53 * a_54 * b_5 + - 72 * a_41^2 * a_42 * a_54^2 * b_5 + - 72 * a_41^2 * a_42 * a_61 * a_64 * b_6 + - 72 * a_41^2 * a_42 * a_62 * a_64 * b_6 + - 72 * a_41^2 * a_42 * a_63 * a_64 * b_6 + - 72 * a_41^2 * a_42 * a_64^2 * b_6 + - 72 * a_41^2 * a_42 * a_64 * a_65 * b_6 + - 72 * a_41^2 * a_43 * a_51 * a_54 * b_5 + - 72 * a_41^2 * a_43 * a_52 * a_54 * b_5 + - 72 * a_41^2 * a_43 * a_53 * a_54 * b_5 + - 72 * a_41^2 * a_43 * a_54^2 * b_5 + - 72 * a_41^2 * a_43 * a_61 * a_64 * b_6 + - 72 * a_41^2 * a_43 * a_62 * a_64 * b_6 + - 72 * a_41^2 * a_43 * a_63 * a_64 * b_6 + - 72 * a_41^2 * a_43 * a_64^2 * b_6 + - 72 * a_41^2 * a_43 * a_64 * a_65 * b_6 + - 72 * a_41 * a_42^2 * a_51 * a_54 * b_5 + - 72 * a_41 * a_42^2 * a_52 * a_54 * b_5 + - 72 * a_41 * a_42^2 * a_53 * a_54 * b_5 + - 72 * a_41 * a_42^2 * a_54^2 * b_5 + - 72 * a_41 * a_42^2 * a_61 * a_64 * b_6 + - 72 * a_41 * a_42^2 * a_62 * a_64 * b_6 + - 72 * a_41 * a_42^2 * a_63 * a_64 * b_6 + - 72 * a_41 * a_42^2 * a_64^2 * b_6 + - 72 * a_41 * a_42^2 * a_64 * a_65 * b_6 + - 144 * a_41 * a_42 * a_43 * a_51 * a_54 * b_5 + - 144 * a_41 * a_42 * a_43 * a_52 * a_54 * b_5 + - 144 * a_41 * a_42 * a_43 * a_53 * a_54 * b_5 + - 144 * a_41 * a_42 * a_43 * a_54^2 * b_5 + - 144 * a_41 * a_42 * a_43 * a_61 * a_64 * b_6 + - 144 * a_41 * a_42 * a_43 * a_62 * a_64 * b_6 + - 144 * a_41 * a_42 * a_43 * a_63 * a_64 * b_6 + - 144 * a_41 * a_42 * a_43 * a_64^2 * b_6 + - 144 * a_41 * a_42 * a_43 * a_64 * a_65 * b_6 + - 72 * a_41 * a_43^2 * a_51 * a_54 * b_5 + - 72 * a_41 * a_43^2 * a_52 * a_54 * b_5 + - 72 * a_41 * a_43^2 * a_53 * a_54 * b_5 + - 72 * a_41 * a_43^2 * a_54^2 * b_5 + - 72 * a_41 * a_43^2 * a_61 * a_64 * b_6 + - 72 * a_41 * a_43^2 * a_62 * a_64 * b_6 + - 72 * a_41 * a_43^2 * a_63 * a_64 * b_6 + - 72 * a_41 * a_43^2 * a_64^2 * b_6 + - 72 * a_41 * a_43^2 * a_64 * a_65 * b_6 + - 24 * a_42^3 * a_51 * a_54 * b_5 + - 24 * a_42^3 * a_52 * a_54 * b_5 + - 24 * a_42^3 * a_53 * a_54 * b_5 + - 24 * a_42^3 * a_54^2 * b_5 + - 24 * a_42^3 * a_61 * a_64 * b_6 + - 24 * a_42^3 * a_62 * a_64 * b_6 + - 24 * a_42^3 * a_63 * a_64 * b_6 + - 24 * a_42^3 * a_64^2 * b_6 + - 24 * a_42^3 * a_64 * a_65 * b_6 + - 72 * a_42^2 * a_43 * a_51 * a_54 * b_5 + - 72 * a_42^2 * a_43 * a_52 * a_54 * b_5 + - 72 * a_42^2 * a_43 * a_53 * a_54 * b_5 + - 72 * a_42^2 * a_43 * a_54^2 * b_5 + - 72 * a_42^2 * a_43 * a_61 * a_64 * b_6 + - 72 * a_42^2 * a_43 * a_62 * a_64 * b_6 + - 72 * a_42^2 * a_43 * a_63 * a_64 * b_6 + - 72 * a_42^2 * a_43 * a_64^2 * b_6 + - 72 * a_42^2 * a_43 * a_64 * a_65 * b_6 + - 72 * a_42 * a_43^2 * a_51 * a_54 * b_5 + - 72 * a_42 * a_43^2 * a_52 * a_54 * b_5 + - 72 * a_42 * a_43^2 * a_53 * a_54 * b_5 + - 72 * a_42 * a_43^2 * a_54^2 * b_5 + - 72 * a_42 * a_43^2 * a_61 * a_64 * b_6 + - 72 * a_42 * a_43^2 * a_62 * a_64 * b_6 + - 72 * a_42 * a_43^2 * a_63 * a_64 * b_6 + - 72 * a_42 * a_43^2 * a_64^2 * b_6 + - 72 * a_42 * a_43^2 * a_64 * a_65 * b_6 + - 24 * a_43^3 * a_51 * a_54 * b_5 + - 24 * a_43^3 * a_52 * a_54 * b_5 + - 24 * a_43^3 * a_53 * a_54 * b_5 + - 24 * a_43^3 * a_54^2 * b_5 + - 24 * a_43^3 * a_61 * a_64 * b_6 + - 24 * a_43^3 * a_62 * a_64 * b_6 + - 24 * a_43^3 * a_63 * a_64 * b_6 + - 24 * a_43^3 * a_64^2 * b_6 + - 24 * a_43^3 * a_64 * a_65 * b_6 + - 24 * a_51^3 * a_61 * a_65 * b_6 + - 24 * a_51^3 * a_62 * a_65 * b_6 + - 24 * a_51^3 * a_63 * a_65 * b_6 + - 24 * a_51^3 * a_64 * a_65 * b_6 + - 24 * a_51^3 * a_65^2 * b_6 + - 72 * a_51^2 * a_52 * a_61 * a_65 * b_6 + - 72 * a_51^2 * a_52 * a_62 * a_65 * b_6 + - 72 * a_51^2 * a_52 * a_63 * a_65 * b_6 + - 72 * a_51^2 * a_52 * a_64 * a_65 * b_6 + - 72 * a_51^2 * a_52 * a_65^2 * b_6 + - 72 * a_51^2 * a_53 * a_61 * a_65 * b_6 + - 72 * a_51^2 * a_53 * a_62 * a_65 * b_6 + - 72 * a_51^2 * a_53 * a_63 * a_65 * b_6 + - 72 * a_51^2 * a_53 * a_64 * a_65 * b_6 + - 72 * a_51^2 * a_53 * a_65^2 * b_6 + - 72 * a_51^2 * a_54 * a_61 * a_65 * b_6 + - 72 * a_51^2 * a_54 * a_62 * a_65 * b_6 + - 72 * a_51^2 * a_54 * a_63 * a_65 * b_6 + - 72 * a_51^2 * a_54 * a_64 * a_65 * b_6 + - 72 * a_51^2 * a_54 * a_65^2 * b_6 + - 72 * a_51 * a_52^2 * a_61 * a_65 * b_6 + - 72 * a_51 * a_52^2 * a_62 * a_65 * b_6 + - 72 * a_51 * a_52^2 * a_63 * a_65 * b_6 + - 72 * a_51 * a_52^2 * a_64 * a_65 * b_6 + - 72 * a_51 * a_52^2 * a_65^2 * b_6 + - 144 * a_51 * a_52 * a_53 * a_61 * a_65 * b_6 + - 144 * a_51 * a_52 * a_53 * a_62 * a_65 * b_6 + - 144 * a_51 * a_52 * a_53 * a_63 * a_65 * b_6 + - 144 * a_51 * a_52 * a_53 * a_64 * a_65 * b_6 + - 144 * a_51 * a_52 * a_53 * a_65^2 * b_6 + - 144 * a_51 * a_52 * a_54 * a_61 * a_65 * b_6 + - 144 * a_51 * a_52 * a_54 * a_62 * a_65 * b_6 + - 144 * a_51 * a_52 * a_54 * a_63 * a_65 * b_6 + - 144 * a_51 * a_52 * a_54 * a_64 * a_65 * b_6 + - 144 * a_51 * a_52 * a_54 * a_65^2 * b_6 + - 72 * a_51 * a_53^2 * a_61 * a_65 * b_6 + - 72 * a_51 * a_53^2 * a_62 * a_65 * b_6 + - 72 * a_51 * a_53^2 * a_63 * a_65 * b_6 + - 72 * a_51 * a_53^2 * a_64 * a_65 * b_6 + - 72 * a_51 * a_53^2 * a_65^2 * b_6 + - 144 * a_51 * a_53 * a_54 * a_61 * a_65 * b_6 + - 144 * a_51 * a_53 * a_54 * a_62 * a_65 * b_6 + - 144 * a_51 * a_53 * a_54 * a_63 * a_65 * b_6 + - 144 * a_51 * a_53 * a_54 * a_64 * a_65 * b_6 + - 144 * a_51 * a_53 * a_54 * a_65^2 * b_6 + - 72 * a_51 * a_54^2 * a_61 * a_65 * b_6 + - 72 * a_51 * a_54^2 * a_62 * a_65 * b_6 + - 72 * a_51 * a_54^2 * a_63 * a_65 * b_6 + - 72 * a_51 * a_54^2 * a_64 * a_65 * b_6 + - 72 * a_51 * a_54^2 * a_65^2 * b_6 + - 24 * a_52^3 * a_61 * a_65 * b_6 + - 24 * a_52^3 * a_62 * a_65 * b_6 + - 24 * a_52^3 * a_63 * a_65 * b_6 + - 24 * a_52^3 * a_64 * a_65 * b_6 + - 24 * a_52^3 * a_65^2 * b_6 + - 72 * a_52^2 * a_53 * a_61 * a_65 * b_6 + - 72 * a_52^2 * a_53 * a_62 * a_65 * b_6 + - 72 * a_52^2 * a_53 * a_63 * a_65 * b_6 + - 72 * a_52^2 * a_53 * a_64 * a_65 * b_6 + - 72 * a_52^2 * a_53 * a_65^2 * b_6 + - 72 * a_52^2 * a_54 * a_61 * a_65 * b_6 + - 72 * a_52^2 * a_54 * a_62 * a_65 * b_6 + - 72 * a_52^2 * a_54 * a_63 * a_65 * b_6 + - 72 * a_52^2 * a_54 * a_64 * a_65 * b_6 + - 72 * a_52^2 * a_54 * a_65^2 * b_6 + - 72 * a_52 * a_53^2 * a_61 * a_65 * b_6 + - 72 * a_52 * a_53^2 * a_62 * a_65 * b_6 + - 72 * a_52 * a_53^2 * a_63 * a_65 * b_6 + - 72 * a_52 * a_53^2 * a_64 * a_65 * b_6 + - 72 * a_52 * a_53^2 * a_65^2 * b_6 + - 144 * a_52 * a_53 * a_54 * a_61 * a_65 * b_6 + - 144 * a_52 * a_53 * a_54 * a_62 * a_65 * b_6 + - 144 * a_52 * a_53 * a_54 * a_63 * a_65 * b_6 + - 144 * a_52 * a_53 * a_54 * a_64 * a_65 * b_6 + - 144 * a_52 * a_53 * a_54 * a_65^2 * b_6 + - 72 * a_52 * a_54^2 * a_61 * a_65 * b_6 + - 72 * a_52 * a_54^2 * a_62 * a_65 * b_6 + - 72 * a_52 * a_54^2 * a_63 * a_65 * b_6 + - 72 * a_52 * a_54^2 * a_64 * a_65 * b_6 + - 72 * a_52 * a_54^2 * a_65^2 * b_6 + - 24 * a_53^3 * a_61 * a_65 * b_6 + - 24 * a_53^3 * a_62 * a_65 * b_6 + - 24 * a_53^3 * a_63 * a_65 * b_6 + - 24 * a_53^3 * a_64 * a_65 * b_6 + - 24 * a_53^3 * a_65^2 * b_6 + - 72 * a_53^2 * a_54 * a_61 * a_65 * b_6 + - 72 * a_53^2 * a_54 * a_62 * a_65 * b_6 + - 72 * a_53^2 * a_54 * a_63 * a_65 * b_6 + - 72 * a_53^2 * a_54 * a_64 * a_65 * b_6 + - 72 * a_53^2 * a_54 * a_65^2 * b_6 + - 72 * a_53 * a_54^2 * a_61 * a_65 * b_6 + - 72 * a_53 * a_54^2 * a_62 * a_65 * b_6 + - 72 * a_53 * a_54^2 * a_63 * a_65 * b_6 + - 72 * a_53 * a_54^2 * a_64 * a_65 * b_6 + - 72 * a_53 * a_54^2 * a_65^2 * b_6 + - 24 * a_54^3 * a_61 * a_65 * b_6 + - 24 * a_54^3 * a_62 * a_65 * b_6 + - 24 * a_54^3 * a_63 * a_65 * b_6 + - 24 * a_54^3 * a_64 * a_65 * b_6 + - 24 * a_54^3 * a_65^2 * b_6 - 1, - 36 * a_21^3 * a_32^2 * b_3 + - 36 * a_21^3 * a_42^2 * b_4 + - 36 * a_21^3 * a_52^2 * b_5 + - 36 * a_21^3 * a_62^2 * b_6 + - 36 * a_21^2 * a_31 * a_42 * a_43 * b_4 + - 36 * a_21^2 * a_31 * a_52 * a_53 * b_5 + - 36 * a_21^2 * a_31 * a_62 * a_63 * b_6 + - 36 * a_21^2 * a_32 * a_42 * a_43 * b_4 + - 36 * a_21^2 * a_32 * a_52 * a_53 * b_5 + - 36 * a_21^2 * a_32 * a_62 * a_63 * b_6 + - 36 * a_21^2 * a_41 * a_52 * a_54 * b_5 + - 36 * a_21^2 * a_41 * a_62 * a_64 * b_6 + - 36 * a_21^2 * a_42 * a_52 * a_54 * b_5 + - 36 * a_21^2 * a_42 * a_62 * a_64 * b_6 + - 36 * a_21^2 * a_43 * a_52 * a_54 * b_5 + - 36 * a_21^2 * a_43 * a_62 * a_64 * b_6 + - 36 * a_21^2 * a_51 * a_62 * a_65 * b_6 + - 36 * a_21^2 * a_52 * a_62 * a_65 * b_6 + - 36 * a_21^2 * a_53 * a_62 * a_65 * b_6 + - 36 * a_21^2 * a_54 * a_62 * a_65 * b_6 + - 36 * a_21 * a_31^2 * a_42 * a_43 * b_4 + - 36 * a_21 * a_31^2 * a_52 * a_53 * b_5 + - 36 * a_21 * a_31^2 * a_62 * a_63 * b_6 + - 72 * a_21 * a_31 * a_32 * a_42 * a_43 * b_4 + - 72 * a_21 * a_31 * a_32 * a_52 * a_53 * b_5 + - 72 * a_21 * a_31 * a_32 * a_62 * a_63 * b_6 + - 36 * a_21 * a_32^2 * a_42 * a_43 * b_4 + - 36 * a_21 * a_32^2 * a_52 * a_53 * b_5 + - 36 * a_21 * a_32^2 * a_62 * a_63 * b_6 + - 36 * a_21 * a_41^2 * a_52 * a_54 * b_5 + - 36 * a_21 * a_41^2 * a_62 * a_64 * b_6 + - 72 * a_21 * a_41 * a_42 * a_52 * a_54 * b_5 + - 72 * a_21 * a_41 * a_42 * a_62 * a_64 * b_6 + - 72 * a_21 * a_41 * a_43 * a_52 * a_54 * b_5 + - 72 * a_21 * a_41 * a_43 * a_62 * a_64 * b_6 + - 36 * a_21 * a_42^2 * a_52 * a_54 * b_5 + - 36 * a_21 * a_42^2 * a_62 * a_64 * b_6 + - 72 * a_21 * a_42 * a_43 * a_52 * a_54 * b_5 + - 72 * a_21 * a_42 * a_43 * a_62 * a_64 * b_6 + - 36 * a_21 * a_43^2 * a_52 * a_54 * b_5 + - 36 * a_21 * a_43^2 * a_62 * a_64 * b_6 + - 36 * a_21 * a_51^2 * a_62 * a_65 * b_6 + - 72 * a_21 * a_51 * a_52 * a_62 * a_65 * b_6 + - 72 * a_21 * a_51 * a_53 * a_62 * a_65 * b_6 + - 72 * a_21 * a_51 * a_54 * a_62 * a_65 * b_6 + - 36 * a_21 * a_52^2 * a_62 * a_65 * b_6 + - 72 * a_21 * a_52 * a_53 * a_62 * a_65 * b_6 + - 72 * a_21 * a_52 * a_54 * a_62 * a_65 * b_6 + - 36 * a_21 * a_53^2 * a_62 * a_65 * b_6 + - 72 * a_21 * a_53 * a_54 * a_62 * a_65 * b_6 + - 36 * a_21 * a_54^2 * a_62 * a_65 * b_6 + - 36 * a_31^3 * a_43^2 * b_4 + - 36 * a_31^3 * a_53^2 * b_5 + - 36 * a_31^3 * a_63^2 * b_6 + - 108 * a_31^2 * a_32 * a_43^2 * b_4 + - 108 * a_31^2 * a_32 * a_53^2 * b_5 + - 108 * a_31^2 * a_32 * a_63^2 * b_6 + - 36 * a_31^2 * a_41 * a_53 * a_54 * b_5 + - 36 * a_31^2 * a_41 * a_63 * a_64 * b_6 + - 36 * a_31^2 * a_42 * a_53 * a_54 * b_5 + - 36 * a_31^2 * a_42 * a_63 * a_64 * b_6 + - 36 * a_31^2 * a_43 * a_53 * a_54 * b_5 + - 36 * a_31^2 * a_43 * a_63 * a_64 * b_6 + - 36 * a_31^2 * a_51 * a_63 * a_65 * b_6 + - 36 * a_31^2 * a_52 * a_63 * a_65 * b_6 + - 36 * a_31^2 * a_53 * a_63 * a_65 * b_6 + - 36 * a_31^2 * a_54 * a_63 * a_65 * b_6 + - 108 * a_31 * a_32^2 * a_43^2 * b_4 + - 108 * a_31 * a_32^2 * a_53^2 * b_5 + - 108 * a_31 * a_32^2 * a_63^2 * b_6 + - 72 * a_31 * a_32 * a_41 * a_53 * a_54 * b_5 + - 72 * a_31 * a_32 * a_41 * a_63 * a_64 * b_6 + - 72 * a_31 * a_32 * a_42 * a_53 * a_54 * b_5 + - 72 * a_31 * a_32 * a_42 * a_63 * a_64 * b_6 + - 72 * a_31 * a_32 * a_43 * a_53 * a_54 * b_5 + - 72 * a_31 * a_32 * a_43 * a_63 * a_64 * b_6 + - 72 * a_31 * a_32 * a_51 * a_63 * a_65 * b_6 + - 72 * a_31 * a_32 * a_52 * a_63 * a_65 * b_6 + - 72 * a_31 * a_32 * a_53 * a_63 * a_65 * b_6 + - 72 * a_31 * a_32 * a_54 * a_63 * a_65 * b_6 + - 36 * a_31 * a_41^2 * a_53 * a_54 * b_5 + - 36 * a_31 * a_41^2 * a_63 * a_64 * b_6 + - 72 * a_31 * a_41 * a_42 * a_53 * a_54 * b_5 + - 72 * a_31 * a_41 * a_42 * a_63 * a_64 * b_6 + - 72 * a_31 * a_41 * a_43 * a_53 * a_54 * b_5 + - 72 * a_31 * a_41 * a_43 * a_63 * a_64 * b_6 + - 36 * a_31 * a_42^2 * a_53 * a_54 * b_5 + - 36 * a_31 * a_42^2 * a_63 * a_64 * b_6 + - 72 * a_31 * a_42 * a_43 * a_53 * a_54 * b_5 + - 72 * a_31 * a_42 * a_43 * a_63 * a_64 * b_6 + - 36 * a_31 * a_43^2 * a_53 * a_54 * b_5 + - 36 * a_31 * a_43^2 * a_63 * a_64 * b_6 + - 36 * a_31 * a_51^2 * a_63 * a_65 * b_6 + - 72 * a_31 * a_51 * a_52 * a_63 * a_65 * b_6 + - 72 * a_31 * a_51 * a_53 * a_63 * a_65 * b_6 + - 72 * a_31 * a_51 * a_54 * a_63 * a_65 * b_6 + - 36 * a_31 * a_52^2 * a_63 * a_65 * b_6 + - 72 * a_31 * a_52 * a_53 * a_63 * a_65 * b_6 + - 72 * a_31 * a_52 * a_54 * a_63 * a_65 * b_6 + - 36 * a_31 * a_53^2 * a_63 * a_65 * b_6 + - 72 * a_31 * a_53 * a_54 * a_63 * a_65 * b_6 + - 36 * a_31 * a_54^2 * a_63 * a_65 * b_6 + - 36 * a_32^3 * a_43^2 * b_4 + - 36 * a_32^3 * a_53^2 * b_5 + - 36 * a_32^3 * a_63^2 * b_6 + - 36 * a_32^2 * a_41 * a_53 * a_54 * b_5 + - 36 * a_32^2 * a_41 * a_63 * a_64 * b_6 + - 36 * a_32^2 * a_42 * a_53 * a_54 * b_5 + - 36 * a_32^2 * a_42 * a_63 * a_64 * b_6 + - 36 * a_32^2 * a_43 * a_53 * a_54 * b_5 + - 36 * a_32^2 * a_43 * a_63 * a_64 * b_6 + - 36 * a_32^2 * a_51 * a_63 * a_65 * b_6 + - 36 * a_32^2 * a_52 * a_63 * a_65 * b_6 + - 36 * a_32^2 * a_53 * a_63 * a_65 * b_6 + - 36 * a_32^2 * a_54 * a_63 * a_65 * b_6 + - 36 * a_32 * a_41^2 * a_53 * a_54 * b_5 + - 36 * a_32 * a_41^2 * a_63 * a_64 * b_6 + - 72 * a_32 * a_41 * a_42 * a_53 * a_54 * b_5 + - 72 * a_32 * a_41 * a_42 * a_63 * a_64 * b_6 + - 72 * a_32 * a_41 * a_43 * a_53 * a_54 * b_5 + - 72 * a_32 * a_41 * a_43 * a_63 * a_64 * b_6 + - 36 * a_32 * a_42^2 * a_53 * a_54 * b_5 + - 36 * a_32 * a_42^2 * a_63 * a_64 * b_6 + - 72 * a_32 * a_42 * a_43 * a_53 * a_54 * b_5 + - 72 * a_32 * a_42 * a_43 * a_63 * a_64 * b_6 + - 36 * a_32 * a_43^2 * a_53 * a_54 * b_5 + - 36 * a_32 * a_43^2 * a_63 * a_64 * b_6 + - 36 * a_32 * a_51^2 * a_63 * a_65 * b_6 + - 72 * a_32 * a_51 * a_52 * a_63 * a_65 * b_6 + - 72 * a_32 * a_51 * a_53 * a_63 * a_65 * b_6 + - 72 * a_32 * a_51 * a_54 * a_63 * a_65 * b_6 + - 36 * a_32 * a_52^2 * a_63 * a_65 * b_6 + - 72 * a_32 * a_52 * a_53 * a_63 * a_65 * b_6 + - 72 * a_32 * a_52 * a_54 * a_63 * a_65 * b_6 + - 36 * a_32 * a_53^2 * a_63 * a_65 * b_6 + - 72 * a_32 * a_53 * a_54 * a_63 * a_65 * b_6 + - 36 * a_32 * a_54^2 * a_63 * a_65 * b_6 + - 36 * a_41^3 * a_54^2 * b_5 + - 36 * a_41^3 * a_64^2 * b_6 + - 108 * a_41^2 * a_42 * a_54^2 * b_5 + - 108 * a_41^2 * a_42 * a_64^2 * b_6 + - 108 * a_41^2 * a_43 * a_54^2 * b_5 + - 108 * a_41^2 * a_43 * a_64^2 * b_6 + - 36 * a_41^2 * a_51 * a_64 * a_65 * b_6 + - 36 * a_41^2 * a_52 * a_64 * a_65 * b_6 + - 36 * a_41^2 * a_53 * a_64 * a_65 * b_6 + - 36 * a_41^2 * a_54 * a_64 * a_65 * b_6 + - 108 * a_41 * a_42^2 * a_54^2 * b_5 + - 108 * a_41 * a_42^2 * a_64^2 * b_6 + - 216 * a_41 * a_42 * a_43 * a_54^2 * b_5 + - 216 * a_41 * a_42 * a_43 * a_64^2 * b_6 + - 72 * a_41 * a_42 * a_51 * a_64 * a_65 * b_6 + - 72 * a_41 * a_42 * a_52 * a_64 * a_65 * b_6 + - 72 * a_41 * a_42 * a_53 * a_64 * a_65 * b_6 + - 72 * a_41 * a_42 * a_54 * a_64 * a_65 * b_6 + - 108 * a_41 * a_43^2 * a_54^2 * b_5 + - 108 * a_41 * a_43^2 * a_64^2 * b_6 + - 72 * a_41 * a_43 * a_51 * a_64 * a_65 * b_6 + - 72 * a_41 * a_43 * a_52 * a_64 * a_65 * b_6 + - 72 * a_41 * a_43 * a_53 * a_64 * a_65 * b_6 + - 72 * a_41 * a_43 * a_54 * a_64 * a_65 * b_6 + - 36 * a_41 * a_51^2 * a_64 * a_65 * b_6 + - 72 * a_41 * a_51 * a_52 * a_64 * a_65 * b_6 + - 72 * a_41 * a_51 * a_53 * a_64 * a_65 * b_6 + - 72 * a_41 * a_51 * a_54 * a_64 * a_65 * b_6 + - 36 * a_41 * a_52^2 * a_64 * a_65 * b_6 + - 72 * a_41 * a_52 * a_53 * a_64 * a_65 * b_6 + - 72 * a_41 * a_52 * a_54 * a_64 * a_65 * b_6 + - 36 * a_41 * a_53^2 * a_64 * a_65 * b_6 + - 72 * a_41 * a_53 * a_54 * a_64 * a_65 * b_6 + - 36 * a_41 * a_54^2 * a_64 * a_65 * b_6 + - 36 * a_42^3 * a_54^2 * b_5 + - 36 * a_42^3 * a_64^2 * b_6 + - 108 * a_42^2 * a_43 * a_54^2 * b_5 + - 108 * a_42^2 * a_43 * a_64^2 * b_6 + - 36 * a_42^2 * a_51 * a_64 * a_65 * b_6 + - 36 * a_42^2 * a_52 * a_64 * a_65 * b_6 + - 36 * a_42^2 * a_53 * a_64 * a_65 * b_6 + - 36 * a_42^2 * a_54 * a_64 * a_65 * b_6 + - 108 * a_42 * a_43^2 * a_54^2 * b_5 + - 108 * a_42 * a_43^2 * a_64^2 * b_6 + - 72 * a_42 * a_43 * a_51 * a_64 * a_65 * b_6 + - 72 * a_42 * a_43 * a_52 * a_64 * a_65 * b_6 + - 72 * a_42 * a_43 * a_53 * a_64 * a_65 * b_6 + - 72 * a_42 * a_43 * a_54 * a_64 * a_65 * b_6 + - 36 * a_42 * a_51^2 * a_64 * a_65 * b_6 + - 72 * a_42 * a_51 * a_52 * a_64 * a_65 * b_6 + - 72 * a_42 * a_51 * a_53 * a_64 * a_65 * b_6 + - 72 * a_42 * a_51 * a_54 * a_64 * a_65 * b_6 + - 36 * a_42 * a_52^2 * a_64 * a_65 * b_6 + - 72 * a_42 * a_52 * a_53 * a_64 * a_65 * b_6 + - 72 * a_42 * a_52 * a_54 * a_64 * a_65 * b_6 + - 36 * a_42 * a_53^2 * a_64 * a_65 * b_6 + - 72 * a_42 * a_53 * a_54 * a_64 * a_65 * b_6 + - 36 * a_42 * a_54^2 * a_64 * a_65 * b_6 + - 36 * a_43^3 * a_54^2 * b_5 + - 36 * a_43^3 * a_64^2 * b_6 + - 36 * a_43^2 * a_51 * a_64 * a_65 * b_6 + - 36 * a_43^2 * a_52 * a_64 * a_65 * b_6 + - 36 * a_43^2 * a_53 * a_64 * a_65 * b_6 + - 36 * a_43^2 * a_54 * a_64 * a_65 * b_6 + - 36 * a_43 * a_51^2 * a_64 * a_65 * b_6 + - 72 * a_43 * a_51 * a_52 * a_64 * a_65 * b_6 + - 72 * a_43 * a_51 * a_53 * a_64 * a_65 * b_6 + - 72 * a_43 * a_51 * a_54 * a_64 * a_65 * b_6 + - 36 * a_43 * a_52^2 * a_64 * a_65 * b_6 + - 72 * a_43 * a_52 * a_53 * a_64 * a_65 * b_6 + - 72 * a_43 * a_52 * a_54 * a_64 * a_65 * b_6 + - 36 * a_43 * a_53^2 * a_64 * a_65 * b_6 + - 72 * a_43 * a_53 * a_54 * a_64 * a_65 * b_6 + - 36 * a_43 * a_54^2 * a_64 * a_65 * b_6 + - 36 * a_51^3 * a_65^2 * b_6 + - 108 * a_51^2 * a_52 * a_65^2 * b_6 + - 108 * a_51^2 * a_53 * a_65^2 * b_6 + - 108 * a_51^2 * a_54 * a_65^2 * b_6 + - 108 * a_51 * a_52^2 * a_65^2 * b_6 + - 216 * a_51 * a_52 * a_53 * a_65^2 * b_6 + - 216 * a_51 * a_52 * a_54 * a_65^2 * b_6 + - 108 * a_51 * a_53^2 * a_65^2 * b_6 + - 216 * a_51 * a_53 * a_54 * a_65^2 * b_6 + - 108 * a_51 * a_54^2 * a_65^2 * b_6 + - 36 * a_52^3 * a_65^2 * b_6 + - 108 * a_52^2 * a_53 * a_65^2 * b_6 + - 108 * a_52^2 * a_54 * a_65^2 * b_6 + - 108 * a_52 * a_53^2 * a_65^2 * b_6 + - 216 * a_52 * a_53 * a_54 * a_65^2 * b_6 + - 108 * a_52 * a_54^2 * a_65^2 * b_6 + - 36 * a_53^3 * a_65^2 * b_6 + - 108 * a_53^2 * a_54 * a_65^2 * b_6 + - 108 * a_53 * a_54^2 * a_65^2 * b_6 + - 36 * a_54^3 * a_65^2 * b_6 - 1, - 18 * a_21^2 * a_31^2 * a_32 * b_3 + - 36 * a_21^2 * a_31 * a_32^2 * b_3 + - 18 * a_21^2 * a_32^3 * b_3 + - 18 * a_21^2 * a_41^2 * a_42 * b_4 + - 36 * a_21^2 * a_41 * a_42^2 * b_4 + - 36 * a_21^2 * a_41 * a_42 * a_43 * b_4 + - 18 * a_21^2 * a_42^3 * b_4 + - 36 * a_21^2 * a_42^2 * a_43 * b_4 + - 18 * a_21^2 * a_42 * a_43^2 * b_4 + - 18 * a_21^2 * a_51^2 * a_52 * b_5 + - 36 * a_21^2 * a_51 * a_52^2 * b_5 + - 36 * a_21^2 * a_51 * a_52 * a_53 * b_5 + - 36 * a_21^2 * a_51 * a_52 * a_54 * b_5 + - 18 * a_21^2 * a_52^3 * b_5 + - 36 * a_21^2 * a_52^2 * a_53 * b_5 + - 36 * a_21^2 * a_52^2 * a_54 * b_5 + - 18 * a_21^2 * a_52 * a_53^2 * b_5 + - 36 * a_21^2 * a_52 * a_53 * a_54 * b_5 + - 18 * a_21^2 * a_52 * a_54^2 * b_5 + - 18 * a_21^2 * a_61^2 * a_62 * b_6 + - 36 * a_21^2 * a_61 * a_62^2 * b_6 + - 36 * a_21^2 * a_61 * a_62 * a_63 * b_6 + - 36 * a_21^2 * a_61 * a_62 * a_64 * b_6 + - 36 * a_21^2 * a_61 * a_62 * a_65 * b_6 + - 18 * a_21^2 * a_62^3 * b_6 + - 36 * a_21^2 * a_62^2 * a_63 * b_6 + - 36 * a_21^2 * a_62^2 * a_64 * b_6 + - 36 * a_21^2 * a_62^2 * a_65 * b_6 + - 18 * a_21^2 * a_62 * a_63^2 * b_6 + - 36 * a_21^2 * a_62 * a_63 * a_64 * b_6 + - 36 * a_21^2 * a_62 * a_63 * a_65 * b_6 + - 18 * a_21^2 * a_62 * a_64^2 * b_6 + - 36 * a_21^2 * a_62 * a_64 * a_65 * b_6 + - 18 * a_21^2 * a_62 * a_65^2 * b_6 + - 18 * a_31^2 * a_41^2 * a_43 * b_4 + - 36 * a_31^2 * a_41 * a_42 * a_43 * b_4 + - 36 * a_31^2 * a_41 * a_43^2 * b_4 + - 18 * a_31^2 * a_42^2 * a_43 * b_4 + - 36 * a_31^2 * a_42 * a_43^2 * b_4 + - 18 * a_31^2 * a_43^3 * b_4 + - 18 * a_31^2 * a_51^2 * a_53 * b_5 + - 36 * a_31^2 * a_51 * a_52 * a_53 * b_5 + - 36 * a_31^2 * a_51 * a_53^2 * b_5 + - 36 * a_31^2 * a_51 * a_53 * a_54 * b_5 + - 18 * a_31^2 * a_52^2 * a_53 * b_5 + - 36 * a_31^2 * a_52 * a_53^2 * b_5 + - 36 * a_31^2 * a_52 * a_53 * a_54 * b_5 + - 18 * a_31^2 * a_53^3 * b_5 + - 36 * a_31^2 * a_53^2 * a_54 * b_5 + - 18 * a_31^2 * a_53 * a_54^2 * b_5 + - 18 * a_31^2 * a_61^2 * a_63 * b_6 + - 36 * a_31^2 * a_61 * a_62 * a_63 * b_6 + - 36 * a_31^2 * a_61 * a_63^2 * b_6 + - 36 * a_31^2 * a_61 * a_63 * a_64 * b_6 + - 36 * a_31^2 * a_61 * a_63 * a_65 * b_6 + - 18 * a_31^2 * a_62^2 * a_63 * b_6 + - 36 * a_31^2 * a_62 * a_63^2 * b_6 + - 36 * a_31^2 * a_62 * a_63 * a_64 * b_6 + - 36 * a_31^2 * a_62 * a_63 * a_65 * b_6 + - 18 * a_31^2 * a_63^3 * b_6 + - 36 * a_31^2 * a_63^2 * a_64 * b_6 + - 36 * a_31^2 * a_63^2 * a_65 * b_6 + - 18 * a_31^2 * a_63 * a_64^2 * b_6 + - 36 * a_31^2 * a_63 * a_64 * a_65 * b_6 + - 18 * a_31^2 * a_63 * a_65^2 * b_6 + - 36 * a_31 * a_32 * a_41^2 * a_43 * b_4 + - 72 * a_31 * a_32 * a_41 * a_42 * a_43 * b_4 + - 72 * a_31 * a_32 * a_41 * a_43^2 * b_4 + - 36 * a_31 * a_32 * a_42^2 * a_43 * b_4 + - 72 * a_31 * a_32 * a_42 * a_43^2 * b_4 + - 36 * a_31 * a_32 * a_43^3 * b_4 + - 36 * a_31 * a_32 * a_51^2 * a_53 * b_5 + - 72 * a_31 * a_32 * a_51 * a_52 * a_53 * b_5 + - 72 * a_31 * a_32 * a_51 * a_53^2 * b_5 + - 72 * a_31 * a_32 * a_51 * a_53 * a_54 * b_5 + - 36 * a_31 * a_32 * a_52^2 * a_53 * b_5 + - 72 * a_31 * a_32 * a_52 * a_53^2 * b_5 + - 72 * a_31 * a_32 * a_52 * a_53 * a_54 * b_5 + - 36 * a_31 * a_32 * a_53^3 * b_5 + - 72 * a_31 * a_32 * a_53^2 * a_54 * b_5 + - 36 * a_31 * a_32 * a_53 * a_54^2 * b_5 + - 36 * a_31 * a_32 * a_61^2 * a_63 * b_6 + - 72 * a_31 * a_32 * a_61 * a_62 * a_63 * b_6 + - 72 * a_31 * a_32 * a_61 * a_63^2 * b_6 + - 72 * a_31 * a_32 * a_61 * a_63 * a_64 * b_6 + - 72 * a_31 * a_32 * a_61 * a_63 * a_65 * b_6 + - 36 * a_31 * a_32 * a_62^2 * a_63 * b_6 + - 72 * a_31 * a_32 * a_62 * a_63^2 * b_6 + - 72 * a_31 * a_32 * a_62 * a_63 * a_64 * b_6 + - 72 * a_31 * a_32 * a_62 * a_63 * a_65 * b_6 + - 36 * a_31 * a_32 * a_63^3 * b_6 + - 72 * a_31 * a_32 * a_63^2 * a_64 * b_6 + - 72 * a_31 * a_32 * a_63^2 * a_65 * b_6 + - 36 * a_31 * a_32 * a_63 * a_64^2 * b_6 + - 72 * a_31 * a_32 * a_63 * a_64 * a_65 * b_6 + - 36 * a_31 * a_32 * a_63 * a_65^2 * b_6 + - 18 * a_32^2 * a_41^2 * a_43 * b_4 + - 36 * a_32^2 * a_41 * a_42 * a_43 * b_4 + - 36 * a_32^2 * a_41 * a_43^2 * b_4 + - 18 * a_32^2 * a_42^2 * a_43 * b_4 + - 36 * a_32^2 * a_42 * a_43^2 * b_4 + - 18 * a_32^2 * a_43^3 * b_4 + - 18 * a_32^2 * a_51^2 * a_53 * b_5 + - 36 * a_32^2 * a_51 * a_52 * a_53 * b_5 + - 36 * a_32^2 * a_51 * a_53^2 * b_5 + - 36 * a_32^2 * a_51 * a_53 * a_54 * b_5 + - 18 * a_32^2 * a_52^2 * a_53 * b_5 + - 36 * a_32^2 * a_52 * a_53^2 * b_5 + - 36 * a_32^2 * a_52 * a_53 * a_54 * b_5 + - 18 * a_32^2 * a_53^3 * b_5 + - 36 * a_32^2 * a_53^2 * a_54 * b_5 + - 18 * a_32^2 * a_53 * a_54^2 * b_5 + - 18 * a_32^2 * a_61^2 * a_63 * b_6 + - 36 * a_32^2 * a_61 * a_62 * a_63 * b_6 + - 36 * a_32^2 * a_61 * a_63^2 * b_6 + - 36 * a_32^2 * a_61 * a_63 * a_64 * b_6 + - 36 * a_32^2 * a_61 * a_63 * a_65 * b_6 + - 18 * a_32^2 * a_62^2 * a_63 * b_6 + - 36 * a_32^2 * a_62 * a_63^2 * b_6 + - 36 * a_32^2 * a_62 * a_63 * a_64 * b_6 + - 36 * a_32^2 * a_62 * a_63 * a_65 * b_6 + - 18 * a_32^2 * a_63^3 * b_6 + - 36 * a_32^2 * a_63^2 * a_64 * b_6 + - 36 * a_32^2 * a_63^2 * a_65 * b_6 + - 18 * a_32^2 * a_63 * a_64^2 * b_6 + - 36 * a_32^2 * a_63 * a_64 * a_65 * b_6 + - 18 * a_32^2 * a_63 * a_65^2 * b_6 + - 18 * a_41^2 * a_51^2 * a_54 * b_5 + - 36 * a_41^2 * a_51 * a_52 * a_54 * b_5 + - 36 * a_41^2 * a_51 * a_53 * a_54 * b_5 + - 36 * a_41^2 * a_51 * a_54^2 * b_5 + - 18 * a_41^2 * a_52^2 * a_54 * b_5 + - 36 * a_41^2 * a_52 * a_53 * a_54 * b_5 + - 36 * a_41^2 * a_52 * a_54^2 * b_5 + - 18 * a_41^2 * a_53^2 * a_54 * b_5 + - 36 * a_41^2 * a_53 * a_54^2 * b_5 + - 18 * a_41^2 * a_54^3 * b_5 + - 18 * a_41^2 * a_61^2 * a_64 * b_6 + - 36 * a_41^2 * a_61 * a_62 * a_64 * b_6 + - 36 * a_41^2 * a_61 * a_63 * a_64 * b_6 + - 36 * a_41^2 * a_61 * a_64^2 * b_6 + - 36 * a_41^2 * a_61 * a_64 * a_65 * b_6 + - 18 * a_41^2 * a_62^2 * a_64 * b_6 + - 36 * a_41^2 * a_62 * a_63 * a_64 * b_6 + - 36 * a_41^2 * a_62 * a_64^2 * b_6 + - 36 * a_41^2 * a_62 * a_64 * a_65 * b_6 + - 18 * a_41^2 * a_63^2 * a_64 * b_6 + - 36 * a_41^2 * a_63 * a_64^2 * b_6 + - 36 * a_41^2 * a_63 * a_64 * a_65 * b_6 + - 18 * a_41^2 * a_64^3 * b_6 + - 36 * a_41^2 * a_64^2 * a_65 * b_6 + - 18 * a_41^2 * a_64 * a_65^2 * b_6 + - 36 * a_41 * a_42 * a_51^2 * a_54 * b_5 + - 72 * a_41 * a_42 * a_51 * a_52 * a_54 * b_5 + - 72 * a_41 * a_42 * a_51 * a_53 * a_54 * b_5 + - 72 * a_41 * a_42 * a_51 * a_54^2 * b_5 + - 36 * a_41 * a_42 * a_52^2 * a_54 * b_5 + - 72 * a_41 * a_42 * a_52 * a_53 * a_54 * b_5 + - 72 * a_41 * a_42 * a_52 * a_54^2 * b_5 + - 36 * a_41 * a_42 * a_53^2 * a_54 * b_5 + - 72 * a_41 * a_42 * a_53 * a_54^2 * b_5 + - 36 * a_41 * a_42 * a_54^3 * b_5 + - 36 * a_41 * a_42 * a_61^2 * a_64 * b_6 + - 72 * a_41 * a_42 * a_61 * a_62 * a_64 * b_6 + - 72 * a_41 * a_42 * a_61 * a_63 * a_64 * b_6 + - 72 * a_41 * a_42 * a_61 * a_64^2 * b_6 + - 72 * a_41 * a_42 * a_61 * a_64 * a_65 * b_6 + - 36 * a_41 * a_42 * a_62^2 * a_64 * b_6 + - 72 * a_41 * a_42 * a_62 * a_63 * a_64 * b_6 + - 72 * a_41 * a_42 * a_62 * a_64^2 * b_6 + - 72 * a_41 * a_42 * a_62 * a_64 * a_65 * b_6 + - 36 * a_41 * a_42 * a_63^2 * a_64 * b_6 + - 72 * a_41 * a_42 * a_63 * a_64^2 * b_6 + - 72 * a_41 * a_42 * a_63 * a_64 * a_65 * b_6 + - 36 * a_41 * a_42 * a_64^3 * b_6 + - 72 * a_41 * a_42 * a_64^2 * a_65 * b_6 + - 36 * a_41 * a_42 * a_64 * a_65^2 * b_6 + - 36 * a_41 * a_43 * a_51^2 * a_54 * b_5 + - 72 * a_41 * a_43 * a_51 * a_52 * a_54 * b_5 + - 72 * a_41 * a_43 * a_51 * a_53 * a_54 * b_5 + - 72 * a_41 * a_43 * a_51 * a_54^2 * b_5 + - 36 * a_41 * a_43 * a_52^2 * a_54 * b_5 + - 72 * a_41 * a_43 * a_52 * a_53 * a_54 * b_5 + - 72 * a_41 * a_43 * a_52 * a_54^2 * b_5 + - 36 * a_41 * a_43 * a_53^2 * a_54 * b_5 + - 72 * a_41 * a_43 * a_53 * a_54^2 * b_5 + - 36 * a_41 * a_43 * a_54^3 * b_5 + - 36 * a_41 * a_43 * a_61^2 * a_64 * b_6 + - 72 * a_41 * a_43 * a_61 * a_62 * a_64 * b_6 + - 72 * a_41 * a_43 * a_61 * a_63 * a_64 * b_6 + - 72 * a_41 * a_43 * a_61 * a_64^2 * b_6 + - 72 * a_41 * a_43 * a_61 * a_64 * a_65 * b_6 + - 36 * a_41 * a_43 * a_62^2 * a_64 * b_6 + - 72 * a_41 * a_43 * a_62 * a_63 * a_64 * b_6 + - 72 * a_41 * a_43 * a_62 * a_64^2 * b_6 + - 72 * a_41 * a_43 * a_62 * a_64 * a_65 * b_6 + - 36 * a_41 * a_43 * a_63^2 * a_64 * b_6 + - 72 * a_41 * a_43 * a_63 * a_64^2 * b_6 + - 72 * a_41 * a_43 * a_63 * a_64 * a_65 * b_6 + - 36 * a_41 * a_43 * a_64^3 * b_6 + - 72 * a_41 * a_43 * a_64^2 * a_65 * b_6 + - 36 * a_41 * a_43 * a_64 * a_65^2 * b_6 + - 18 * a_42^2 * a_51^2 * a_54 * b_5 + - 36 * a_42^2 * a_51 * a_52 * a_54 * b_5 + - 36 * a_42^2 * a_51 * a_53 * a_54 * b_5 + - 36 * a_42^2 * a_51 * a_54^2 * b_5 + - 18 * a_42^2 * a_52^2 * a_54 * b_5 + - 36 * a_42^2 * a_52 * a_53 * a_54 * b_5 + - 36 * a_42^2 * a_52 * a_54^2 * b_5 + - 18 * a_42^2 * a_53^2 * a_54 * b_5 + - 36 * a_42^2 * a_53 * a_54^2 * b_5 + - 18 * a_42^2 * a_54^3 * b_5 + - 18 * a_42^2 * a_61^2 * a_64 * b_6 + - 36 * a_42^2 * a_61 * a_62 * a_64 * b_6 + - 36 * a_42^2 * a_61 * a_63 * a_64 * b_6 + - 36 * a_42^2 * a_61 * a_64^2 * b_6 + - 36 * a_42^2 * a_61 * a_64 * a_65 * b_6 + - 18 * a_42^2 * a_62^2 * a_64 * b_6 + - 36 * a_42^2 * a_62 * a_63 * a_64 * b_6 + - 36 * a_42^2 * a_62 * a_64^2 * b_6 + - 36 * a_42^2 * a_62 * a_64 * a_65 * b_6 + - 18 * a_42^2 * a_63^2 * a_64 * b_6 + - 36 * a_42^2 * a_63 * a_64^2 * b_6 + - 36 * a_42^2 * a_63 * a_64 * a_65 * b_6 + - 18 * a_42^2 * a_64^3 * b_6 + - 36 * a_42^2 * a_64^2 * a_65 * b_6 + - 18 * a_42^2 * a_64 * a_65^2 * b_6 + - 36 * a_42 * a_43 * a_51^2 * a_54 * b_5 + - 72 * a_42 * a_43 * a_51 * a_52 * a_54 * b_5 + - 72 * a_42 * a_43 * a_51 * a_53 * a_54 * b_5 + - 72 * a_42 * a_43 * a_51 * a_54^2 * b_5 + - 36 * a_42 * a_43 * a_52^2 * a_54 * b_5 + - 72 * a_42 * a_43 * a_52 * a_53 * a_54 * b_5 + - 72 * a_42 * a_43 * a_52 * a_54^2 * b_5 + - 36 * a_42 * a_43 * a_53^2 * a_54 * b_5 + - 72 * a_42 * a_43 * a_53 * a_54^2 * b_5 + - 36 * a_42 * a_43 * a_54^3 * b_5 + - 36 * a_42 * a_43 * a_61^2 * a_64 * b_6 + - 72 * a_42 * a_43 * a_61 * a_62 * a_64 * b_6 + - 72 * a_42 * a_43 * a_61 * a_63 * a_64 * b_6 + - 72 * a_42 * a_43 * a_61 * a_64^2 * b_6 + - 72 * a_42 * a_43 * a_61 * a_64 * a_65 * b_6 + - 36 * a_42 * a_43 * a_62^2 * a_64 * b_6 + - 72 * a_42 * a_43 * a_62 * a_63 * a_64 * b_6 + - 72 * a_42 * a_43 * a_62 * a_64^2 * b_6 + - 72 * a_42 * a_43 * a_62 * a_64 * a_65 * b_6 + - 36 * a_42 * a_43 * a_63^2 * a_64 * b_6 + - 72 * a_42 * a_43 * a_63 * a_64^2 * b_6 + - 72 * a_42 * a_43 * a_63 * a_64 * a_65 * b_6 + - 36 * a_42 * a_43 * a_64^3 * b_6 + - 72 * a_42 * a_43 * a_64^2 * a_65 * b_6 + - 36 * a_42 * a_43 * a_64 * a_65^2 * b_6 + - 18 * a_43^2 * a_51^2 * a_54 * b_5 + - 36 * a_43^2 * a_51 * a_52 * a_54 * b_5 + - 36 * a_43^2 * a_51 * a_53 * a_54 * b_5 + - 36 * a_43^2 * a_51 * a_54^2 * b_5 + - 18 * a_43^2 * a_52^2 * a_54 * b_5 + - 36 * a_43^2 * a_52 * a_53 * a_54 * b_5 + - 36 * a_43^2 * a_52 * a_54^2 * b_5 + - 18 * a_43^2 * a_53^2 * a_54 * b_5 + - 36 * a_43^2 * a_53 * a_54^2 * b_5 + - 18 * a_43^2 * a_54^3 * b_5 + - 18 * a_43^2 * a_61^2 * a_64 * b_6 + - 36 * a_43^2 * a_61 * a_62 * a_64 * b_6 + - 36 * a_43^2 * a_61 * a_63 * a_64 * b_6 + - 36 * a_43^2 * a_61 * a_64^2 * b_6 + - 36 * a_43^2 * a_61 * a_64 * a_65 * b_6 + - 18 * a_43^2 * a_62^2 * a_64 * b_6 + - 36 * a_43^2 * a_62 * a_63 * a_64 * b_6 + - 36 * a_43^2 * a_62 * a_64^2 * b_6 + - 36 * a_43^2 * a_62 * a_64 * a_65 * b_6 + - 18 * a_43^2 * a_63^2 * a_64 * b_6 + - 36 * a_43^2 * a_63 * a_64^2 * b_6 + - 36 * a_43^2 * a_63 * a_64 * a_65 * b_6 + - 18 * a_43^2 * a_64^3 * b_6 + - 36 * a_43^2 * a_64^2 * a_65 * b_6 + - 18 * a_43^2 * a_64 * a_65^2 * b_6 + - 18 * a_51^2 * a_61^2 * a_65 * b_6 + - 36 * a_51^2 * a_61 * a_62 * a_65 * b_6 + - 36 * a_51^2 * a_61 * a_63 * a_65 * b_6 + - 36 * a_51^2 * a_61 * a_64 * a_65 * b_6 + - 36 * a_51^2 * a_61 * a_65^2 * b_6 + - 18 * a_51^2 * a_62^2 * a_65 * b_6 + - 36 * a_51^2 * a_62 * a_63 * a_65 * b_6 + - 36 * a_51^2 * a_62 * a_64 * a_65 * b_6 + - 36 * a_51^2 * a_62 * a_65^2 * b_6 + - 18 * a_51^2 * a_63^2 * a_65 * b_6 + - 36 * a_51^2 * a_63 * a_64 * a_65 * b_6 + - 36 * a_51^2 * a_63 * a_65^2 * b_6 + - 18 * a_51^2 * a_64^2 * a_65 * b_6 + - 36 * a_51^2 * a_64 * a_65^2 * b_6 + - 18 * a_51^2 * a_65^3 * b_6 + - 36 * a_51 * a_52 * a_61^2 * a_65 * b_6 + - 72 * a_51 * a_52 * a_61 * a_62 * a_65 * b_6 + - 72 * a_51 * a_52 * a_61 * a_63 * a_65 * b_6 + - 72 * a_51 * a_52 * a_61 * a_64 * a_65 * b_6 + - 72 * a_51 * a_52 * a_61 * a_65^2 * b_6 + - 36 * a_51 * a_52 * a_62^2 * a_65 * b_6 + - 72 * a_51 * a_52 * a_62 * a_63 * a_65 * b_6 + - 72 * a_51 * a_52 * a_62 * a_64 * a_65 * b_6 + - 72 * a_51 * a_52 * a_62 * a_65^2 * b_6 + - 36 * a_51 * a_52 * a_63^2 * a_65 * b_6 + - 72 * a_51 * a_52 * a_63 * a_64 * a_65 * b_6 + - 72 * a_51 * a_52 * a_63 * a_65^2 * b_6 + - 36 * a_51 * a_52 * a_64^2 * a_65 * b_6 + - 72 * a_51 * a_52 * a_64 * a_65^2 * b_6 + - 36 * a_51 * a_52 * a_65^3 * b_6 + - 36 * a_51 * a_53 * a_61^2 * a_65 * b_6 + - 72 * a_51 * a_53 * a_61 * a_62 * a_65 * b_6 + - 72 * a_51 * a_53 * a_61 * a_63 * a_65 * b_6 + - 72 * a_51 * a_53 * a_61 * a_64 * a_65 * b_6 + - 72 * a_51 * a_53 * a_61 * a_65^2 * b_6 + - 36 * a_51 * a_53 * a_62^2 * a_65 * b_6 + - 72 * a_51 * a_53 * a_62 * a_63 * a_65 * b_6 + - 72 * a_51 * a_53 * a_62 * a_64 * a_65 * b_6 + - 72 * a_51 * a_53 * a_62 * a_65^2 * b_6 + - 36 * a_51 * a_53 * a_63^2 * a_65 * b_6 + - 72 * a_51 * a_53 * a_63 * a_64 * a_65 * b_6 + - 72 * a_51 * a_53 * a_63 * a_65^2 * b_6 + - 36 * a_51 * a_53 * a_64^2 * a_65 * b_6 + - 72 * a_51 * a_53 * a_64 * a_65^2 * b_6 + - 36 * a_51 * a_53 * a_65^3 * b_6 + - 36 * a_51 * a_54 * a_61^2 * a_65 * b_6 + - 72 * a_51 * a_54 * a_61 * a_62 * a_65 * b_6 + - 72 * a_51 * a_54 * a_61 * a_63 * a_65 * b_6 + - 72 * a_51 * a_54 * a_61 * a_64 * a_65 * b_6 + - 72 * a_51 * a_54 * a_61 * a_65^2 * b_6 + - 36 * a_51 * a_54 * a_62^2 * a_65 * b_6 + - 72 * a_51 * a_54 * a_62 * a_63 * a_65 * b_6 + - 72 * a_51 * a_54 * a_62 * a_64 * a_65 * b_6 + - 72 * a_51 * a_54 * a_62 * a_65^2 * b_6 + - 36 * a_51 * a_54 * a_63^2 * a_65 * b_6 + - 72 * a_51 * a_54 * a_63 * a_64 * a_65 * b_6 + - 72 * a_51 * a_54 * a_63 * a_65^2 * b_6 + - 36 * a_51 * a_54 * a_64^2 * a_65 * b_6 + - 72 * a_51 * a_54 * a_64 * a_65^2 * b_6 + - 36 * a_51 * a_54 * a_65^3 * b_6 + - 18 * a_52^2 * a_61^2 * a_65 * b_6 + - 36 * a_52^2 * a_61 * a_62 * a_65 * b_6 + - 36 * a_52^2 * a_61 * a_63 * a_65 * b_6 + - 36 * a_52^2 * a_61 * a_64 * a_65 * b_6 + - 36 * a_52^2 * a_61 * a_65^2 * b_6 + - 18 * a_52^2 * a_62^2 * a_65 * b_6 + - 36 * a_52^2 * a_62 * a_63 * a_65 * b_6 + - 36 * a_52^2 * a_62 * a_64 * a_65 * b_6 + - 36 * a_52^2 * a_62 * a_65^2 * b_6 + - 18 * a_52^2 * a_63^2 * a_65 * b_6 + - 36 * a_52^2 * a_63 * a_64 * a_65 * b_6 + - 36 * a_52^2 * a_63 * a_65^2 * b_6 + - 18 * a_52^2 * a_64^2 * a_65 * b_6 + - 36 * a_52^2 * a_64 * a_65^2 * b_6 + - 18 * a_52^2 * a_65^3 * b_6 + - 36 * a_52 * a_53 * a_61^2 * a_65 * b_6 + - 72 * a_52 * a_53 * a_61 * a_62 * a_65 * b_6 + - 72 * a_52 * a_53 * a_61 * a_63 * a_65 * b_6 + - 72 * a_52 * a_53 * a_61 * a_64 * a_65 * b_6 + - 72 * a_52 * a_53 * a_61 * a_65^2 * b_6 + - 36 * a_52 * a_53 * a_62^2 * a_65 * b_6 + - 72 * a_52 * a_53 * a_62 * a_63 * a_65 * b_6 + - 72 * a_52 * a_53 * a_62 * a_64 * a_65 * b_6 + - 72 * a_52 * a_53 * a_62 * a_65^2 * b_6 + - 36 * a_52 * a_53 * a_63^2 * a_65 * b_6 + - 72 * a_52 * a_53 * a_63 * a_64 * a_65 * b_6 + - 72 * a_52 * a_53 * a_63 * a_65^2 * b_6 + - 36 * a_52 * a_53 * a_64^2 * a_65 * b_6 + - 72 * a_52 * a_53 * a_64 * a_65^2 * b_6 + - 36 * a_52 * a_53 * a_65^3 * b_6 + - 36 * a_52 * a_54 * a_61^2 * a_65 * b_6 + - 72 * a_52 * a_54 * a_61 * a_62 * a_65 * b_6 + - 72 * a_52 * a_54 * a_61 * a_63 * a_65 * b_6 + - 72 * a_52 * a_54 * a_61 * a_64 * a_65 * b_6 + - 72 * a_52 * a_54 * a_61 * a_65^2 * b_6 + - 36 * a_52 * a_54 * a_62^2 * a_65 * b_6 + - 72 * a_52 * a_54 * a_62 * a_63 * a_65 * b_6 + - 72 * a_52 * a_54 * a_62 * a_64 * a_65 * b_6 + - 72 * a_52 * a_54 * a_62 * a_65^2 * b_6 + - 36 * a_52 * a_54 * a_63^2 * a_65 * b_6 + - 72 * a_52 * a_54 * a_63 * a_64 * a_65 * b_6 + - 72 * a_52 * a_54 * a_63 * a_65^2 * b_6 + - 36 * a_52 * a_54 * a_64^2 * a_65 * b_6 + - 72 * a_52 * a_54 * a_64 * a_65^2 * b_6 + - 36 * a_52 * a_54 * a_65^3 * b_6 + - 18 * a_53^2 * a_61^2 * a_65 * b_6 + - 36 * a_53^2 * a_61 * a_62 * a_65 * b_6 + - 36 * a_53^2 * a_61 * a_63 * a_65 * b_6 + - 36 * a_53^2 * a_61 * a_64 * a_65 * b_6 + - 36 * a_53^2 * a_61 * a_65^2 * b_6 + - 18 * a_53^2 * a_62^2 * a_65 * b_6 + - 36 * a_53^2 * a_62 * a_63 * a_65 * b_6 + - 36 * a_53^2 * a_62 * a_64 * a_65 * b_6 + - 36 * a_53^2 * a_62 * a_65^2 * b_6 + - 18 * a_53^2 * a_63^2 * a_65 * b_6 + - 36 * a_53^2 * a_63 * a_64 * a_65 * b_6 + - 36 * a_53^2 * a_63 * a_65^2 * b_6 + - 18 * a_53^2 * a_64^2 * a_65 * b_6 + - 36 * a_53^2 * a_64 * a_65^2 * b_6 + - 18 * a_53^2 * a_65^3 * b_6 + - 36 * a_53 * a_54 * a_61^2 * a_65 * b_6 + - 72 * a_53 * a_54 * a_61 * a_62 * a_65 * b_6 + - 72 * a_53 * a_54 * a_61 * a_63 * a_65 * b_6 + - 72 * a_53 * a_54 * a_61 * a_64 * a_65 * b_6 + - 72 * a_53 * a_54 * a_61 * a_65^2 * b_6 + - 36 * a_53 * a_54 * a_62^2 * a_65 * b_6 + - 72 * a_53 * a_54 * a_62 * a_63 * a_65 * b_6 + - 72 * a_53 * a_54 * a_62 * a_64 * a_65 * b_6 + - 72 * a_53 * a_54 * a_62 * a_65^2 * b_6 + - 36 * a_53 * a_54 * a_63^2 * a_65 * b_6 + - 72 * a_53 * a_54 * a_63 * a_64 * a_65 * b_6 + - 72 * a_53 * a_54 * a_63 * a_65^2 * b_6 + - 36 * a_53 * a_54 * a_64^2 * a_65 * b_6 + - 72 * a_53 * a_54 * a_64 * a_65^2 * b_6 + - 36 * a_53 * a_54 * a_65^3 * b_6 + - 18 * a_54^2 * a_61^2 * a_65 * b_6 + - 36 * a_54^2 * a_61 * a_62 * a_65 * b_6 + - 36 * a_54^2 * a_61 * a_63 * a_65 * b_6 + - 36 * a_54^2 * a_61 * a_64 * a_65 * b_6 + - 36 * a_54^2 * a_61 * a_65^2 * b_6 + - 18 * a_54^2 * a_62^2 * a_65 * b_6 + - 36 * a_54^2 * a_62 * a_63 * a_65 * b_6 + - 36 * a_54^2 * a_62 * a_64 * a_65 * b_6 + - 36 * a_54^2 * a_62 * a_65^2 * b_6 + - 18 * a_54^2 * a_63^2 * a_65 * b_6 + - 36 * a_54^2 * a_63 * a_64 * a_65 * b_6 + - 36 * a_54^2 * a_63 * a_65^2 * b_6 + - 18 * a_54^2 * a_64^2 * a_65 * b_6 + - 36 * a_54^2 * a_64 * a_65^2 * b_6 + - 18 * a_54^2 * a_65^3 * b_6 - 1, - 24 * a_21^2 * a_31 * a_32^2 * b_3 + - 24 * a_21^2 * a_32^3 * b_3 + - 24 * a_21^2 * a_41 * a_42^2 * b_4 + - 24 * a_21^2 * a_42^3 * b_4 + - 24 * a_21^2 * a_42^2 * a_43 * b_4 + - 24 * a_21^2 * a_51 * a_52^2 * b_5 + - 24 * a_21^2 * a_52^3 * b_5 + - 24 * a_21^2 * a_52^2 * a_53 * b_5 + - 24 * a_21^2 * a_52^2 * a_54 * b_5 + - 24 * a_21^2 * a_61 * a_62^2 * b_6 + - 24 * a_21^2 * a_62^3 * b_6 + - 24 * a_21^2 * a_62^2 * a_63 * b_6 + - 24 * a_21^2 * a_62^2 * a_64 * b_6 + - 24 * a_21^2 * a_62^2 * a_65 * b_6 + - 48 * a_21 * a_31 * a_41 * a_42 * a_43 * b_4 + - 48 * a_21 * a_31 * a_42^2 * a_43 * b_4 + - 48 * a_21 * a_31 * a_42 * a_43^2 * b_4 + - 48 * a_21 * a_31 * a_51 * a_52 * a_53 * b_5 + - 48 * a_21 * a_31 * a_52^2 * a_53 * b_5 + - 48 * a_21 * a_31 * a_52 * a_53^2 * b_5 + - 48 * a_21 * a_31 * a_52 * a_53 * a_54 * b_5 + - 48 * a_21 * a_31 * a_61 * a_62 * a_63 * b_6 + - 48 * a_21 * a_31 * a_62^2 * a_63 * b_6 + - 48 * a_21 * a_31 * a_62 * a_63^2 * b_6 + - 48 * a_21 * a_31 * a_62 * a_63 * a_64 * b_6 + - 48 * a_21 * a_31 * a_62 * a_63 * a_65 * b_6 + - 48 * a_21 * a_32 * a_41 * a_42 * a_43 * b_4 + - 48 * a_21 * a_32 * a_42^2 * a_43 * b_4 + - 48 * a_21 * a_32 * a_42 * a_43^2 * b_4 + - 48 * a_21 * a_32 * a_51 * a_52 * a_53 * b_5 + - 48 * a_21 * a_32 * a_52^2 * a_53 * b_5 + - 48 * a_21 * a_32 * a_52 * a_53^2 * b_5 + - 48 * a_21 * a_32 * a_52 * a_53 * a_54 * b_5 + - 48 * a_21 * a_32 * a_61 * a_62 * a_63 * b_6 + - 48 * a_21 * a_32 * a_62^2 * a_63 * b_6 + - 48 * a_21 * a_32 * a_62 * a_63^2 * b_6 + - 48 * a_21 * a_32 * a_62 * a_63 * a_64 * b_6 + - 48 * a_21 * a_32 * a_62 * a_63 * a_65 * b_6 + - 48 * a_21 * a_41 * a_51 * a_52 * a_54 * b_5 + - 48 * a_21 * a_41 * a_52^2 * a_54 * b_5 + - 48 * a_21 * a_41 * a_52 * a_53 * a_54 * b_5 + - 48 * a_21 * a_41 * a_52 * a_54^2 * b_5 + - 48 * a_21 * a_41 * a_61 * a_62 * a_64 * b_6 + - 48 * a_21 * a_41 * a_62^2 * a_64 * b_6 + - 48 * a_21 * a_41 * a_62 * a_63 * a_64 * b_6 + - 48 * a_21 * a_41 * a_62 * a_64^2 * b_6 + - 48 * a_21 * a_41 * a_62 * a_64 * a_65 * b_6 + - 48 * a_21 * a_42 * a_51 * a_52 * a_54 * b_5 + - 48 * a_21 * a_42 * a_52^2 * a_54 * b_5 + - 48 * a_21 * a_42 * a_52 * a_53 * a_54 * b_5 + - 48 * a_21 * a_42 * a_52 * a_54^2 * b_5 + - 48 * a_21 * a_42 * a_61 * a_62 * a_64 * b_6 + - 48 * a_21 * a_42 * a_62^2 * a_64 * b_6 + - 48 * a_21 * a_42 * a_62 * a_63 * a_64 * b_6 + - 48 * a_21 * a_42 * a_62 * a_64^2 * b_6 + - 48 * a_21 * a_42 * a_62 * a_64 * a_65 * b_6 + - 48 * a_21 * a_43 * a_51 * a_52 * a_54 * b_5 + - 48 * a_21 * a_43 * a_52^2 * a_54 * b_5 + - 48 * a_21 * a_43 * a_52 * a_53 * a_54 * b_5 + - 48 * a_21 * a_43 * a_52 * a_54^2 * b_5 + - 48 * a_21 * a_43 * a_61 * a_62 * a_64 * b_6 + - 48 * a_21 * a_43 * a_62^2 * a_64 * b_6 + - 48 * a_21 * a_43 * a_62 * a_63 * a_64 * b_6 + - 48 * a_21 * a_43 * a_62 * a_64^2 * b_6 + - 48 * a_21 * a_43 * a_62 * a_64 * a_65 * b_6 + - 48 * a_21 * a_51 * a_61 * a_62 * a_65 * b_6 + - 48 * a_21 * a_51 * a_62^2 * a_65 * b_6 + - 48 * a_21 * a_51 * a_62 * a_63 * a_65 * b_6 + - 48 * a_21 * a_51 * a_62 * a_64 * a_65 * b_6 + - 48 * a_21 * a_51 * a_62 * a_65^2 * b_6 + - 48 * a_21 * a_52 * a_61 * a_62 * a_65 * b_6 + - 48 * a_21 * a_52 * a_62^2 * a_65 * b_6 + - 48 * a_21 * a_52 * a_62 * a_63 * a_65 * b_6 + - 48 * a_21 * a_52 * a_62 * a_64 * a_65 * b_6 + - 48 * a_21 * a_52 * a_62 * a_65^2 * b_6 + - 48 * a_21 * a_53 * a_61 * a_62 * a_65 * b_6 + - 48 * a_21 * a_53 * a_62^2 * a_65 * b_6 + - 48 * a_21 * a_53 * a_62 * a_63 * a_65 * b_6 + - 48 * a_21 * a_53 * a_62 * a_64 * a_65 * b_6 + - 48 * a_21 * a_53 * a_62 * a_65^2 * b_6 + - 48 * a_21 * a_54 * a_61 * a_62 * a_65 * b_6 + - 48 * a_21 * a_54 * a_62^2 * a_65 * b_6 + - 48 * a_21 * a_54 * a_62 * a_63 * a_65 * b_6 + - 48 * a_21 * a_54 * a_62 * a_64 * a_65 * b_6 + - 48 * a_21 * a_54 * a_62 * a_65^2 * b_6 + - 24 * a_31^2 * a_41 * a_43^2 * b_4 + - 24 * a_31^2 * a_42 * a_43^2 * b_4 + - 24 * a_31^2 * a_43^3 * b_4 + - 24 * a_31^2 * a_51 * a_53^2 * b_5 + - 24 * a_31^2 * a_52 * a_53^2 * b_5 + - 24 * a_31^2 * a_53^3 * b_5 + - 24 * a_31^2 * a_53^2 * a_54 * b_5 + - 24 * a_31^2 * a_61 * a_63^2 * b_6 + - 24 * a_31^2 * a_62 * a_63^2 * b_6 + - 24 * a_31^2 * a_63^3 * b_6 + - 24 * a_31^2 * a_63^2 * a_64 * b_6 + - 24 * a_31^2 * a_63^2 * a_65 * b_6 + - 48 * a_31 * a_32 * a_41 * a_43^2 * b_4 + - 48 * a_31 * a_32 * a_42 * a_43^2 * b_4 + - 48 * a_31 * a_32 * a_43^3 * b_4 + - 48 * a_31 * a_32 * a_51 * a_53^2 * b_5 + - 48 * a_31 * a_32 * a_52 * a_53^2 * b_5 + - 48 * a_31 * a_32 * a_53^3 * b_5 + - 48 * a_31 * a_32 * a_53^2 * a_54 * b_5 + - 48 * a_31 * a_32 * a_61 * a_63^2 * b_6 + - 48 * a_31 * a_32 * a_62 * a_63^2 * b_6 + - 48 * a_31 * a_32 * a_63^3 * b_6 + - 48 * a_31 * a_32 * a_63^2 * a_64 * b_6 + - 48 * a_31 * a_32 * a_63^2 * a_65 * b_6 + - 48 * a_31 * a_41 * a_51 * a_53 * a_54 * b_5 + - 48 * a_31 * a_41 * a_52 * a_53 * a_54 * b_5 + - 48 * a_31 * a_41 * a_53^2 * a_54 * b_5 + - 48 * a_31 * a_41 * a_53 * a_54^2 * b_5 + - 48 * a_31 * a_41 * a_61 * a_63 * a_64 * b_6 + - 48 * a_31 * a_41 * a_62 * a_63 * a_64 * b_6 + - 48 * a_31 * a_41 * a_63^2 * a_64 * b_6 + - 48 * a_31 * a_41 * a_63 * a_64^2 * b_6 + - 48 * a_31 * a_41 * a_63 * a_64 * a_65 * b_6 + - 48 * a_31 * a_42 * a_51 * a_53 * a_54 * b_5 + - 48 * a_31 * a_42 * a_52 * a_53 * a_54 * b_5 + - 48 * a_31 * a_42 * a_53^2 * a_54 * b_5 + - 48 * a_31 * a_42 * a_53 * a_54^2 * b_5 + - 48 * a_31 * a_42 * a_61 * a_63 * a_64 * b_6 + - 48 * a_31 * a_42 * a_62 * a_63 * a_64 * b_6 + - 48 * a_31 * a_42 * a_63^2 * a_64 * b_6 + - 48 * a_31 * a_42 * a_63 * a_64^2 * b_6 + - 48 * a_31 * a_42 * a_63 * a_64 * a_65 * b_6 + - 48 * a_31 * a_43 * a_51 * a_53 * a_54 * b_5 + - 48 * a_31 * a_43 * a_52 * a_53 * a_54 * b_5 + - 48 * a_31 * a_43 * a_53^2 * a_54 * b_5 + - 48 * a_31 * a_43 * a_53 * a_54^2 * b_5 + - 48 * a_31 * a_43 * a_61 * a_63 * a_64 * b_6 + - 48 * a_31 * a_43 * a_62 * a_63 * a_64 * b_6 + - 48 * a_31 * a_43 * a_63^2 * a_64 * b_6 + - 48 * a_31 * a_43 * a_63 * a_64^2 * b_6 + - 48 * a_31 * a_43 * a_63 * a_64 * a_65 * b_6 + - 48 * a_31 * a_51 * a_61 * a_63 * a_65 * b_6 + - 48 * a_31 * a_51 * a_62 * a_63 * a_65 * b_6 + - 48 * a_31 * a_51 * a_63^2 * a_65 * b_6 + - 48 * a_31 * a_51 * a_63 * a_64 * a_65 * b_6 + - 48 * a_31 * a_51 * a_63 * a_65^2 * b_6 + - 48 * a_31 * a_52 * a_61 * a_63 * a_65 * b_6 + - 48 * a_31 * a_52 * a_62 * a_63 * a_65 * b_6 + - 48 * a_31 * a_52 * a_63^2 * a_65 * b_6 + - 48 * a_31 * a_52 * a_63 * a_64 * a_65 * b_6 + - 48 * a_31 * a_52 * a_63 * a_65^2 * b_6 + - 48 * a_31 * a_53 * a_61 * a_63 * a_65 * b_6 + - 48 * a_31 * a_53 * a_62 * a_63 * a_65 * b_6 + - 48 * a_31 * a_53 * a_63^2 * a_65 * b_6 + - 48 * a_31 * a_53 * a_63 * a_64 * a_65 * b_6 + - 48 * a_31 * a_53 * a_63 * a_65^2 * b_6 + - 48 * a_31 * a_54 * a_61 * a_63 * a_65 * b_6 + - 48 * a_31 * a_54 * a_62 * a_63 * a_65 * b_6 + - 48 * a_31 * a_54 * a_63^2 * a_65 * b_6 + - 48 * a_31 * a_54 * a_63 * a_64 * a_65 * b_6 + - 48 * a_31 * a_54 * a_63 * a_65^2 * b_6 + - 24 * a_32^2 * a_41 * a_43^2 * b_4 + - 24 * a_32^2 * a_42 * a_43^2 * b_4 + - 24 * a_32^2 * a_43^3 * b_4 + - 24 * a_32^2 * a_51 * a_53^2 * b_5 + - 24 * a_32^2 * a_52 * a_53^2 * b_5 + - 24 * a_32^2 * a_53^3 * b_5 + - 24 * a_32^2 * a_53^2 * a_54 * b_5 + - 24 * a_32^2 * a_61 * a_63^2 * b_6 + - 24 * a_32^2 * a_62 * a_63^2 * b_6 + - 24 * a_32^2 * a_63^3 * b_6 + - 24 * a_32^2 * a_63^2 * a_64 * b_6 + - 24 * a_32^2 * a_63^2 * a_65 * b_6 + - 48 * a_32 * a_41 * a_51 * a_53 * a_54 * b_5 + - 48 * a_32 * a_41 * a_52 * a_53 * a_54 * b_5 + - 48 * a_32 * a_41 * a_53^2 * a_54 * b_5 + - 48 * a_32 * a_41 * a_53 * a_54^2 * b_5 + - 48 * a_32 * a_41 * a_61 * a_63 * a_64 * b_6 + - 48 * a_32 * a_41 * a_62 * a_63 * a_64 * b_6 + - 48 * a_32 * a_41 * a_63^2 * a_64 * b_6 + - 48 * a_32 * a_41 * a_63 * a_64^2 * b_6 + - 48 * a_32 * a_41 * a_63 * a_64 * a_65 * b_6 + - 48 * a_32 * a_42 * a_51 * a_53 * a_54 * b_5 + - 48 * a_32 * a_42 * a_52 * a_53 * a_54 * b_5 + - 48 * a_32 * a_42 * a_53^2 * a_54 * b_5 + - 48 * a_32 * a_42 * a_53 * a_54^2 * b_5 + - 48 * a_32 * a_42 * a_61 * a_63 * a_64 * b_6 + - 48 * a_32 * a_42 * a_62 * a_63 * a_64 * b_6 + - 48 * a_32 * a_42 * a_63^2 * a_64 * b_6 + - 48 * a_32 * a_42 * a_63 * a_64^2 * b_6 + - 48 * a_32 * a_42 * a_63 * a_64 * a_65 * b_6 + - 48 * a_32 * a_43 * a_51 * a_53 * a_54 * b_5 + - 48 * a_32 * a_43 * a_52 * a_53 * a_54 * b_5 + - 48 * a_32 * a_43 * a_53^2 * a_54 * b_5 + - 48 * a_32 * a_43 * a_53 * a_54^2 * b_5 + - 48 * a_32 * a_43 * a_61 * a_63 * a_64 * b_6 + - 48 * a_32 * a_43 * a_62 * a_63 * a_64 * b_6 + - 48 * a_32 * a_43 * a_63^2 * a_64 * b_6 + - 48 * a_32 * a_43 * a_63 * a_64^2 * b_6 + - 48 * a_32 * a_43 * a_63 * a_64 * a_65 * b_6 + - 48 * a_32 * a_51 * a_61 * a_63 * a_65 * b_6 + - 48 * a_32 * a_51 * a_62 * a_63 * a_65 * b_6 + - 48 * a_32 * a_51 * a_63^2 * a_65 * b_6 + - 48 * a_32 * a_51 * a_63 * a_64 * a_65 * b_6 + - 48 * a_32 * a_51 * a_63 * a_65^2 * b_6 + - 48 * a_32 * a_52 * a_61 * a_63 * a_65 * b_6 + - 48 * a_32 * a_52 * a_62 * a_63 * a_65 * b_6 + - 48 * a_32 * a_52 * a_63^2 * a_65 * b_6 + - 48 * a_32 * a_52 * a_63 * a_64 * a_65 * b_6 + - 48 * a_32 * a_52 * a_63 * a_65^2 * b_6 + - 48 * a_32 * a_53 * a_61 * a_63 * a_65 * b_6 + - 48 * a_32 * a_53 * a_62 * a_63 * a_65 * b_6 + - 48 * a_32 * a_53 * a_63^2 * a_65 * b_6 + - 48 * a_32 * a_53 * a_63 * a_64 * a_65 * b_6 + - 48 * a_32 * a_53 * a_63 * a_65^2 * b_6 + - 48 * a_32 * a_54 * a_61 * a_63 * a_65 * b_6 + - 48 * a_32 * a_54 * a_62 * a_63 * a_65 * b_6 + - 48 * a_32 * a_54 * a_63^2 * a_65 * b_6 + - 48 * a_32 * a_54 * a_63 * a_64 * a_65 * b_6 + - 48 * a_32 * a_54 * a_63 * a_65^2 * b_6 + - 24 * a_41^2 * a_51 * a_54^2 * b_5 + - 24 * a_41^2 * a_52 * a_54^2 * b_5 + - 24 * a_41^2 * a_53 * a_54^2 * b_5 + - 24 * a_41^2 * a_54^3 * b_5 + - 24 * a_41^2 * a_61 * a_64^2 * b_6 + - 24 * a_41^2 * a_62 * a_64^2 * b_6 + - 24 * a_41^2 * a_63 * a_64^2 * b_6 + - 24 * a_41^2 * a_64^3 * b_6 + - 24 * a_41^2 * a_64^2 * a_65 * b_6 + - 48 * a_41 * a_42 * a_51 * a_54^2 * b_5 + - 48 * a_41 * a_42 * a_52 * a_54^2 * b_5 + - 48 * a_41 * a_42 * a_53 * a_54^2 * b_5 + - 48 * a_41 * a_42 * a_54^3 * b_5 + - 48 * a_41 * a_42 * a_61 * a_64^2 * b_6 + - 48 * a_41 * a_42 * a_62 * a_64^2 * b_6 + - 48 * a_41 * a_42 * a_63 * a_64^2 * b_6 + - 48 * a_41 * a_42 * a_64^3 * b_6 + - 48 * a_41 * a_42 * a_64^2 * a_65 * b_6 + - 48 * a_41 * a_43 * a_51 * a_54^2 * b_5 + - 48 * a_41 * a_43 * a_52 * a_54^2 * b_5 + - 48 * a_41 * a_43 * a_53 * a_54^2 * b_5 + - 48 * a_41 * a_43 * a_54^3 * b_5 + - 48 * a_41 * a_43 * a_61 * a_64^2 * b_6 + - 48 * a_41 * a_43 * a_62 * a_64^2 * b_6 + - 48 * a_41 * a_43 * a_63 * a_64^2 * b_6 + - 48 * a_41 * a_43 * a_64^3 * b_6 + - 48 * a_41 * a_43 * a_64^2 * a_65 * b_6 + - 48 * a_41 * a_51 * a_61 * a_64 * a_65 * b_6 + - 48 * a_41 * a_51 * a_62 * a_64 * a_65 * b_6 + - 48 * a_41 * a_51 * a_63 * a_64 * a_65 * b_6 + - 48 * a_41 * a_51 * a_64^2 * a_65 * b_6 + - 48 * a_41 * a_51 * a_64 * a_65^2 * b_6 + - 48 * a_41 * a_52 * a_61 * a_64 * a_65 * b_6 + - 48 * a_41 * a_52 * a_62 * a_64 * a_65 * b_6 + - 48 * a_41 * a_52 * a_63 * a_64 * a_65 * b_6 + - 48 * a_41 * a_52 * a_64^2 * a_65 * b_6 + - 48 * a_41 * a_52 * a_64 * a_65^2 * b_6 + - 48 * a_41 * a_53 * a_61 * a_64 * a_65 * b_6 + - 48 * a_41 * a_53 * a_62 * a_64 * a_65 * b_6 + - 48 * a_41 * a_53 * a_63 * a_64 * a_65 * b_6 + - 48 * a_41 * a_53 * a_64^2 * a_65 * b_6 + - 48 * a_41 * a_53 * a_64 * a_65^2 * b_6 + - 48 * a_41 * a_54 * a_61 * a_64 * a_65 * b_6 + - 48 * a_41 * a_54 * a_62 * a_64 * a_65 * b_6 + - 48 * a_41 * a_54 * a_63 * a_64 * a_65 * b_6 + - 48 * a_41 * a_54 * a_64^2 * a_65 * b_6 + - 48 * a_41 * a_54 * a_64 * a_65^2 * b_6 + - 24 * a_42^2 * a_51 * a_54^2 * b_5 + - 24 * a_42^2 * a_52 * a_54^2 * b_5 + - 24 * a_42^2 * a_53 * a_54^2 * b_5 + - 24 * a_42^2 * a_54^3 * b_5 + - 24 * a_42^2 * a_61 * a_64^2 * b_6 + - 24 * a_42^2 * a_62 * a_64^2 * b_6 + - 24 * a_42^2 * a_63 * a_64^2 * b_6 + - 24 * a_42^2 * a_64^3 * b_6 + - 24 * a_42^2 * a_64^2 * a_65 * b_6 + - 48 * a_42 * a_43 * a_51 * a_54^2 * b_5 + - 48 * a_42 * a_43 * a_52 * a_54^2 * b_5 + - 48 * a_42 * a_43 * a_53 * a_54^2 * b_5 + - 48 * a_42 * a_43 * a_54^3 * b_5 + - 48 * a_42 * a_43 * a_61 * a_64^2 * b_6 + - 48 * a_42 * a_43 * a_62 * a_64^2 * b_6 + - 48 * a_42 * a_43 * a_63 * a_64^2 * b_6 + - 48 * a_42 * a_43 * a_64^3 * b_6 + - 48 * a_42 * a_43 * a_64^2 * a_65 * b_6 + - 48 * a_42 * a_51 * a_61 * a_64 * a_65 * b_6 + - 48 * a_42 * a_51 * a_62 * a_64 * a_65 * b_6 + - 48 * a_42 * a_51 * a_63 * a_64 * a_65 * b_6 + - 48 * a_42 * a_51 * a_64^2 * a_65 * b_6 + - 48 * a_42 * a_51 * a_64 * a_65^2 * b_6 + - 48 * a_42 * a_52 * a_61 * a_64 * a_65 * b_6 + - 48 * a_42 * a_52 * a_62 * a_64 * a_65 * b_6 + - 48 * a_42 * a_52 * a_63 * a_64 * a_65 * b_6 + - 48 * a_42 * a_52 * a_64^2 * a_65 * b_6 + - 48 * a_42 * a_52 * a_64 * a_65^2 * b_6 + - 48 * a_42 * a_53 * a_61 * a_64 * a_65 * b_6 + - 48 * a_42 * a_53 * a_62 * a_64 * a_65 * b_6 + - 48 * a_42 * a_53 * a_63 * a_64 * a_65 * b_6 + - 48 * a_42 * a_53 * a_64^2 * a_65 * b_6 + - 48 * a_42 * a_53 * a_64 * a_65^2 * b_6 + - 48 * a_42 * a_54 * a_61 * a_64 * a_65 * b_6 + - 48 * a_42 * a_54 * a_62 * a_64 * a_65 * b_6 + - 48 * a_42 * a_54 * a_63 * a_64 * a_65 * b_6 + - 48 * a_42 * a_54 * a_64^2 * a_65 * b_6 + - 48 * a_42 * a_54 * a_64 * a_65^2 * b_6 + - 24 * a_43^2 * a_51 * a_54^2 * b_5 + - 24 * a_43^2 * a_52 * a_54^2 * b_5 + - 24 * a_43^2 * a_53 * a_54^2 * b_5 + - 24 * a_43^2 * a_54^3 * b_5 + - 24 * a_43^2 * a_61 * a_64^2 * b_6 + - 24 * a_43^2 * a_62 * a_64^2 * b_6 + - 24 * a_43^2 * a_63 * a_64^2 * b_6 + - 24 * a_43^2 * a_64^3 * b_6 + - 24 * a_43^2 * a_64^2 * a_65 * b_6 + - 48 * a_43 * a_51 * a_61 * a_64 * a_65 * b_6 + - 48 * a_43 * a_51 * a_62 * a_64 * a_65 * b_6 + - 48 * a_43 * a_51 * a_63 * a_64 * a_65 * b_6 + - 48 * a_43 * a_51 * a_64^2 * a_65 * b_6 + - 48 * a_43 * a_51 * a_64 * a_65^2 * b_6 + - 48 * a_43 * a_52 * a_61 * a_64 * a_65 * b_6 + - 48 * a_43 * a_52 * a_62 * a_64 * a_65 * b_6 + - 48 * a_43 * a_52 * a_63 * a_64 * a_65 * b_6 + - 48 * a_43 * a_52 * a_64^2 * a_65 * b_6 + - 48 * a_43 * a_52 * a_64 * a_65^2 * b_6 + - 48 * a_43 * a_53 * a_61 * a_64 * a_65 * b_6 + - 48 * a_43 * a_53 * a_62 * a_64 * a_65 * b_6 + - 48 * a_43 * a_53 * a_63 * a_64 * a_65 * b_6 + - 48 * a_43 * a_53 * a_64^2 * a_65 * b_6 + - 48 * a_43 * a_53 * a_64 * a_65^2 * b_6 + - 48 * a_43 * a_54 * a_61 * a_64 * a_65 * b_6 + - 48 * a_43 * a_54 * a_62 * a_64 * a_65 * b_6 + - 48 * a_43 * a_54 * a_63 * a_64 * a_65 * b_6 + - 48 * a_43 * a_54 * a_64^2 * a_65 * b_6 + - 48 * a_43 * a_54 * a_64 * a_65^2 * b_6 + - 24 * a_51^2 * a_61 * a_65^2 * b_6 + - 24 * a_51^2 * a_62 * a_65^2 * b_6 + - 24 * a_51^2 * a_63 * a_65^2 * b_6 + - 24 * a_51^2 * a_64 * a_65^2 * b_6 + - 24 * a_51^2 * a_65^3 * b_6 + - 48 * a_51 * a_52 * a_61 * a_65^2 * b_6 + - 48 * a_51 * a_52 * a_62 * a_65^2 * b_6 + - 48 * a_51 * a_52 * a_63 * a_65^2 * b_6 + - 48 * a_51 * a_52 * a_64 * a_65^2 * b_6 + - 48 * a_51 * a_52 * a_65^3 * b_6 + - 48 * a_51 * a_53 * a_61 * a_65^2 * b_6 + - 48 * a_51 * a_53 * a_62 * a_65^2 * b_6 + - 48 * a_51 * a_53 * a_63 * a_65^2 * b_6 + - 48 * a_51 * a_53 * a_64 * a_65^2 * b_6 + - 48 * a_51 * a_53 * a_65^3 * b_6 + - 48 * a_51 * a_54 * a_61 * a_65^2 * b_6 + - 48 * a_51 * a_54 * a_62 * a_65^2 * b_6 + - 48 * a_51 * a_54 * a_63 * a_65^2 * b_6 + - 48 * a_51 * a_54 * a_64 * a_65^2 * b_6 + - 48 * a_51 * a_54 * a_65^3 * b_6 + - 24 * a_52^2 * a_61 * a_65^2 * b_6 + - 24 * a_52^2 * a_62 * a_65^2 * b_6 + - 24 * a_52^2 * a_63 * a_65^2 * b_6 + - 24 * a_52^2 * a_64 * a_65^2 * b_6 + - 24 * a_52^2 * a_65^3 * b_6 + - 48 * a_52 * a_53 * a_61 * a_65^2 * b_6 + - 48 * a_52 * a_53 * a_62 * a_65^2 * b_6 + - 48 * a_52 * a_53 * a_63 * a_65^2 * b_6 + - 48 * a_52 * a_53 * a_64 * a_65^2 * b_6 + - 48 * a_52 * a_53 * a_65^3 * b_6 + - 48 * a_52 * a_54 * a_61 * a_65^2 * b_6 + - 48 * a_52 * a_54 * a_62 * a_65^2 * b_6 + - 48 * a_52 * a_54 * a_63 * a_65^2 * b_6 + - 48 * a_52 * a_54 * a_64 * a_65^2 * b_6 + - 48 * a_52 * a_54 * a_65^3 * b_6 + - 24 * a_53^2 * a_61 * a_65^2 * b_6 + - 24 * a_53^2 * a_62 * a_65^2 * b_6 + - 24 * a_53^2 * a_63 * a_65^2 * b_6 + - 24 * a_53^2 * a_64 * a_65^2 * b_6 + - 24 * a_53^2 * a_65^3 * b_6 + - 48 * a_53 * a_54 * a_61 * a_65^2 * b_6 + - 48 * a_53 * a_54 * a_62 * a_65^2 * b_6 + - 48 * a_53 * a_54 * a_63 * a_65^2 * b_6 + - 48 * a_53 * a_54 * a_64 * a_65^2 * b_6 + - 48 * a_53 * a_54 * a_65^3 * b_6 + - 24 * a_54^2 * a_61 * a_65^2 * b_6 + - 24 * a_54^2 * a_62 * a_65^2 * b_6 + - 24 * a_54^2 * a_63 * a_65^2 * b_6 + - 24 * a_54^2 * a_64 * a_65^2 * b_6 + - 24 * a_54^2 * a_65^3 * b_6 - 1, - 12 * a_21 * a_31^3 * a_32 * b_3 + - 36 * a_21 * a_31^2 * a_32^2 * b_3 + - 36 * a_21 * a_31 * a_32^3 * b_3 + - 12 * a_21 * a_32^4 * b_3 + - 12 * a_21 * a_41^3 * a_42 * b_4 + - 36 * a_21 * a_41^2 * a_42^2 * b_4 + - 36 * a_21 * a_41^2 * a_42 * a_43 * b_4 + - 36 * a_21 * a_41 * a_42^3 * b_4 + - 72 * a_21 * a_41 * a_42^2 * a_43 * b_4 + - 36 * a_21 * a_41 * a_42 * a_43^2 * b_4 + - 12 * a_21 * a_42^4 * b_4 + - 36 * a_21 * a_42^3 * a_43 * b_4 + - 36 * a_21 * a_42^2 * a_43^2 * b_4 + - 12 * a_21 * a_42 * a_43^3 * b_4 + - 12 * a_21 * a_51^3 * a_52 * b_5 + - 36 * a_21 * a_51^2 * a_52^2 * b_5 + - 36 * a_21 * a_51^2 * a_52 * a_53 * b_5 + - 36 * a_21 * a_51^2 * a_52 * a_54 * b_5 + - 36 * a_21 * a_51 * a_52^3 * b_5 + - 72 * a_21 * a_51 * a_52^2 * a_53 * b_5 + - 72 * a_21 * a_51 * a_52^2 * a_54 * b_5 + - 36 * a_21 * a_51 * a_52 * a_53^2 * b_5 + - 72 * a_21 * a_51 * a_52 * a_53 * a_54 * b_5 + - 36 * a_21 * a_51 * a_52 * a_54^2 * b_5 + - 12 * a_21 * a_52^4 * b_5 + - 36 * a_21 * a_52^3 * a_53 * b_5 + - 36 * a_21 * a_52^3 * a_54 * b_5 + - 36 * a_21 * a_52^2 * a_53^2 * b_5 + - 72 * a_21 * a_52^2 * a_53 * a_54 * b_5 + - 36 * a_21 * a_52^2 * a_54^2 * b_5 + - 12 * a_21 * a_52 * a_53^3 * b_5 + - 36 * a_21 * a_52 * a_53^2 * a_54 * b_5 + - 36 * a_21 * a_52 * a_53 * a_54^2 * b_5 + - 12 * a_21 * a_52 * a_54^3 * b_5 + - 12 * a_21 * a_61^3 * a_62 * b_6 + - 36 * a_21 * a_61^2 * a_62^2 * b_6 + - 36 * a_21 * a_61^2 * a_62 * a_63 * b_6 + - 36 * a_21 * a_61^2 * a_62 * a_64 * b_6 + - 36 * a_21 * a_61^2 * a_62 * a_65 * b_6 + - 36 * a_21 * a_61 * a_62^3 * b_6 + - 72 * a_21 * a_61 * a_62^2 * a_63 * b_6 + - 72 * a_21 * a_61 * a_62^2 * a_64 * b_6 + - 72 * a_21 * a_61 * a_62^2 * a_65 * b_6 + - 36 * a_21 * a_61 * a_62 * a_63^2 * b_6 + - 72 * a_21 * a_61 * a_62 * a_63 * a_64 * b_6 + - 72 * a_21 * a_61 * a_62 * a_63 * a_65 * b_6 + - 36 * a_21 * a_61 * a_62 * a_64^2 * b_6 + - 72 * a_21 * a_61 * a_62 * a_64 * a_65 * b_6 + - 36 * a_21 * a_61 * a_62 * a_65^2 * b_6 + - 12 * a_21 * a_62^4 * b_6 + - 36 * a_21 * a_62^3 * a_63 * b_6 + - 36 * a_21 * a_62^3 * a_64 * b_6 + - 36 * a_21 * a_62^3 * a_65 * b_6 + - 36 * a_21 * a_62^2 * a_63^2 * b_6 + - 72 * a_21 * a_62^2 * a_63 * a_64 * b_6 + - 72 * a_21 * a_62^2 * a_63 * a_65 * b_6 + - 36 * a_21 * a_62^2 * a_64^2 * b_6 + - 72 * a_21 * a_62^2 * a_64 * a_65 * b_6 + - 36 * a_21 * a_62^2 * a_65^2 * b_6 + - 12 * a_21 * a_62 * a_63^3 * b_6 + - 36 * a_21 * a_62 * a_63^2 * a_64 * b_6 + - 36 * a_21 * a_62 * a_63^2 * a_65 * b_6 + - 36 * a_21 * a_62 * a_63 * a_64^2 * b_6 + - 72 * a_21 * a_62 * a_63 * a_64 * a_65 * b_6 + - 36 * a_21 * a_62 * a_63 * a_65^2 * b_6 + - 12 * a_21 * a_62 * a_64^3 * b_6 + - 36 * a_21 * a_62 * a_64^2 * a_65 * b_6 + - 36 * a_21 * a_62 * a_64 * a_65^2 * b_6 + - 12 * a_21 * a_62 * a_65^3 * b_6 + - 12 * a_31 * a_41^3 * a_43 * b_4 + - 36 * a_31 * a_41^2 * a_42 * a_43 * b_4 + - 36 * a_31 * a_41^2 * a_43^2 * b_4 + - 36 * a_31 * a_41 * a_42^2 * a_43 * b_4 + - 72 * a_31 * a_41 * a_42 * a_43^2 * b_4 + - 36 * a_31 * a_41 * a_43^3 * b_4 + - 12 * a_31 * a_42^3 * a_43 * b_4 + - 36 * a_31 * a_42^2 * a_43^2 * b_4 + - 36 * a_31 * a_42 * a_43^3 * b_4 + - 12 * a_31 * a_43^4 * b_4 + - 12 * a_31 * a_51^3 * a_53 * b_5 + - 36 * a_31 * a_51^2 * a_52 * a_53 * b_5 + - 36 * a_31 * a_51^2 * a_53^2 * b_5 + - 36 * a_31 * a_51^2 * a_53 * a_54 * b_5 + - 36 * a_31 * a_51 * a_52^2 * a_53 * b_5 + - 72 * a_31 * a_51 * a_52 * a_53^2 * b_5 + - 72 * a_31 * a_51 * a_52 * a_53 * a_54 * b_5 + - 36 * a_31 * a_51 * a_53^3 * b_5 + - 72 * a_31 * a_51 * a_53^2 * a_54 * b_5 + - 36 * a_31 * a_51 * a_53 * a_54^2 * b_5 + - 12 * a_31 * a_52^3 * a_53 * b_5 + - 36 * a_31 * a_52^2 * a_53^2 * b_5 + - 36 * a_31 * a_52^2 * a_53 * a_54 * b_5 + - 36 * a_31 * a_52 * a_53^3 * b_5 + - 72 * a_31 * a_52 * a_53^2 * a_54 * b_5 + - 36 * a_31 * a_52 * a_53 * a_54^2 * b_5 + - 12 * a_31 * a_53^4 * b_5 + - 36 * a_31 * a_53^3 * a_54 * b_5 + - 36 * a_31 * a_53^2 * a_54^2 * b_5 + - 12 * a_31 * a_53 * a_54^3 * b_5 + - 12 * a_31 * a_61^3 * a_63 * b_6 + - 36 * a_31 * a_61^2 * a_62 * a_63 * b_6 + - 36 * a_31 * a_61^2 * a_63^2 * b_6 + - 36 * a_31 * a_61^2 * a_63 * a_64 * b_6 + - 36 * a_31 * a_61^2 * a_63 * a_65 * b_6 + - 36 * a_31 * a_61 * a_62^2 * a_63 * b_6 + - 72 * a_31 * a_61 * a_62 * a_63^2 * b_6 + - 72 * a_31 * a_61 * a_62 * a_63 * a_64 * b_6 + - 72 * a_31 * a_61 * a_62 * a_63 * a_65 * b_6 + - 36 * a_31 * a_61 * a_63^3 * b_6 + - 72 * a_31 * a_61 * a_63^2 * a_64 * b_6 + - 72 * a_31 * a_61 * a_63^2 * a_65 * b_6 + - 36 * a_31 * a_61 * a_63 * a_64^2 * b_6 + - 72 * a_31 * a_61 * a_63 * a_64 * a_65 * b_6 + - 36 * a_31 * a_61 * a_63 * a_65^2 * b_6 + - 12 * a_31 * a_62^3 * a_63 * b_6 + - 36 * a_31 * a_62^2 * a_63^2 * b_6 + - 36 * a_31 * a_62^2 * a_63 * a_64 * b_6 + - 36 * a_31 * a_62^2 * a_63 * a_65 * b_6 + - 36 * a_31 * a_62 * a_63^3 * b_6 + - 72 * a_31 * a_62 * a_63^2 * a_64 * b_6 + - 72 * a_31 * a_62 * a_63^2 * a_65 * b_6 + - 36 * a_31 * a_62 * a_63 * a_64^2 * b_6 + - 72 * a_31 * a_62 * a_63 * a_64 * a_65 * b_6 + - 36 * a_31 * a_62 * a_63 * a_65^2 * b_6 + - 12 * a_31 * a_63^4 * b_6 + - 36 * a_31 * a_63^3 * a_64 * b_6 + - 36 * a_31 * a_63^3 * a_65 * b_6 + - 36 * a_31 * a_63^2 * a_64^2 * b_6 + - 72 * a_31 * a_63^2 * a_64 * a_65 * b_6 + - 36 * a_31 * a_63^2 * a_65^2 * b_6 + - 12 * a_31 * a_63 * a_64^3 * b_6 + - 36 * a_31 * a_63 * a_64^2 * a_65 * b_6 + - 36 * a_31 * a_63 * a_64 * a_65^2 * b_6 + - 12 * a_31 * a_63 * a_65^3 * b_6 + - 12 * a_32 * a_41^3 * a_43 * b_4 + - 36 * a_32 * a_41^2 * a_42 * a_43 * b_4 + - 36 * a_32 * a_41^2 * a_43^2 * b_4 + - 36 * a_32 * a_41 * a_42^2 * a_43 * b_4 + - 72 * a_32 * a_41 * a_42 * a_43^2 * b_4 + - 36 * a_32 * a_41 * a_43^3 * b_4 + - 12 * a_32 * a_42^3 * a_43 * b_4 + - 36 * a_32 * a_42^2 * a_43^2 * b_4 + - 36 * a_32 * a_42 * a_43^3 * b_4 + - 12 * a_32 * a_43^4 * b_4 + - 12 * a_32 * a_51^3 * a_53 * b_5 + - 36 * a_32 * a_51^2 * a_52 * a_53 * b_5 + - 36 * a_32 * a_51^2 * a_53^2 * b_5 + - 36 * a_32 * a_51^2 * a_53 * a_54 * b_5 + - 36 * a_32 * a_51 * a_52^2 * a_53 * b_5 + - 72 * a_32 * a_51 * a_52 * a_53^2 * b_5 + - 72 * a_32 * a_51 * a_52 * a_53 * a_54 * b_5 + - 36 * a_32 * a_51 * a_53^3 * b_5 + - 72 * a_32 * a_51 * a_53^2 * a_54 * b_5 + - 36 * a_32 * a_51 * a_53 * a_54^2 * b_5 + - 12 * a_32 * a_52^3 * a_53 * b_5 + - 36 * a_32 * a_52^2 * a_53^2 * b_5 + - 36 * a_32 * a_52^2 * a_53 * a_54 * b_5 + - 36 * a_32 * a_52 * a_53^3 * b_5 + - 72 * a_32 * a_52 * a_53^2 * a_54 * b_5 + - 36 * a_32 * a_52 * a_53 * a_54^2 * b_5 + - 12 * a_32 * a_53^4 * b_5 + - 36 * a_32 * a_53^3 * a_54 * b_5 + - 36 * a_32 * a_53^2 * a_54^2 * b_5 + - 12 * a_32 * a_53 * a_54^3 * b_5 + - 12 * a_32 * a_61^3 * a_63 * b_6 + - 36 * a_32 * a_61^2 * a_62 * a_63 * b_6 + - 36 * a_32 * a_61^2 * a_63^2 * b_6 + - 36 * a_32 * a_61^2 * a_63 * a_64 * b_6 + - 36 * a_32 * a_61^2 * a_63 * a_65 * b_6 + - 36 * a_32 * a_61 * a_62^2 * a_63 * b_6 + - 72 * a_32 * a_61 * a_62 * a_63^2 * b_6 + - 72 * a_32 * a_61 * a_62 * a_63 * a_64 * b_6 + - 72 * a_32 * a_61 * a_62 * a_63 * a_65 * b_6 + - 36 * a_32 * a_61 * a_63^3 * b_6 + - 72 * a_32 * a_61 * a_63^2 * a_64 * b_6 + - 72 * a_32 * a_61 * a_63^2 * a_65 * b_6 + - 36 * a_32 * a_61 * a_63 * a_64^2 * b_6 + - 72 * a_32 * a_61 * a_63 * a_64 * a_65 * b_6 + - 36 * a_32 * a_61 * a_63 * a_65^2 * b_6 + - 12 * a_32 * a_62^3 * a_63 * b_6 + - 36 * a_32 * a_62^2 * a_63^2 * b_6 + - 36 * a_32 * a_62^2 * a_63 * a_64 * b_6 + - 36 * a_32 * a_62^2 * a_63 * a_65 * b_6 + - 36 * a_32 * a_62 * a_63^3 * b_6 + - 72 * a_32 * a_62 * a_63^2 * a_64 * b_6 + - 72 * a_32 * a_62 * a_63^2 * a_65 * b_6 + - 36 * a_32 * a_62 * a_63 * a_64^2 * b_6 + - 72 * a_32 * a_62 * a_63 * a_64 * a_65 * b_6 + - 36 * a_32 * a_62 * a_63 * a_65^2 * b_6 + - 12 * a_32 * a_63^4 * b_6 + - 36 * a_32 * a_63^3 * a_64 * b_6 + - 36 * a_32 * a_63^3 * a_65 * b_6 + - 36 * a_32 * a_63^2 * a_64^2 * b_6 + - 72 * a_32 * a_63^2 * a_64 * a_65 * b_6 + - 36 * a_32 * a_63^2 * a_65^2 * b_6 + - 12 * a_32 * a_63 * a_64^3 * b_6 + - 36 * a_32 * a_63 * a_64^2 * a_65 * b_6 + - 36 * a_32 * a_63 * a_64 * a_65^2 * b_6 + - 12 * a_32 * a_63 * a_65^3 * b_6 + - 12 * a_41 * a_51^3 * a_54 * b_5 + - 36 * a_41 * a_51^2 * a_52 * a_54 * b_5 + - 36 * a_41 * a_51^2 * a_53 * a_54 * b_5 + - 36 * a_41 * a_51^2 * a_54^2 * b_5 + - 36 * a_41 * a_51 * a_52^2 * a_54 * b_5 + - 72 * a_41 * a_51 * a_52 * a_53 * a_54 * b_5 + - 72 * a_41 * a_51 * a_52 * a_54^2 * b_5 + - 36 * a_41 * a_51 * a_53^2 * a_54 * b_5 + - 72 * a_41 * a_51 * a_53 * a_54^2 * b_5 + - 36 * a_41 * a_51 * a_54^3 * b_5 + - 12 * a_41 * a_52^3 * a_54 * b_5 + - 36 * a_41 * a_52^2 * a_53 * a_54 * b_5 + - 36 * a_41 * a_52^2 * a_54^2 * b_5 + - 36 * a_41 * a_52 * a_53^2 * a_54 * b_5 + - 72 * a_41 * a_52 * a_53 * a_54^2 * b_5 + - 36 * a_41 * a_52 * a_54^3 * b_5 + - 12 * a_41 * a_53^3 * a_54 * b_5 + - 36 * a_41 * a_53^2 * a_54^2 * b_5 + - 36 * a_41 * a_53 * a_54^3 * b_5 + - 12 * a_41 * a_54^4 * b_5 + - 12 * a_41 * a_61^3 * a_64 * b_6 + - 36 * a_41 * a_61^2 * a_62 * a_64 * b_6 + - 36 * a_41 * a_61^2 * a_63 * a_64 * b_6 + - 36 * a_41 * a_61^2 * a_64^2 * b_6 + - 36 * a_41 * a_61^2 * a_64 * a_65 * b_6 + - 36 * a_41 * a_61 * a_62^2 * a_64 * b_6 + - 72 * a_41 * a_61 * a_62 * a_63 * a_64 * b_6 + - 72 * a_41 * a_61 * a_62 * a_64^2 * b_6 + - 72 * a_41 * a_61 * a_62 * a_64 * a_65 * b_6 + - 36 * a_41 * a_61 * a_63^2 * a_64 * b_6 + - 72 * a_41 * a_61 * a_63 * a_64^2 * b_6 + - 72 * a_41 * a_61 * a_63 * a_64 * a_65 * b_6 + - 36 * a_41 * a_61 * a_64^3 * b_6 + - 72 * 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a_65 * b_6 + - 36 * a_51 * a_62^2 * a_63 * a_65 * b_6 + - 36 * a_51 * a_62^2 * a_64 * a_65 * b_6 + - 36 * a_51 * a_62^2 * a_65^2 * b_6 + - 36 * a_51 * a_62 * a_63^2 * a_65 * b_6 + - 72 * a_51 * a_62 * a_63 * a_64 * a_65 * b_6 + - 72 * a_51 * a_62 * a_63 * a_65^2 * b_6 + - 36 * a_51 * a_62 * a_64^2 * a_65 * b_6 + - 72 * a_51 * a_62 * a_64 * a_65^2 * b_6 + - 36 * a_51 * a_62 * a_65^3 * b_6 + - 12 * a_51 * a_63^3 * a_65 * b_6 + - 36 * a_51 * a_63^2 * a_64 * a_65 * b_6 + - 36 * a_51 * a_63^2 * a_65^2 * b_6 + - 36 * a_51 * a_63 * a_64^2 * a_65 * b_6 + - 72 * a_51 * a_63 * a_64 * a_65^2 * b_6 + - 36 * a_51 * a_63 * a_65^3 * b_6 + - 12 * a_51 * a_64^3 * a_65 * b_6 + - 36 * a_51 * a_64^2 * a_65^2 * b_6 + - 36 * a_51 * a_64 * a_65^3 * b_6 + - 12 * a_51 * a_65^4 * b_6 + - 12 * a_52 * a_61^3 * a_65 * b_6 + - 36 * a_52 * a_61^2 * a_62 * a_65 * b_6 + - 36 * a_52 * a_61^2 * a_63 * a_65 * b_6 + - 36 * a_52 * a_61^2 * a_64 * a_65 * b_6 + - 36 * a_52 * a_61^2 * a_65^2 * b_6 + - 36 * a_52 * a_61 * a_62^2 * a_65 * b_6 + - 72 * a_52 * a_61 * a_62 * a_63 * a_65 * b_6 + - 72 * a_52 * a_61 * a_62 * a_64 * a_65 * b_6 + - 72 * a_52 * a_61 * a_62 * a_65^2 * b_6 + - 36 * a_52 * a_61 * a_63^2 * a_65 * b_6 + - 72 * a_52 * a_61 * a_63 * a_64 * a_65 * b_6 + - 72 * a_52 * a_61 * a_63 * a_65^2 * b_6 + - 36 * a_52 * a_61 * a_64^2 * a_65 * b_6 + - 72 * a_52 * a_61 * a_64 * a_65^2 * b_6 + - 36 * a_52 * a_61 * a_65^3 * b_6 + - 12 * a_52 * a_62^3 * a_65 * b_6 + - 36 * a_52 * a_62^2 * a_63 * a_65 * b_6 + - 36 * a_52 * a_62^2 * a_64 * a_65 * b_6 + - 36 * a_52 * a_62^2 * a_65^2 * b_6 + - 36 * a_52 * a_62 * a_63^2 * a_65 * b_6 + - 72 * a_52 * a_62 * a_63 * a_64 * a_65 * b_6 + - 72 * a_52 * a_62 * a_63 * a_65^2 * b_6 + - 36 * a_52 * a_62 * a_64^2 * a_65 * b_6 + - 72 * a_52 * a_62 * a_64 * a_65^2 * b_6 + - 36 * a_52 * a_62 * a_65^3 * b_6 + - 12 * a_52 * a_63^3 * a_65 * b_6 + - 36 * a_52 * a_63^2 * a_64 * a_65 * b_6 + - 36 * a_52 * a_63^2 * a_65^2 * b_6 + - 36 * a_52 * a_63 * a_64^2 * a_65 * b_6 + - 72 * a_52 * a_63 * a_64 * a_65^2 * b_6 + - 36 * a_52 * a_63 * a_65^3 * b_6 + - 12 * a_52 * a_64^3 * a_65 * b_6 + - 36 * a_52 * a_64^2 * a_65^2 * b_6 + - 36 * a_52 * a_64 * a_65^3 * b_6 + - 12 * a_52 * a_65^4 * b_6 + - 12 * a_53 * a_61^3 * a_65 * b_6 + - 36 * a_53 * a_61^2 * a_62 * a_65 * b_6 + - 36 * a_53 * a_61^2 * a_63 * a_65 * b_6 + - 36 * a_53 * a_61^2 * a_64 * a_65 * b_6 + - 36 * a_53 * a_61^2 * a_65^2 * b_6 + - 36 * a_53 * a_61 * a_62^2 * a_65 * b_6 + - 72 * a_53 * a_61 * a_62 * a_63 * a_65 * b_6 + - 72 * a_53 * a_61 * a_62 * a_64 * a_65 * b_6 + - 72 * a_53 * a_61 * a_62 * a_65^2 * b_6 + - 36 * a_53 * a_61 * a_63^2 * a_65 * b_6 + - 72 * a_53 * a_61 * a_63 * a_64 * a_65 * b_6 + - 72 * a_53 * a_61 * a_63 * a_65^2 * b_6 + - 36 * a_53 * a_61 * a_64^2 * a_65 * b_6 + - 72 * a_53 * a_61 * a_64 * a_65^2 * b_6 + - 36 * a_53 * a_61 * a_65^3 * b_6 + - 12 * a_53 * a_62^3 * a_65 * b_6 + - 36 * a_53 * a_62^2 * a_63 * a_65 * b_6 + - 36 * a_53 * a_62^2 * a_64 * a_65 * b_6 + - 36 * a_53 * a_62^2 * a_65^2 * b_6 + - 36 * a_53 * a_62 * a_63^2 * a_65 * b_6 + - 72 * a_53 * a_62 * a_63 * a_64 * a_65 * b_6 + - 72 * a_53 * a_62 * a_63 * a_65^2 * b_6 + - 36 * a_53 * a_62 * a_64^2 * a_65 * b_6 + - 72 * a_53 * a_62 * a_64 * a_65^2 * b_6 + - 36 * a_53 * a_62 * a_65^3 * b_6 + - 12 * a_53 * a_63^3 * a_65 * b_6 + - 36 * a_53 * a_63^2 * a_64 * a_65 * b_6 + - 36 * a_53 * a_63^2 * a_65^2 * b_6 + - 36 * a_53 * a_63 * a_64^2 * a_65 * b_6 + - 72 * a_53 * a_63 * a_64 * a_65^2 * b_6 + - 36 * a_53 * a_63 * a_65^3 * b_6 + - 12 * a_53 * a_64^3 * a_65 * b_6 + - 36 * a_53 * a_64^2 * a_65^2 * b_6 + - 36 * a_53 * a_64 * a_65^3 * b_6 + - 12 * a_53 * a_65^4 * b_6 + - 12 * a_54 * a_61^3 * a_65 * b_6 + - 36 * a_54 * a_61^2 * a_62 * a_65 * b_6 + - 36 * a_54 * a_61^2 * a_63 * a_65 * b_6 + - 36 * a_54 * a_61^2 * a_64 * a_65 * b_6 + - 36 * a_54 * a_61^2 * a_65^2 * b_6 + - 36 * a_54 * a_61 * a_62^2 * a_65 * b_6 + - 72 * a_54 * a_61 * a_62 * a_63 * a_65 * b_6 + - 72 * a_54 * a_61 * a_62 * a_64 * a_65 * b_6 + - 72 * a_54 * a_61 * a_62 * a_65^2 * b_6 + - 36 * a_54 * a_61 * a_63^2 * a_65 * b_6 + - 72 * a_54 * a_61 * a_63 * a_64 * a_65 * b_6 + - 72 * a_54 * a_61 * a_63 * a_65^2 * b_6 + - 36 * a_54 * a_61 * a_64^2 * a_65 * b_6 + - 72 * a_54 * a_61 * a_64 * a_65^2 * b_6 + - 36 * a_54 * a_61 * a_65^3 * b_6 + - 12 * a_54 * a_62^3 * a_65 * b_6 + - 36 * a_54 * a_62^2 * a_63 * a_65 * b_6 + - 36 * a_54 * a_62^2 * a_64 * a_65 * b_6 + - 36 * a_54 * a_62^2 * a_65^2 * b_6 + - 36 * a_54 * a_62 * a_63^2 * a_65 * b_6 + - 72 * a_54 * a_62 * a_63 * a_64 * a_65 * b_6 + - 72 * a_54 * a_62 * a_63 * a_65^2 * b_6 + - 36 * a_54 * a_62 * a_64^2 * a_65 * b_6 + - 72 * a_54 * a_62 * a_64 * a_65^2 * b_6 + - 36 * a_54 * a_62 * a_65^3 * b_6 + - 12 * a_54 * a_63^3 * a_65 * b_6 + - 36 * a_54 * a_63^2 * a_64 * a_65 * b_6 + - 36 * a_54 * a_63^2 * a_65^2 * b_6 + - 36 * a_54 * a_63 * a_64^2 * a_65 * b_6 + - 72 * a_54 * a_63 * a_64 * a_65^2 * b_6 + - 36 * a_54 * a_63 * a_65^3 * b_6 + - 12 * a_54 * a_64^3 * a_65 * b_6 + - 36 * a_54 * a_64^2 * a_65^2 * b_6 + - 36 * a_54 * a_64 * a_65^3 * b_6 + - 12 * a_54 * a_65^4 * b_6 - 1, - 6 * a_21^5 * b_2 + - 6 * a_31^5 * b_3 + - 30 * a_31^4 * a_32 * b_3 + - 60 * a_31^3 * a_32^2 * b_3 + - 60 * a_31^2 * a_32^3 * b_3 + - 30 * a_31 * a_32^4 * b_3 + - 6 * a_32^5 * b_3 + - 6 * a_41^5 * b_4 + - 30 * a_41^4 * a_42 * b_4 + - 30 * a_41^4 * a_43 * b_4 + - 60 * a_41^3 * a_42^2 * b_4 + - 120 * a_41^3 * a_42 * a_43 * b_4 + - 60 * a_41^3 * a_43^2 * b_4 + - 60 * a_41^2 * a_42^3 * b_4 + - 180 * a_41^2 * a_42^2 * a_43 * b_4 + - 180 * a_41^2 * a_42 * a_43^2 * b_4 + - 60 * a_41^2 * a_43^3 * b_4 + - 30 * a_41 * a_42^4 * b_4 + - 120 * a_41 * a_42^3 * a_43 * b_4 + - 180 * a_41 * a_42^2 * a_43^2 * b_4 + - 120 * a_41 * a_42 * a_43^3 * b_4 + - 30 * a_41 * a_43^4 * b_4 + - 6 * a_42^5 * b_4 + - 30 * a_42^4 * a_43 * b_4 + - 60 * a_42^3 * a_43^2 * b_4 + - 60 * a_42^2 * a_43^3 * b_4 + - 30 * a_42 * a_43^4 * b_4 + - 6 * a_43^5 * b_4 + - 6 * a_51^5 * b_5 + - 30 * a_51^4 * a_52 * b_5 + - 30 * a_51^4 * a_53 * b_5 + - 30 * a_51^4 * a_54 * b_5 + - 60 * a_51^3 * a_52^2 * b_5 + - 120 * a_51^3 * a_52 * a_53 * b_5 + - 120 * a_51^3 * a_52 * a_54 * b_5 + - 60 * a_51^3 * a_53^2 * b_5 + - 120 * a_51^3 * a_53 * a_54 * b_5 + - 60 * a_51^3 * a_54^2 * b_5 + - 60 * a_51^2 * a_52^3 * b_5 + - 180 * a_51^2 * a_52^2 * a_53 * b_5 + - 180 * a_51^2 * a_52^2 * a_54 * b_5 + - 180 * a_51^2 * a_52 * a_53^2 * b_5 + - 360 * a_51^2 * a_52 * a_53 * a_54 * b_5 + - 180 * a_51^2 * a_52 * a_54^2 * b_5 + - 60 * a_51^2 * a_53^3 * b_5 + - 180 * a_51^2 * a_53^2 * a_54 * b_5 + - 180 * a_51^2 * a_53 * a_54^2 * b_5 + - 60 * a_51^2 * a_54^3 * b_5 + - 30 * a_51 * a_52^4 * b_5 + - 120 * a_51 * a_52^3 * a_53 * b_5 + - 120 * a_51 * a_52^3 * a_54 * b_5 + - 180 * a_51 * a_52^2 * a_53^2 * b_5 + - 360 * a_51 * a_52^2 * a_53 * a_54 * b_5 + - 180 * a_51 * a_52^2 * a_54^2 * b_5 + - 120 * a_51 * a_52 * a_53^3 * b_5 + - 360 * a_51 * a_52 * a_53^2 * a_54 * b_5 + - 360 * a_51 * a_52 * a_53 * a_54^2 * b_5 + - 120 * a_51 * a_52 * a_54^3 * b_5 + - 30 * a_51 * a_53^4 * b_5 + - 120 * a_51 * a_53^3 * a_54 * b_5 + - 180 * a_51 * a_53^2 * a_54^2 * b_5 + - 120 * a_51 * a_53 * a_54^3 * b_5 + - 30 * a_51 * a_54^4 * b_5 + - 6 * a_52^5 * b_5 + - 30 * a_52^4 * a_53 * b_5 + - 30 * a_52^4 * a_54 * b_5 + - 60 * a_52^3 * a_53^2 * b_5 + - 120 * a_52^3 * a_53 * a_54 * b_5 + - 60 * a_52^3 * a_54^2 * b_5 + - 60 * a_52^2 * a_53^3 * b_5 + - 180 * a_52^2 * a_53^2 * a_54 * b_5 + - 180 * a_52^2 * a_53 * a_54^2 * b_5 + - 60 * a_52^2 * a_54^3 * b_5 + - 30 * a_52 * a_53^4 * b_5 + - 120 * a_52 * a_53^3 * a_54 * b_5 + - 180 * a_52 * a_53^2 * a_54^2 * b_5 + - 120 * a_52 * a_53 * a_54^3 * b_5 + - 30 * a_52 * a_54^4 * b_5 + - 6 * a_53^5 * b_5 + - 30 * a_53^4 * a_54 * b_5 + - 60 * a_53^3 * a_54^2 * b_5 + - 60 * a_53^2 * a_54^3 * b_5 + - 30 * a_53 * a_54^4 * b_5 + - 6 * a_54^5 * b_5 + - 6 * a_61^5 * b_6 + - 30 * a_61^4 * a_62 * b_6 + - 30 * a_61^4 * a_63 * b_6 + - 30 * a_61^4 * a_64 * b_6 + - 30 * a_61^4 * a_65 * b_6 + - 60 * a_61^3 * a_62^2 * b_6 + - 120 * a_61^3 * a_62 * a_63 * b_6 + - 120 * a_61^3 * a_62 * a_64 * b_6 + - 120 * a_61^3 * a_62 * a_65 * b_6 + - 60 * a_61^3 * a_63^2 * b_6 + - 120 * a_61^3 * a_63 * a_64 * b_6 + - 120 * a_61^3 * a_63 * a_65 * b_6 + - 60 * a_61^3 * a_64^2 * b_6 + - 120 * a_61^3 * a_64 * a_65 * b_6 + - 60 * a_61^3 * a_65^2 * b_6 + - 60 * a_61^2 * a_62^3 * b_6 + - 180 * a_61^2 * a_62^2 * a_63 * b_6 + - 180 * a_61^2 * a_62^2 * a_64 * b_6 + - 180 * a_61^2 * a_62^2 * a_65 * b_6 + - 180 * a_61^2 * a_62 * a_63^2 * b_6 + - 360 * a_61^2 * a_62 * a_63 * a_64 * b_6 + - 360 * a_61^2 * a_62 * a_63 * a_65 * b_6 + - 180 * a_61^2 * a_62 * a_64^2 * b_6 + - 360 * a_61^2 * a_62 * a_64 * a_65 * b_6 + - 180 * a_61^2 * a_62 * a_65^2 * b_6 + - 60 * a_61^2 * a_63^3 * b_6 + - 180 * a_61^2 * a_63^2 * a_64 * b_6 + - 180 * a_61^2 * a_63^2 * a_65 * b_6 + - 180 * a_61^2 * a_63 * a_64^2 * b_6 + - 360 * a_61^2 * a_63 * a_64 * a_65 * b_6 + - 180 * a_61^2 * a_63 * a_65^2 * b_6 + - 60 * a_61^2 * a_64^3 * b_6 + - 180 * a_61^2 * a_64^2 * a_65 * b_6 + - 180 * a_61^2 * a_64 * a_65^2 * b_6 + - 60 * a_61^2 * a_65^3 * b_6 + - 30 * a_61 * a_62^4 * b_6 + - 120 * a_61 * a_62^3 * a_63 * b_6 + - 120 * a_61 * a_62^3 * a_64 * b_6 + - 120 * a_61 * a_62^3 * a_65 * b_6 + - 180 * a_61 * a_62^2 * a_63^2 * b_6 + - 360 * a_61 * a_62^2 * a_63 * a_64 * b_6 + - 360 * a_61 * a_62^2 * a_63 * a_65 * b_6 + - 180 * a_61 * a_62^2 * a_64^2 * b_6 + - 360 * a_61 * a_62^2 * a_64 * a_65 * b_6 + - 180 * a_61 * a_62^2 * a_65^2 * b_6 + - 120 * a_61 * a_62 * a_63^3 * b_6 + - 360 * a_61 * a_62 * a_63^2 * a_64 * b_6 + - 360 * a_61 * a_62 * a_63^2 * a_65 * b_6 + - 360 * a_61 * a_62 * a_63 * a_64^2 * b_6 + - 720 * a_61 * a_62 * a_63 * a_64 * a_65 * b_6 + - 360 * a_61 * a_62 * a_63 * a_65^2 * b_6 + - 120 * a_61 * a_62 * a_64^3 * b_6 + - 360 * a_61 * a_62 * a_64^2 * a_65 * b_6 + - 360 * a_61 * a_62 * a_64 * a_65^2 * b_6 + - 120 * a_61 * a_62 * a_65^3 * b_6 + - 30 * a_61 * a_63^4 * b_6 + - 120 * a_61 * a_63^3 * a_64 * b_6 + - 120 * a_61 * a_63^3 * a_65 * b_6 + - 180 * a_61 * a_63^2 * a_64^2 * b_6 + - 360 * a_61 * a_63^2 * a_64 * a_65 * b_6 + - 180 * a_61 * a_63^2 * a_65^2 * b_6 + - 120 * a_61 * a_63 * a_64^3 * b_6 + - 360 * a_61 * a_63 * a_64^2 * a_65 * b_6 + - 360 * a_61 * a_63 * a_64 * a_65^2 * b_6 + - 120 * a_61 * a_63 * a_65^3 * b_6 + - 30 * a_61 * a_64^4 * b_6 + - 120 * a_61 * a_64^3 * a_65 * b_6 + - 180 * a_61 * a_64^2 * a_65^2 * b_6 + - 120 * a_61 * a_64 * a_65^3 * b_6 + - 30 * a_61 * a_65^4 * b_6 + - 6 * a_62^5 * b_6 + - 30 * a_62^4 * a_63 * b_6 + - 30 * a_62^4 * a_64 * b_6 + - 30 * a_62^4 * a_65 * b_6 + - 60 * a_62^3 * a_63^2 * b_6 + - 120 * a_62^3 * a_63 * a_64 * b_6 + - 120 * a_62^3 * a_63 * a_65 * b_6 + - 60 * a_62^3 * a_64^2 * b_6 + - 120 * a_62^3 * a_64 * a_65 * b_6 + - 60 * a_62^3 * a_65^2 * b_6 + - 60 * a_62^2 * a_63^3 * b_6 + - 180 * a_62^2 * a_63^2 * a_64 * b_6 + - 180 * a_62^2 * a_63^2 * a_65 * b_6 + - 180 * a_62^2 * a_63 * a_64^2 * b_6 + - 360 * a_62^2 * a_63 * a_64 * a_65 * b_6 + - 180 * a_62^2 * a_63 * a_65^2 * b_6 + - 60 * a_62^2 * a_64^3 * b_6 + - 180 * a_62^2 * a_64^2 * a_65 * b_6 + - 180 * a_62^2 * a_64 * a_65^2 * b_6 + - 60 * a_62^2 * a_65^3 * b_6 + - 30 * a_62 * a_63^4 * b_6 + - 120 * a_62 * a_63^3 * a_64 * b_6 + - 120 * a_62 * a_63^3 * a_65 * b_6 + - 180 * a_62 * a_63^2 * a_64^2 * b_6 + - 360 * a_62 * a_63^2 * a_64 * a_65 * b_6 + - 180 * a_62 * a_63^2 * a_65^2 * b_6 + - 120 * a_62 * a_63 * a_64^3 * b_6 + - 360 * a_62 * a_63 * a_64^2 * a_65 * b_6 + - 360 * a_62 * a_63 * a_64 * a_65^2 * b_6 + - 120 * a_62 * a_63 * a_65^3 * b_6 + - 30 * a_62 * a_64^4 * b_6 + - 120 * a_62 * a_64^3 * a_65 * b_6 + - 180 * a_62 * a_64^2 * a_65^2 * b_6 + - 120 * a_62 * a_64 * a_65^3 * b_6 + - 30 * a_62 * a_65^4 * b_6 + - 6 * a_63^5 * b_6 + - 30 * a_63^4 * a_64 * b_6 + - 30 * a_63^4 * a_65 * b_6 + - 60 * a_63^3 * a_64^2 * b_6 + - 120 * a_63^3 * a_64 * a_65 * b_6 + - 60 * a_63^3 * a_65^2 * b_6 + - 60 * a_63^2 * a_64^3 * b_6 + - 180 * a_63^2 * a_64^2 * a_65 * b_6 + - 180 * a_63^2 * a_64 * a_65^2 * b_6 + - 60 * a_63^2 * a_65^3 * b_6 + - 30 * a_63 * a_64^4 * b_6 + - 120 * a_63 * a_64^3 * a_65 * b_6 + - 180 * a_63 * a_64^2 * a_65^2 * b_6 + - 120 * a_63 * a_64 * a_65^3 * b_6 + - 30 * a_63 * a_65^4 * b_6 + - 6 * a_64^5 * b_6 + - 30 * a_64^4 * a_65 * b_6 + - 60 * a_64^3 * a_65^2 * b_6 + - 60 * a_64^2 * a_65^3 * b_6 + - 30 * a_64 * a_65^4 * b_6 + - 6 * a_65^5 * b_6 - 1 -] diff --git a/benchmark/scripts/runge-kutta/aa-runge-kutta-8-7.jl b/benchmark/scripts/runge-kutta/aa-runge-kutta-8-7.jl deleted file mode 100644 index 75a41632..00000000 --- a/benchmark/scripts/runge-kutta/aa-runge-kutta-8-7.jl +++ /dev/null @@ -1,3794 +0,0 @@ -R, -( - a_21, - a_31, - a_32, - a_41, - a_42, - a_43, - a_51, - a_52, - a_53, - a_54, - a_61, - a_62, - a_63, - a_64, - a_65, - a_71, - a_72, - a_73, - a_74, - a_75, - a_76, - a_81, - a_82, - a_83, - a_84, - a_85, - a_86, - a_87, - b_1, - b_2, - b_3, - b_4, - b_5, - b_6, - b_7, - b_8 -) = polynomial_ring( - QQ, - [ - "a_21", - "a_31", - "a_32", - "a_41", - "a_42", - "a_43", - "a_51", - "a_52", - "a_53", - "a_54", - "a_61", - "a_62", - "a_63", - "a_64", - "a_65", - "a_71", - "a_72", - "a_73", - "a_74", - "a_75", - "a_76", - "a_81", - "a_82", - "a_83", - "a_84", - "a_85", - "a_86", - "a_87", - "b_1", - "b_2", - "b_3", - "b_4", - "b_5", - "b_6", - "b_7", - "b_8" - ] -) - -system = [ - b_1 + b_2 + b_3 + b_4 + b_5 + b_6 + b_7 + b_8 - 1, - 2 * a_21 * b_2 + - 2 * b_3 * (a_31 + a_32) + - 2 * b_4 * (a_41 + a_42 + a_43) + - 2 * b_5 * (a_51 + a_52 + a_53 + a_54) + - 2 * b_6 * (a_61 + a_62 + a_63 + a_64 + a_65) + - 2 * b_7 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) + - 2 * b_8 * (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87) - 1, - 6 * a_21 * a_32 * b_3 + - 6 * b_4 * (a_21 * a_42 + a_43 * (a_31 + a_32)) + - 6 * b_5 * (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) + - 6 * - b_6 * - ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - ) + - 6 * - b_7 * - ( - a_21 * a_72 + - a_73 * (a_31 + a_32) + - a_74 * (a_41 + a_42 + a_43) + - a_75 * (a_51 + a_52 + a_53 + a_54) + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65) - ) + - 6 * - b_8 * - ( - a_21 * a_82 + - a_83 * (a_31 + a_32) + - a_84 * (a_41 + a_42 + a_43) + - a_85 * (a_51 + a_52 + a_53 + a_54) + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65) + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) - ) - 1, - 3 * a_21^2 * b_2 + - 3 * b_3 * (a_31 + a_32)^2 + - 3 * b_4 * (a_41 + a_42 + a_43)^2 + - 3 * b_5 * (a_51 + a_52 + a_53 + a_54)^2 + - 3 * b_6 * (a_61 + a_62 + a_63 + a_64 + a_65)^2 + - 3 * b_7 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2 + - 3 * b_8 * (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^2 - 1, - 24 * a_21 * a_32 * a_43 * b_4 + - 24 * b_5 * (a_21 * a_32 * a_53 + a_54 * (a_21 * a_42 + a_43 * (a_31 + a_32))) + - 24 * - b_6 * - ( - a_21 * a_32 * a_63 + - a_64 * (a_21 * a_42 + a_43 * (a_31 + a_32)) + - a_65 * (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) - ) + - 24 * - b_7 * - ( - a_21 * a_32 * a_73 + - a_74 * (a_21 * a_42 + a_43 * (a_31 + a_32)) + - a_75 * (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) + - a_76 * ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - ) - ) + - 24 * - b_8 * - ( - a_21 * a_32 * a_83 + - a_84 * (a_21 * a_42 + a_43 * (a_31 + a_32)) + - a_85 * (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) + - a_86 * ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - ) + - a_87 * ( - a_21 * a_72 + - a_73 * (a_31 + a_32) + - a_74 * (a_41 + a_42 + a_43) + - a_75 * (a_51 + a_52 + a_53 + a_54) + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65) - ) - ) - 1, - 12 * a_21^2 * a_32 * b_3 + - 12 * b_4 * (a_21^2 * a_42 + a_43 * (a_31 + a_32)^2) + - 12 * b_5 * (a_21^2 * a_52 + a_53 * (a_31 + a_32)^2 + a_54 * (a_41 + a_42 + a_43)^2) + - 12 * - b_6 * - ( - a_21^2 * a_62 + - a_63 * (a_31 + a_32)^2 + - a_64 * (a_41 + a_42 + a_43)^2 + - a_65 * (a_51 + a_52 + a_53 + a_54)^2 - ) + - 12 * - b_7 * - ( - a_21^2 * a_72 + - a_73 * (a_31 + a_32)^2 + - a_74 * (a_41 + a_42 + a_43)^2 + - a_75 * (a_51 + a_52 + a_53 + a_54)^2 + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65)^2 - ) + - 12 * - b_8 * - ( - a_21^2 * a_82 + - a_83 * (a_31 + a_32)^2 + - a_84 * (a_41 + a_42 + a_43)^2 + - a_85 * (a_51 + a_52 + a_53 + a_54)^2 + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65)^2 + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2 - ) - 1, - 8 * a_21 * a_32 * b_3 * (a_31 + a_32) + - 8 * b_4 * (a_21 * a_42 + a_43 * (a_31 + a_32)) * (a_41 + a_42 + a_43) + - 8 * - b_5 * - (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) * - (a_51 + a_52 + a_53 + a_54) + - 8 * - b_6 * - ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - ) * - (a_61 + a_62 + a_63 + a_64 + a_65) + - 8 * - b_7 * - ( - a_21 * a_72 + - a_73 * (a_31 + a_32) + - a_74 * (a_41 + a_42 + a_43) + - a_75 * (a_51 + a_52 + a_53 + a_54) + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65) - ) * - (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) + - 8 * - b_8 * - ( - a_21 * a_82 + - a_83 * (a_31 + a_32) + - a_84 * (a_41 + a_42 + a_43) + - a_85 * (a_51 + a_52 + a_53 + a_54) + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65) + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) - ) * - (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87) - 1, - 4 * a_21^3 * b_2 + - 4 * b_3 * (a_31 + a_32)^3 + - 4 * b_4 * (a_41 + a_42 + a_43)^3 + - 4 * b_5 * (a_51 + a_52 + a_53 + a_54)^3 + - 4 * b_6 * (a_61 + a_62 + a_63 + a_64 + a_65)^3 + - 4 * b_7 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^3 + - 4 * b_8 * (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^3 - 1, - 120 * a_21 * a_32 * a_43 * a_54 * b_5 + - 120 * - b_6 * - ( - a_21 * a_32 * a_43 * a_64 + - a_65 * (a_21 * a_32 * a_53 + a_54 * (a_21 * a_42 + a_43 * (a_31 + a_32))) - ) + - 120 * - b_7 * - ( - a_21 * a_32 * a_43 * a_74 + - a_75 * (a_21 * a_32 * a_53 + a_54 * (a_21 * a_42 + a_43 * 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a_43)^2 + - a_85 * (a_51 + a_52 + a_53 + a_54)^2 + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65)^2 + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2 - )^2 - 1, - 42 * a_21^3 * a_32^2 * b_3 * (a_31 + a_32) + - 42 * - b_4 * - (a_21 * a_42 + a_43 * (a_31 + a_32)) * - (a_21^2 * a_42 + a_43 * (a_31 + a_32)^2) * - (a_41 + a_42 + a_43) + - 42 * - b_5 * - (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) * - (a_21^2 * a_52 + a_53 * (a_31 + a_32)^2 + a_54 * (a_41 + a_42 + a_43)^2) * - (a_51 + a_52 + a_53 + a_54) + - 42 * - b_6 * - ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - ) * - ( - a_21^2 * a_62 + - a_63 * (a_31 + a_32)^2 + - a_64 * (a_41 + a_42 + a_43)^2 + - a_65 * (a_51 + a_52 + a_53 + a_54)^2 - ) * - (a_61 + a_62 + a_63 + a_64 + a_65) + - 42 * - b_7 * - ( - a_21 * a_72 + - a_73 * (a_31 + a_32) + - a_74 * (a_41 + a_42 + a_43) + - a_75 * (a_51 + a_52 + a_53 + a_54) + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65) - ) * - ( - a_21^2 * a_72 + - a_73 * (a_31 + a_32)^2 + - a_74 * (a_41 + a_42 + a_43)^2 + - a_75 * (a_51 + a_52 + a_53 + a_54)^2 + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65)^2 - ) * - (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) + - 42 * - b_8 * - ( - a_21 * a_82 + - a_83 * (a_31 + a_32) + - a_84 * (a_41 + a_42 + a_43) + - a_85 * (a_51 + a_52 + a_53 + a_54) + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65) + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) - ) * - ( - a_21^2 * a_82 + - a_83 * (a_31 + a_32)^2 + - a_84 * (a_41 + a_42 + a_43)^2 + - a_85 * (a_51 + a_52 + a_53 + a_54)^2 + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65)^2 + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2 - ) * - (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87) - 1, - 21 * a_21^2 * a_32 * b_3 * (a_31 + a_32)^3 + - 21 * b_4 * (a_21^2 * a_42 + a_43 * (a_31 + a_32)^2) * (a_41 + a_42 + a_43)^3 + - 21 * - b_5 * - (a_21^2 * a_52 + a_53 * (a_31 + a_32)^2 + a_54 * (a_41 + a_42 + a_43)^2) * - (a_51 + a_52 + a_53 + a_54)^3 + - 21 * - b_6 * - ( - a_21^2 * a_62 + - a_63 * (a_31 + a_32)^2 + - a_64 * (a_41 + a_42 + a_43)^2 + - a_65 * (a_51 + a_52 + a_53 + a_54)^2 - ) * - (a_61 + a_62 + a_63 + a_64 + a_65)^3 + - 21 * - b_7 * - ( - a_21^2 * a_72 + - a_73 * (a_31 + a_32)^2 + - a_74 * (a_41 + a_42 + a_43)^2 + - a_75 * (a_51 + a_52 + a_53 + a_54)^2 + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65)^2 - ) * - (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^3 + - 21 * - b_8 * - ( - a_21^2 * a_82 + - a_83 * (a_31 + a_32)^2 + - a_84 * (a_41 + a_42 + a_43)^2 + - a_85 * (a_51 + a_52 + a_53 + a_54)^2 + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65)^2 + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2 - ) * - (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^3 - 1, - 56 * a_21^3 * a_32^3 * b_3 + - 56 * b_4 * (a_21 * a_42 + a_43 * (a_31 + a_32))^3 + - 56 * b_5 * (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43))^3 + - 56 * - b_6 * - ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - )^3 + - 56 * - b_7 * - ( - a_21 * a_72 + - a_73 * (a_31 + a_32) + - a_74 * (a_41 + a_42 + a_43) + - a_75 * (a_51 + a_52 + a_53 + a_54) + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65) - )^3 + - 56 * - b_8 * - ( - a_21 * a_82 + - a_83 * (a_31 + a_32) + - a_84 * (a_41 + a_42 + a_43) + - a_85 * (a_51 + a_52 + a_53 + a_54) + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65) + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) - )^3 - 1, - 28 * a_21^2 * a_32^2 * b_3 * (a_31 + a_32)^2 + - 28 * b_4 * (a_21 * a_42 + a_43 * (a_31 + a_32))^2 * (a_41 + a_42 + a_43)^2 + - 28 * - b_5 * - (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43))^2 * - (a_51 + a_52 + a_53 + a_54)^2 + - 28 * - b_6 * - ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - )^2 * - (a_61 + a_62 + a_63 + a_64 + a_65)^2 + - 28 * - b_7 * - ( - a_21 * a_72 + - a_73 * (a_31 + a_32) + - a_74 * (a_41 + a_42 + a_43) + - a_75 * (a_51 + a_52 + a_53 + a_54) + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65) - )^2 * - (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2 + - 28 * - b_8 * - ( - a_21 * a_82 + - a_83 * (a_31 + a_32) + - a_84 * (a_41 + a_42 + a_43) + - a_85 * (a_51 + a_52 + a_53 + a_54) + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65) + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) - )^2 * - (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^2 - 1, - 14 * a_21 * a_32 * b_3 * (a_31 + a_32)^4 + - 14 * b_4 * (a_21 * a_42 + a_43 * (a_31 + a_32)) * (a_41 + a_42 + a_43)^4 + - 14 * - b_5 * - (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) * - (a_51 + a_52 + a_53 + a_54)^4 + - 14 * - b_6 * - ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - ) * - (a_61 + a_62 + a_63 + a_64 + a_65)^4 + - 14 * - b_7 * - ( - a_21 * a_72 + - a_73 * (a_31 + a_32) + - a_74 * (a_41 + a_42 + a_43) + - a_75 * (a_51 + a_52 + a_53 + a_54) + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65) - ) * - (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^4 + - 14 * - b_8 * - ( - a_21 * a_82 + - a_83 * (a_31 + a_32) + - a_84 * (a_41 + a_42 + a_43) + - a_85 * (a_51 + a_52 + a_53 + a_54) + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65) + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) - ) * - (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^4 - 1, - 7 * a_21^6 * b_2 + - 7 * b_3 * (a_31 + a_32)^6 + - 7 * b_4 * (a_41 + a_42 + a_43)^6 + - 7 * b_5 * (a_51 + a_52 + a_53 + a_54)^6 + - 7 * b_6 * (a_61 + a_62 + a_63 + a_64 + a_65)^6 + - 7 * b_7 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^6 + - 7 * b_8 * (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^6 - 1 -] diff --git a/benchmark/scripts/runge-kutta/aa-runge-kutta-8-7_gf.jl b/benchmark/scripts/runge-kutta/aa-runge-kutta-8-7_gf.jl deleted file mode 100644 index 00ffc986..00000000 --- a/benchmark/scripts/runge-kutta/aa-runge-kutta-8-7_gf.jl +++ /dev/null @@ -1,3794 +0,0 @@ -R, -( - a_21, - a_31, - a_32, - a_41, - a_42, - a_43, - a_51, - a_52, - a_53, - a_54, - a_61, - a_62, - a_63, - a_64, - a_65, - a_71, - a_72, - a_73, - a_74, - a_75, - a_76, - a_81, - a_82, - a_83, - a_84, - a_85, - a_86, - a_87, - b_1, - b_2, - b_3, - b_4, - b_5, - b_6, - b_7, - b_8 -) = polynomial_ring( - GF(2^31 - 1), - [ - "a_21", - "a_31", - "a_32", - "a_41", - "a_42", - "a_43", - "a_51", - "a_52", - "a_53", - "a_54", - "a_61", - "a_62", - "a_63", - "a_64", - "a_65", - "a_71", - "a_72", - "a_73", - "a_74", - "a_75", - "a_76", - "a_81", - "a_82", - "a_83", - "a_84", - "a_85", - "a_86", - "a_87", - "b_1", - "b_2", - "b_3", - "b_4", - "b_5", - "b_6", - "b_7", - "b_8" - ] -) - -system = [ - b_1 + b_2 + b_3 + b_4 + b_5 + b_6 + b_7 + b_8 - 1, - 2 * a_21 * b_2 + - 2 * b_3 * (a_31 + a_32) + - 2 * b_4 * (a_41 + a_42 + a_43) + - 2 * b_5 * (a_51 + a_52 + a_53 + a_54) + - 2 * b_6 * (a_61 + a_62 + a_63 + a_64 + a_65) + - 2 * b_7 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) + - 2 * b_8 * (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87) - 1, - 6 * a_21 * a_32 * b_3 + - 6 * b_4 * (a_21 * a_42 + a_43 * (a_31 + a_32)) + - 6 * b_5 * (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) + - 6 * - b_6 * - ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - ) + - 6 * - b_7 * - ( - a_21 * a_72 + - a_73 * (a_31 + a_32) + - a_74 * (a_41 + a_42 + a_43) + - a_75 * (a_51 + a_52 + a_53 + a_54) + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65) - ) + - 6 * - b_8 * - ( - a_21 * a_82 + - a_83 * (a_31 + a_32) + - a_84 * (a_41 + a_42 + a_43) + - a_85 * (a_51 + a_52 + a_53 + a_54) + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65) + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) - ) - 1, - 3 * a_21^2 * b_2 + - 3 * b_3 * (a_31 + a_32)^2 + - 3 * b_4 * (a_41 + a_42 + a_43)^2 + - 3 * b_5 * (a_51 + a_52 + a_53 + a_54)^2 + - 3 * b_6 * (a_61 + a_62 + a_63 + a_64 + a_65)^2 + - 3 * b_7 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2 + - 3 * b_8 * (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^2 - 1, - 24 * a_21 * a_32 * a_43 * b_4 + - 24 * b_5 * (a_21 * a_32 * a_53 + a_54 * (a_21 * a_42 + a_43 * (a_31 + a_32))) + - 24 * - b_6 * - ( - a_21 * a_32 * a_63 + - a_64 * (a_21 * a_42 + a_43 * (a_31 + a_32)) + - a_65 * (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) - ) + - 24 * - b_7 * - ( - a_21 * a_32 * a_73 + - a_74 * (a_21 * a_42 + a_43 * (a_31 + a_32)) + - a_75 * (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) + - a_76 * ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - ) - ) + - 24 * - b_8 * - ( - a_21 * a_32 * a_83 + - a_84 * (a_21 * a_42 + a_43 * (a_31 + a_32)) + - a_85 * (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) + - a_86 * ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - ) + - a_87 * ( - a_21 * a_72 + - a_73 * (a_31 + a_32) + - a_74 * (a_41 + a_42 + a_43) + - a_75 * (a_51 + a_52 + a_53 + a_54) + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65) - ) - ) - 1, - 12 * a_21^2 * a_32 * b_3 + - 12 * b_4 * (a_21^2 * a_42 + a_43 * (a_31 + a_32)^2) + - 12 * b_5 * (a_21^2 * a_52 + a_53 * (a_31 + a_32)^2 + a_54 * (a_41 + a_42 + a_43)^2) + - 12 * - b_6 * - ( - a_21^2 * a_62 + - a_63 * (a_31 + a_32)^2 + - a_64 * (a_41 + a_42 + a_43)^2 + - a_65 * (a_51 + a_52 + a_53 + a_54)^2 - ) + - 12 * - b_7 * - ( - a_21^2 * a_72 + - a_73 * (a_31 + a_32)^2 + - a_74 * (a_41 + a_42 + a_43)^2 + - a_75 * (a_51 + a_52 + a_53 + a_54)^2 + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65)^2 - ) + - 12 * - b_8 * - ( - a_21^2 * a_82 + - a_83 * (a_31 + a_32)^2 + - a_84 * (a_41 + a_42 + a_43)^2 + - a_85 * (a_51 + a_52 + a_53 + a_54)^2 + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65)^2 + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2 - ) - 1, - 8 * a_21 * a_32 * b_3 * (a_31 + a_32) + - 8 * b_4 * (a_21 * a_42 + a_43 * (a_31 + a_32)) * (a_41 + a_42 + a_43) + - 8 * - b_5 * - (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) * - (a_51 + a_52 + a_53 + a_54) + - 8 * - b_6 * - ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - ) * - (a_61 + a_62 + a_63 + a_64 + a_65) + - 8 * - b_7 * - ( - a_21 * a_72 + - a_73 * (a_31 + a_32) + - a_74 * (a_41 + a_42 + a_43) + - a_75 * (a_51 + a_52 + a_53 + a_54) + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65) - ) * - (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) + - 8 * - b_8 * - ( - a_21 * a_82 + - a_83 * (a_31 + a_32) + - a_84 * (a_41 + a_42 + a_43) + - a_85 * (a_51 + a_52 + a_53 + a_54) + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65) + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) - ) * - (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87) - 1, - 4 * a_21^3 * b_2 + - 4 * b_3 * (a_31 + a_32)^3 + - 4 * b_4 * (a_41 + a_42 + a_43)^3 + - 4 * b_5 * (a_51 + a_52 + a_53 + a_54)^3 + - 4 * b_6 * (a_61 + a_62 + a_63 + a_64 + a_65)^3 + - 4 * b_7 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^3 + - 4 * b_8 * (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^3 - 1, - 120 * a_21 * a_32 * a_43 * a_54 * b_5 + - 120 * - b_6 * - ( - a_21 * a_32 * a_43 * a_64 + - a_65 * (a_21 * a_32 * a_53 + a_54 * (a_21 * a_42 + a_43 * (a_31 + a_32))) - ) + - 120 * - b_7 * - ( - a_21 * a_32 * a_43 * a_74 + - a_75 * (a_21 * a_32 * a_53 + a_54 * (a_21 * a_42 + a_43 * (a_31 + a_32))) + - a_76 * ( - a_21 * a_32 * a_63 + - a_64 * (a_21 * a_42 + a_43 * (a_31 + a_32)) + - a_65 * (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) - ) - ) + - 120 * - b_8 * - ( - a_21 * a_32 * a_43 * a_84 + - a_85 * (a_21 * a_32 * a_53 + a_54 * (a_21 * a_42 + a_43 * (a_31 + a_32))) + - a_86 * ( - a_21 * a_32 * a_63 + - a_64 * (a_21 * a_42 + a_43 * (a_31 + a_32)) + - a_65 * (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) - ) + - a_87 * ( - a_21 * a_32 * a_73 + - a_74 * (a_21 * a_42 + a_43 * (a_31 + a_32)) + - a_75 * (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) + - a_76 * ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - ) - ) - ) - 1, - 60 * a_21^2 * a_32 * a_43 * b_4 + - 60 * b_5 * (a_21^2 * a_32 * a_53 + a_54 * (a_21^2 * a_42 + a_43 * (a_31 + a_32)^2)) + - 60 * - b_6 * - ( - a_21^2 * a_32 * a_63 + - a_64 * (a_21^2 * a_42 + a_43 * (a_31 + a_32)^2) + - a_65 * (a_21^2 * a_52 + a_53 * (a_31 + a_32)^2 + a_54 * (a_41 + a_42 + a_43)^2) - ) + - 60 * - b_7 * - ( - a_21^2 * a_32 * a_73 + - a_74 * (a_21^2 * a_42 + a_43 * (a_31 + a_32)^2) + - a_75 * (a_21^2 * a_52 + a_53 * (a_31 + a_32)^2 + a_54 * (a_41 + a_42 + a_43)^2) + - a_76 * ( - a_21^2 * a_62 + - a_63 * (a_31 + a_32)^2 + - a_64 * (a_41 + a_42 + a_43)^2 + - a_65 * (a_51 + a_52 + a_53 + a_54)^2 - ) - ) + - 60 * - b_8 * - ( - a_21^2 * a_32 * a_83 + - a_84 * (a_21^2 * a_42 + a_43 * (a_31 + a_32)^2) + - a_85 * (a_21^2 * a_52 + a_53 * (a_31 + a_32)^2 + a_54 * (a_41 + a_42 + a_43)^2) + - a_86 * ( - a_21^2 * a_62 + - a_63 * (a_31 + a_32)^2 + - a_64 * (a_41 + a_42 + a_43)^2 + - a_65 * (a_51 + a_52 + a_53 + a_54)^2 - ) + - a_87 * ( - a_21^2 * a_72 + - a_73 * (a_31 + a_32)^2 + - a_74 * (a_41 + a_42 + a_43)^2 + - a_75 * (a_51 + a_52 + a_53 + a_54)^2 + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65)^2 - ) - ) - 1, - 40 * a_21 * a_32 * a_43 * b_4 * (a_31 + a_32) + - 40 * - b_5 * - ( - a_21 * a_32 * a_53 * (a_31 + a_32) + - a_54 * (a_21 * a_42 + a_43 * (a_31 + a_32)) * (a_41 + a_42 + a_43) - ) + - 40 * - b_6 * - ( - a_21 * a_32 * a_63 * (a_31 + a_32) + - a_64 * (a_21 * a_42 + a_43 * (a_31 + a_32)) * (a_41 + a_42 + a_43) + - a_65 * - (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) * - (a_51 + a_52 + a_53 + a_54) - ) + - 40 * - b_7 * - ( - a_21 * a_32 * a_73 * (a_31 + a_32) + - a_74 * (a_21 * a_42 + a_43 * (a_31 + a_32)) * (a_41 + a_42 + a_43) + - a_75 * - (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) * - (a_51 + a_52 + a_53 + a_54) + - a_76 * - ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + 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a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - ) * - (a_61 + a_62 + a_63 + a_64 + a_65) + - 84 * - b_7 * - ( - a_21 * a_32 * a_73 + - a_74 * (a_21 * a_42 + a_43 * (a_31 + a_32)) + - a_75 * (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) + - a_76 * ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - ) - ) * - ( - a_21 * a_72 + - a_73 * (a_31 + a_32) + - a_74 * (a_41 + a_42 + a_43) + - a_75 * (a_51 + a_52 + a_53 + a_54) + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65) - ) * - (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) + - 84 * - b_8 * - ( - a_21 * a_32 * a_83 + - a_84 * (a_21 * a_42 + a_43 * (a_31 + a_32)) + - a_85 * (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) + - a_86 * ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - ) + - a_87 * ( - a_21 * a_72 + - a_73 * (a_31 + a_32) + - a_74 * (a_41 + a_42 + a_43) + - a_75 * (a_51 + a_52 + a_53 + a_54) + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65) - ) - ) * - ( - a_21 * a_82 + - a_83 * (a_31 + a_32) + - a_84 * (a_41 + a_42 + a_43) + - a_85 * (a_51 + a_52 + a_53 + a_54) + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65) + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) - ) * - (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87) - 1, - 42 * a_21 * a_32 * a_43 * b_4 * (a_41 + a_42 + a_43)^3 + - 42 * - b_5 * - (a_21 * a_32 * a_53 + a_54 * (a_21 * a_42 + a_43 * (a_31 + a_32))) * - (a_51 + a_52 + a_53 + a_54)^3 + - 42 * - b_6 * - ( - a_21 * a_32 * a_63 + - a_64 * (a_21 * a_42 + a_43 * (a_31 + a_32)) + - a_65 * (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) - ) * - (a_61 + a_62 + a_63 + a_64 + a_65)^3 + - 42 * - b_7 * - ( - a_21 * a_32 * a_73 + - a_74 * (a_21 * a_42 + a_43 * (a_31 + a_32)) + - a_75 * (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) + - a_76 * ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - ) - ) * - (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^3 + - 42 * - b_8 * - ( - a_21 * a_32 * a_83 + - a_84 * (a_21 * a_42 + a_43 * (a_31 + a_32)) + - a_85 * (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) + - a_86 * ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - ) + - a_87 * ( - a_21 * a_72 + - a_73 * (a_31 + a_32) + - a_74 * (a_41 + a_42 + a_43) + - a_75 * (a_51 + a_52 + a_53 + a_54) + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65) - ) - ) * - (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^3 - 1, - 42 * a_21^5 * a_32 * b_3 + - 42 * b_4 * (a_21^5 * a_42 + a_43 * (a_31 + a_32)^5) + - 42 * b_5 * (a_21^5 * a_52 + a_53 * (a_31 + a_32)^5 + a_54 * (a_41 + a_42 + a_43)^5) + - 42 * - b_6 * - ( - a_21^5 * a_62 + - a_63 * (a_31 + a_32)^5 + - a_64 * (a_41 + a_42 + a_43)^5 + - a_65 * (a_51 + a_52 + a_53 + a_54)^5 - ) + - 42 * - b_7 * - ( - a_21^5 * a_72 + - a_73 * (a_31 + a_32)^5 + - a_74 * (a_41 + a_42 + a_43)^5 + - a_75 * (a_51 + a_52 + a_53 + a_54)^5 + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65)^5 - ) + - 42 * - b_8 * - ( - a_21^5 * a_82 + - a_83 * (a_31 + a_32)^5 + - a_84 * (a_41 + a_42 + a_43)^5 + - a_85 * (a_51 + a_52 + a_53 + a_54)^5 + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65)^5 + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^5 - ) - 1, - 35 * a_21^4 * a_32 * b_3 * (a_31 + a_32) + - 35 * b_4 * (a_21^4 * a_42 + a_43 * (a_31 + a_32)^4) * (a_41 + a_42 + a_43) + - 35 * - b_5 * - (a_21^4 * a_52 + a_53 * (a_31 + a_32)^4 + a_54 * (a_41 + a_42 + a_43)^4) * - (a_51 + a_52 + a_53 + a_54) + - 35 * - b_6 * - ( - a_21^4 * a_62 + - a_63 * (a_31 + a_32)^4 + - a_64 * (a_41 + a_42 + a_43)^4 + - a_65 * (a_51 + a_52 + a_53 + a_54)^4 - ) * - (a_61 + a_62 + a_63 + a_64 + a_65) + - 35 * - b_7 * - ( - a_21^4 * a_72 + - a_73 * (a_31 + a_32)^4 + - a_74 * (a_41 + a_42 + a_43)^4 + - a_75 * (a_51 + a_52 + a_53 + a_54)^4 + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65)^4 - ) * - (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) + - 35 * - b_8 * - ( - a_21^4 * a_82 + - a_83 * (a_31 + a_32)^4 + - a_84 * (a_41 + a_42 + a_43)^4 + - a_85 * (a_51 + a_52 + a_53 + a_54)^4 + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65)^4 + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^4 - ) * - (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87) - 1, - 56 * a_21^4 * a_32^2 * b_3 + - 56 * b_4 * (a_21 * a_42 + a_43 * (a_31 + a_32)) * (a_21^3 * a_42 + a_43 * (a_31 + a_32)^3) + - 56 * - b_5 * - (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) * - (a_21^3 * a_52 + a_53 * (a_31 + a_32)^3 + a_54 * (a_41 + a_42 + a_43)^3) + - 56 * - b_6 * - ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - ) * - ( - a_21^3 * a_62 + - a_63 * (a_31 + a_32)^3 + - a_64 * (a_41 + a_42 + a_43)^3 + - a_65 * (a_51 + a_52 + a_53 + a_54)^3 - ) + - 56 * - b_7 * - ( - a_21 * a_72 + - a_73 * (a_31 + a_32) + - a_74 * (a_41 + a_42 + a_43) + - a_75 * (a_51 + a_52 + a_53 + a_54) + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65) - ) * - ( - a_21^3 * a_72 + - a_73 * (a_31 + a_32)^3 + - a_74 * (a_41 + a_42 + a_43)^3 + - a_75 * (a_51 + a_52 + a_53 + a_54)^3 + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65)^3 - ) + - 56 * - b_8 * - ( - a_21 * a_82 + - a_83 * (a_31 + a_32) + - a_84 * (a_41 + a_42 + a_43) + - a_85 * (a_51 + a_52 + a_53 + a_54) + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65) + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) - ) * - ( - a_21^3 * a_82 + - a_83 * (a_31 + a_32)^3 + - a_84 * (a_41 + a_42 + a_43)^3 + - a_85 * (a_51 + a_52 + a_53 + a_54)^3 + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65)^3 + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^3 - ) - 1, - 28 * a_21^3 * a_32 * b_3 * (a_31 + a_32)^2 + - 28 * b_4 * (a_21^3 * a_42 + a_43 * (a_31 + a_32)^3) * (a_41 + a_42 + a_43)^2 + - 28 * - b_5 * - (a_21^3 * a_52 + a_53 * (a_31 + a_32)^3 + a_54 * (a_41 + a_42 + a_43)^3) * - (a_51 + a_52 + a_53 + a_54)^2 + - 28 * - b_6 * - ( - a_21^3 * a_62 + - a_63 * (a_31 + a_32)^3 + - a_64 * (a_41 + a_42 + a_43)^3 + - a_65 * (a_51 + a_52 + a_53 + a_54)^3 - ) * - (a_61 + a_62 + a_63 + a_64 + a_65)^2 + - 28 * - b_7 * - ( - a_21^3 * a_72 + - a_73 * (a_31 + a_32)^3 + - a_74 * (a_41 + a_42 + a_43)^3 + - a_75 * (a_51 + a_52 + a_53 + a_54)^3 + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65)^3 - ) * - (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2 + - 28 * - b_8 * - ( - a_21^3 * a_82 + - a_83 * (a_31 + a_32)^3 + - a_84 * (a_41 + a_42 + a_43)^3 + - a_85 * (a_51 + a_52 + a_53 + a_54)^3 + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65)^3 + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^3 - ) * - (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^2 - 1, - 63 * a_21^4 * a_32^2 * b_3 + - 63 * b_4 * (a_21^2 * a_42 + a_43 * (a_31 + a_32)^2)^2 + - 63 * b_5 * (a_21^2 * a_52 + a_53 * (a_31 + a_32)^2 + a_54 * (a_41 + a_42 + a_43)^2)^2 + - 63 * - b_6 * - ( - a_21^2 * a_62 + - a_63 * (a_31 + a_32)^2 + - a_64 * (a_41 + a_42 + a_43)^2 + - a_65 * (a_51 + a_52 + a_53 + a_54)^2 - )^2 + - 63 * - b_7 * - ( - a_21^2 * a_72 + - a_73 * (a_31 + a_32)^2 + - a_74 * (a_41 + a_42 + a_43)^2 + - a_75 * (a_51 + a_52 + a_53 + a_54)^2 + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65)^2 - )^2 + - 63 * - b_8 * - ( - a_21^2 * a_82 + - a_83 * (a_31 + a_32)^2 + - a_84 * (a_41 + a_42 + a_43)^2 + - a_85 * (a_51 + a_52 + a_53 + a_54)^2 + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65)^2 + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2 - )^2 - 1, - 42 * a_21^3 * a_32^2 * b_3 * (a_31 + a_32) + - 42 * - b_4 * - (a_21 * a_42 + a_43 * (a_31 + a_32)) * - (a_21^2 * a_42 + a_43 * (a_31 + a_32)^2) * - (a_41 + a_42 + a_43) + - 42 * - b_5 * - (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) * - (a_21^2 * a_52 + a_53 * (a_31 + a_32)^2 + a_54 * (a_41 + a_42 + a_43)^2) * - (a_51 + a_52 + a_53 + a_54) + - 42 * - b_6 * - ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - ) * - ( - a_21^2 * a_62 + - a_63 * (a_31 + a_32)^2 + - a_64 * (a_41 + a_42 + a_43)^2 + - a_65 * (a_51 + a_52 + a_53 + a_54)^2 - ) * - (a_61 + a_62 + a_63 + a_64 + a_65) + - 42 * - b_7 * - ( - a_21 * a_72 + - a_73 * (a_31 + a_32) + - a_74 * (a_41 + a_42 + a_43) + - a_75 * (a_51 + a_52 + a_53 + a_54) + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65) - ) * - ( - a_21^2 * a_72 + - a_73 * (a_31 + a_32)^2 + - a_74 * (a_41 + a_42 + a_43)^2 + - a_75 * (a_51 + a_52 + a_53 + a_54)^2 + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65)^2 - ) * - (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) + - 42 * - b_8 * - ( - a_21 * a_82 + - a_83 * (a_31 + a_32) + - a_84 * (a_41 + a_42 + a_43) + - a_85 * (a_51 + a_52 + a_53 + a_54) + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65) + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) - ) * - ( - a_21^2 * a_82 + - a_83 * (a_31 + a_32)^2 + - a_84 * (a_41 + a_42 + a_43)^2 + - a_85 * (a_51 + a_52 + a_53 + a_54)^2 + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65)^2 + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2 - ) * - (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87) - 1, - 21 * a_21^2 * a_32 * b_3 * (a_31 + a_32)^3 + - 21 * b_4 * (a_21^2 * a_42 + a_43 * (a_31 + a_32)^2) * (a_41 + a_42 + a_43)^3 + - 21 * - b_5 * - (a_21^2 * a_52 + a_53 * (a_31 + a_32)^2 + a_54 * (a_41 + a_42 + a_43)^2) * - (a_51 + a_52 + a_53 + a_54)^3 + - 21 * - b_6 * - ( - a_21^2 * a_62 + - a_63 * (a_31 + a_32)^2 + - a_64 * (a_41 + a_42 + a_43)^2 + - a_65 * (a_51 + a_52 + a_53 + a_54)^2 - ) * - (a_61 + a_62 + a_63 + a_64 + a_65)^3 + - 21 * - b_7 * - ( - a_21^2 * a_72 + - a_73 * (a_31 + a_32)^2 + - a_74 * (a_41 + a_42 + a_43)^2 + - a_75 * (a_51 + a_52 + a_53 + a_54)^2 + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65)^2 - ) * - (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^3 + - 21 * - b_8 * - ( - a_21^2 * a_82 + - a_83 * (a_31 + a_32)^2 + - a_84 * (a_41 + a_42 + a_43)^2 + - a_85 * (a_51 + a_52 + a_53 + a_54)^2 + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65)^2 + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2 - ) * - (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^3 - 1, - 56 * a_21^3 * a_32^3 * b_3 + - 56 * b_4 * (a_21 * a_42 + a_43 * (a_31 + a_32))^3 + - 56 * b_5 * (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43))^3 + - 56 * - b_6 * - ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - )^3 + - 56 * - b_7 * - ( - a_21 * a_72 + - a_73 * (a_31 + a_32) + - a_74 * (a_41 + a_42 + a_43) + - a_75 * (a_51 + a_52 + a_53 + a_54) + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65) - )^3 + - 56 * - b_8 * - ( - a_21 * a_82 + - a_83 * (a_31 + a_32) + - a_84 * (a_41 + a_42 + a_43) + - a_85 * (a_51 + a_52 + a_53 + a_54) + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65) + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) - )^3 - 1, - 28 * a_21^2 * a_32^2 * b_3 * (a_31 + a_32)^2 + - 28 * b_4 * (a_21 * a_42 + a_43 * (a_31 + a_32))^2 * (a_41 + a_42 + a_43)^2 + - 28 * - b_5 * - (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43))^2 * - (a_51 + a_52 + a_53 + a_54)^2 + - 28 * - b_6 * - ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - )^2 * - (a_61 + a_62 + a_63 + a_64 + a_65)^2 + - 28 * - b_7 * - ( - a_21 * a_72 + - a_73 * (a_31 + a_32) + - a_74 * (a_41 + a_42 + a_43) + - a_75 * (a_51 + a_52 + a_53 + a_54) + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65) - )^2 * - (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2 + - 28 * - b_8 * - ( - a_21 * a_82 + - a_83 * (a_31 + a_32) + - a_84 * (a_41 + a_42 + a_43) + - a_85 * (a_51 + a_52 + a_53 + a_54) + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65) + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) - )^2 * - (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^2 - 1, - 14 * a_21 * a_32 * b_3 * (a_31 + a_32)^4 + - 14 * b_4 * (a_21 * a_42 + a_43 * (a_31 + a_32)) * (a_41 + a_42 + a_43)^4 + - 14 * - b_5 * - (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) * - (a_51 + a_52 + a_53 + a_54)^4 + - 14 * - b_6 * - ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - ) * - (a_61 + a_62 + a_63 + a_64 + a_65)^4 + - 14 * - b_7 * - ( - a_21 * a_72 + - a_73 * (a_31 + a_32) + - a_74 * (a_41 + a_42 + a_43) + - a_75 * (a_51 + a_52 + a_53 + a_54) + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65) - ) * - (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^4 + - 14 * - b_8 * - ( - a_21 * a_82 + - a_83 * (a_31 + a_32) + - a_84 * (a_41 + a_42 + a_43) + - a_85 * (a_51 + a_52 + a_53 + a_54) + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65) + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) - ) * - (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^4 - 1, - 7 * a_21^6 * b_2 + - 7 * b_3 * (a_31 + a_32)^6 + - 7 * b_4 * (a_41 + a_42 + a_43)^6 + - 7 * b_5 * (a_51 + a_52 + a_53 + a_54)^6 + - 7 * b_6 * (a_61 + a_62 + a_63 + a_64 + a_65)^6 + - 7 * b_7 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^6 + - 7 * b_8 * (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^6 - 1 -] diff --git a/benchmark/scripts/runge-kutta/big_maxpairs_1000_gf.jl b/benchmark/scripts/runge-kutta/big_maxpairs_1000_gf.jl deleted file mode 100644 index 0820504d..00000000 --- a/benchmark/scripts/runge-kutta/big_maxpairs_1000_gf.jl +++ /dev/null @@ -1,20 +0,0 @@ -using DynamicPolynomials, Nemo -using Groebner -using Printf - -include((@__DIR__) * "/rss_tracker.jl") -include((@__DIR__) * "/aa-runge-kutta-8-7_gf.jl"); - -setup_memuse_tracker() - -const maxpairs = 500 - -# Compile -n = Groebner.Examples.noonn(3); -Groebner.groebner(n, ordering=DegRevLex(), maxpairs=maxpairs); - -# Run! -@time gb = - Groebner.groebner(system, ordering=DegRevLex(), maxpairs=maxpairs, monoms=Packed{UInt8}()); - -GC.gc() diff --git a/benchmark/scripts/runge-kutta/big_maxpairs_inf.jl b/benchmark/scripts/runge-kutta/big_maxpairs_inf.jl deleted file mode 100644 index dd47480f..00000000 --- a/benchmark/scripts/runge-kutta/big_maxpairs_inf.jl +++ /dev/null @@ -1,19 +0,0 @@ -using DynamicPolynomials, Nemo -using Groebner -using Printf - -include((@__DIR__) * "/rss_tracker.jl") -include((@__DIR__) * "/aa-runge-kutta-8-7.jl"); - -setup_memuse_tracker() - -const maxpairs = typemax(Int) - -# Compile -n = Groebner.Examples.noonn(3); -Groebner.groebner(n, ordering=Groebner.DegRevLex(), maxpairs=maxpairs); - -# Run! -@time gb = Groebner.groebner(system, ordering=Groebner.DegRevLex(), maxpairs=maxpairs); - -GC.gc() diff --git a/benchmark/scripts/runge-kutta/big_singular.jl b/benchmark/scripts/runge-kutta/big_singular.jl deleted file mode 100644 index 44e4e144..00000000 --- a/benchmark/scripts/runge-kutta/big_singular.jl +++ /dev/null @@ -1,35 +0,0 @@ -import Pkg -Pkg.activate("../singular") - -import AbstractAlgebra -import Singular -using Nemo - -include((@__DIR__) * "/rss_tracker.jl") -include((@__DIR__) * "/aa-runge-kutta-6-6.jl"); - -function aa_to_singular(poly) - Rxx = parent(poly) - Rqq = AbstractAlgebra.base_ring(Rxx) - xstrings = map(string, AbstractAlgebra.gens(Rxx)) - base = Singular.QQ - new_ring, _ = Singular.polynomial_ring(base, xstrings, internal_ordering=:degrevlex) - AbstractAlgebra.change_base_ring(AbstractAlgebra.base_ring(new_ring), poly, parent=new_ring) -end - -setup_memuse_tracker() - -singular_system = map(aa_to_singular, system) -singular_ring = parent(singular_system[1]) - -println(ordering(singular_ring)) - -# Run! -singular_ideal = Singular.Ideal(singular_ring, singular_system) -# @time gb = Singular.std(singular_ideal); - -# Run slimgb -singular_ideal = Singular.Ideal(singular_ring, singular_system) -@time gb = Singular.slimgb(singular_ideal); - -GC.gc() diff --git a/benchmark/scripts/runge-kutta/maxpairs_inf.jl b/benchmark/scripts/runge-kutta/maxpairs_inf.jl deleted file mode 100644 index cfeea1cf..00000000 --- a/benchmark/scripts/runge-kutta/maxpairs_inf.jl +++ /dev/null @@ -1,11 +0,0 @@ -using Nemo -# using Groebner -using Printf - -include((@__DIR__) * "/rss_tracker.jl") -include((@__DIR__) * "/aa-runge-kutta-8-7_gf.jl"); - -setup_memuse_tracker() - -# Run! -@time gb = Groebner.groebner(system, ordering=Groebner.DegRevLex(), loglevel=:debug); diff --git a/benchmark/scripts/runge-kutta/rss_tracker.jl b/benchmark/scripts/runge-kutta/rss_tracker.jl deleted file mode 100644 index 96170a60..00000000 --- a/benchmark/scripts/runge-kutta/rss_tracker.jl +++ /dev/null @@ -1,18 +0,0 @@ -using Printf - -function setup_memuse_tracker() - tracker = Ref(0) - function mem_use(tracker) - finalizer(mem_use, tracker) - out = Core.CoreSTDOUT() - Core.write( - Core.CoreSTDOUT(), - @sprintf "GC live: %9.3f MiB, " Base.gc_live_bytes() / 2^20 - ) - Core.write(Core.CoreSTDOUT(), @sprintf "Max. RSS: %9.3f MiB\n" Sys.maxrss() / 2^20) - nothing - end - - finalizer(mem_use, tracker) - nothing -end diff --git a/benchmark/scripts/runge-kutta/run.jl b/benchmark/scripts/runge-kutta/run.jl deleted file mode 100644 index 56605e2a..00000000 --- a/benchmark/scripts/runge-kutta/run.jl +++ /dev/null @@ -1,71 +0,0 @@ -using DynamicPolynomials -using Groebner -import Nemo - -function setup_memuse_tracker() - tracker = Ref(0) - function mem_use(tracker) - finalizer(mem_use, tracker) - out = Core.CoreSTDOUT() - Core.write(out, "Memory usage:\n") - Core.write(Core.CoreSTDOUT(), "GC live: $(Base.gc_live_bytes() / 2^20) MiB\n") - Core.write(Core.CoreSTDOUT(), "Max. RSS: $(Sys.maxrss() / 2^20) MiB\n") - nothing - end - - finalizer(mem_use, tracker) - nothing -end - -setup_memuse_tracker() - -macro pr(ex, args...) - return quote - Profile.clear() - Profile.init(n=10^8, delay=1e-5) - Profile.@profile $(esc(ex)) - view_profile(; $(esc.(args)...)) - end -end - -using Nemo -include((@__DIR__) * "/aa-runge-kutta-6-6.jl"); - -n = Groebner.Examples.noonn(3) -Groebner.groebner(n, ordering=Groebner.DegRevLex()); - -@time gb = Groebner.groebner(system, ordering=Groebner.DegRevLex()); - -GC.gc() - -vs = split( - "a_21 a_31 a_32 a_41 a_42 a_43 a_51 a_52 a_53 a_54 a_61 a_62 a_63 a_64 a_65 a_71 a_72 a_73 a_74 a_75 a_76 a_81 a_82 a_83 a_84 a_85 a_86 a_87 b_1 b_2 b_3 b_4 b_5 b_6 b_7 b_8" -) -vs -ord = Groebner.WeightedOrdering([[10 for i in 1:28]..., [1 for i in 1:8]...]) - -gb = Groebner.groebner( - system, - linalg=:prob - # ordering=ord -); - -println(gb) - -using AbstractAlgebra -include((@__DIR__) * "/aa-runge-kutta-6-6.jl"); -length(system) -gens(parent(system[1])) - -system_autoreduced = deepcopy(system); -for i in 1:length(system) - f = system_autoreduced[i] - I = system[i .!= 1:length(system)] - system_autoreduced[i] = AbstractAlgebra.normal_form(f, I) -end; - -@pr gb = Groebner.groebner(system, linalg=:prob, ordering=DegRevLex()); - -@polyvar x y z a b c -s = [y, x, z, a + b^2 + c^3] -g = groebner(s, ordering=Groebner.WeightedOrdering([1, 10, 10, 1, 1, 1])) diff --git a/benchmark/scripts/runge-kutta/run_2.jl b/benchmark/scripts/runge-kutta/run_2.jl deleted file mode 100644 index 686c1759..00000000 --- a/benchmark/scripts/runge-kutta/run_2.jl +++ /dev/null @@ -1,11 +0,0 @@ -# using DynamicPolynomials, Nemo -# using Groebner - -# include((@__DIR__) * "/rss_tracker.jl") -include((@__DIR__) * "/aa-runge-kutta-6-6.jl"); - -# setup_memuse_tracker() - -Groebner.logging_enabled() = true - -@time gb = Groebner.groebner(system, loglevel=-1, ordering=Groebner.DegRevLex()); diff --git a/benchmark/scripts/runge-kutta/runge-kutta-4-4.jl b/benchmark/scripts/runge-kutta/runge-kutta-4-4.jl deleted file mode 100644 index 768acd15..00000000 --- a/benchmark/scripts/runge-kutta/runge-kutta-4-4.jl +++ /dev/null @@ -1,54 +0,0 @@ -@polyvar a_21 a_31 a_32 a_41 a_42 a_43 b_1 b_2 b_3 b_4 - -system = [ - b_1 + b_2 + b_3 + b_4 - 1, - 2 * a_21 * b_2 + - 2 * a_31 * b_3 + - 2 * a_32 * b_3 + - 2 * a_41 * b_4 + - 2 * a_42 * b_4 + - 2 * a_43 * b_4 - 1, - 6 * a_21 * a_32 * b_3 + 6 * a_21 * a_42 * b_4 + 6 * a_31 * a_43 * b_4 + 6 * a_32 * a_43 * b_4 - 1, - 3 * a_21^2 * b_2 + - 3 * a_31^2 * b_3 + - 6 * a_31 * a_32 * b_3 + - 3 * a_32^2 * b_3 + - 3 * a_41^2 * b_4 + - 6 * a_41 * a_42 * b_4 + - 6 * a_41 * a_43 * b_4 + - 3 * a_42^2 * b_4 + - 6 * a_42 * a_43 * b_4 + - 3 * a_43^2 * b_4 - 1, - 24 * a_21 * a_32 * a_43 * b_4 - 1, - 12 * a_21^2 * a_32 * b_3 + - 12 * a_21^2 * a_42 * b_4 + - 12 * a_31^2 * a_43 * b_4 + - 24 * a_31 * a_32 * a_43 * b_4 + - 12 * a_32^2 * a_43 * b_4 - 1, - 8 * a_21 * a_31 * a_32 * b_3 + - 8 * a_21 * a_32^2 * b_3 + - 8 * a_21 * a_41 * a_42 * b_4 + - 8 * a_21 * a_42^2 * b_4 + - 8 * a_21 * a_42 * a_43 * b_4 + - 8 * a_31 * a_41 * a_43 * b_4 + - 8 * a_31 * a_42 * a_43 * b_4 + - 8 * a_31 * a_43^2 * b_4 + - 8 * a_32 * a_41 * a_43 * b_4 + - 8 * a_32 * a_42 * a_43 * b_4 + - 8 * a_32 * a_43^2 * b_4 - 1, - 4 * a_21^3 * b_2 + - 4 * a_31^3 * b_3 + - 12 * a_31^2 * a_32 * b_3 + - 12 * a_31 * a_32^2 * b_3 + - 4 * a_32^3 * b_3 + - 4 * a_41^3 * b_4 + - 12 * a_41^2 * a_42 * b_4 + - 12 * a_41^2 * a_43 * b_4 + - 12 * a_41 * a_42^2 * b_4 + - 24 * a_41 * a_42 * a_43 * b_4 + - 12 * a_41 * a_43^2 * b_4 + - 4 * a_42^3 * b_4 + - 12 * a_42^2 * a_43 * b_4 + - 12 * a_42 * a_43^2 * b_4 + - 4 * a_43^3 * b_4 - 1 -] diff --git a/benchmark/scripts/runge-kutta/runge-kutta-6-6.jl b/benchmark/scripts/runge-kutta/runge-kutta-6-6.jl deleted file mode 100644 index 6437d933..00000000 --- a/benchmark/scripts/runge-kutta/runge-kutta-6-6.jl +++ /dev/null @@ -1,4108 +0,0 @@ -@polyvar a_21 a_31 a_32 a_41 a_42 a_43 a_51 a_52 a_53 a_54 a_61 a_62 a_63 a_64 a_65 b_1 b_2 b_3 b_4 b_5 b_6 - -system = [ - b_1 + b_2 + b_3 + b_4 + b_5 + b_6 - 1, - 2 * a_21 * b_2 + - 2 * a_31 * b_3 + - 2 * a_32 * b_3 + - 2 * a_41 * b_4 + - 2 * a_42 * b_4 + - 2 * a_43 * b_4 + - 2 * a_51 * b_5 + - 2 * a_52 * b_5 + - 2 * a_53 * b_5 + - 2 * a_54 * b_5 + - 2 * a_61 * b_6 + - 2 * a_62 * b_6 + - 2 * a_63 * b_6 + - 2 * a_64 * b_6 + - 2 * a_65 * b_6 - 1, - 6 * a_21 * a_32 * b_3 + - 6 * a_21 * a_42 * b_4 + - 6 * a_21 * a_52 * b_5 + - 6 * a_21 * a_62 * b_6 + - 6 * a_31 * a_43 * b_4 + - 6 * a_31 * a_53 * b_5 + - 6 * a_31 * a_63 * b_6 + - 6 * a_32 * a_43 * b_4 + - 6 * a_32 * a_53 * b_5 + - 6 * a_32 * a_63 * b_6 + - 6 * a_41 * a_54 * b_5 + - 6 * a_41 * a_64 * b_6 + - 6 * a_42 * a_54 * b_5 + - 6 * a_42 * a_64 * b_6 + - 6 * a_43 * a_54 * b_5 + - 6 * a_43 * a_64 * b_6 + - 6 * a_51 * a_65 * b_6 + - 6 * a_52 * a_65 * b_6 + - 6 * a_53 * a_65 * b_6 + - 6 * a_54 * a_65 * b_6 - 1, - 3 * a_21^2 * b_2 + - 3 * a_31^2 * b_3 + - 6 * a_31 * a_32 * b_3 + - 3 * a_32^2 * b_3 + - 3 * a_41^2 * b_4 + - 6 * a_41 * a_42 * b_4 + - 6 * a_41 * a_43 * b_4 + - 3 * a_42^2 * b_4 + - 6 * a_42 * a_43 * b_4 + - 3 * a_43^2 * b_4 + - 3 * a_51^2 * b_5 + - 6 * a_51 * a_52 * b_5 + - 6 * a_51 * a_53 * b_5 + - 6 * a_51 * a_54 * b_5 + - 3 * a_52^2 * b_5 + - 6 * a_52 * a_53 * b_5 + - 6 * a_52 * a_54 * b_5 + - 3 * a_53^2 * b_5 + - 6 * a_53 * a_54 * b_5 + - 3 * a_54^2 * b_5 + - 3 * a_61^2 * b_6 + - 6 * a_61 * a_62 * b_6 + - 6 * a_61 * a_63 * b_6 + - 6 * a_61 * a_64 * b_6 + - 6 * a_61 * a_65 * b_6 + - 3 * a_62^2 * b_6 + - 6 * a_62 * a_63 * b_6 + - 6 * a_62 * a_64 * b_6 + - 6 * a_62 * a_65 * b_6 + - 3 * a_63^2 * b_6 + - 6 * a_63 * a_64 * b_6 + - 6 * a_63 * a_65 * b_6 + - 3 * a_64^2 * b_6 + - 6 * a_64 * a_65 * b_6 + - 3 * a_65^2 * b_6 - 1, - 24 * a_21 * a_32 * a_43 * b_4 + - 24 * a_21 * a_32 * a_53 * b_5 + - 24 * a_21 * a_32 * a_63 * b_6 + - 24 * a_21 * a_42 * a_54 * b_5 + - 24 * a_21 * a_42 * a_64 * b_6 + - 24 * a_21 * a_52 * a_65 * b_6 + - 24 * a_31 * a_43 * a_54 * b_5 + - 24 * a_31 * a_43 * a_64 * b_6 + - 24 * a_31 * a_53 * a_65 * b_6 + - 24 * a_32 * a_43 * a_54 * b_5 + - 24 * a_32 * a_43 * a_64 * b_6 + - 24 * a_32 * a_53 * a_65 * b_6 + - 24 * a_41 * a_54 * a_65 * b_6 + - 24 * a_42 * a_54 * a_65 * b_6 + - 24 * a_43 * a_54 * a_65 * b_6 - 1, - 12 * a_21^2 * a_32 * b_3 + - 12 * a_21^2 * a_42 * b_4 + - 12 * a_21^2 * a_52 * b_5 + - 12 * a_21^2 * a_62 * b_6 + - 12 * a_31^2 * a_43 * b_4 + - 12 * a_31^2 * a_53 * b_5 + - 12 * a_31^2 * a_63 * b_6 + - 24 * a_31 * a_32 * a_43 * b_4 + - 24 * a_31 * a_32 * a_53 * b_5 + - 24 * a_31 * a_32 * a_63 * b_6 + - 12 * a_32^2 * a_43 * b_4 + - 12 * a_32^2 * a_53 * b_5 + - 12 * a_32^2 * a_63 * b_6 + - 12 * a_41^2 * a_54 * b_5 + - 12 * a_41^2 * a_64 * b_6 + - 24 * a_41 * a_42 * a_54 * b_5 + - 24 * a_41 * a_42 * a_64 * b_6 + - 24 * a_41 * a_43 * a_54 * b_5 + - 24 * a_41 * a_43 * a_64 * b_6 + - 12 * a_42^2 * a_54 * b_5 + - 12 * a_42^2 * a_64 * b_6 + - 24 * a_42 * a_43 * a_54 * b_5 + - 24 * a_42 * a_43 * a_64 * b_6 + - 12 * a_43^2 * a_54 * b_5 + - 12 * a_43^2 * a_64 * b_6 + - 12 * a_51^2 * a_65 * b_6 + - 24 * a_51 * a_52 * a_65 * b_6 + - 24 * a_51 * a_53 * a_65 * b_6 + - 24 * a_51 * a_54 * a_65 * b_6 + - 12 * a_52^2 * a_65 * b_6 + - 24 * a_52 * a_53 * a_65 * b_6 + - 24 * a_52 * a_54 * a_65 * b_6 + - 12 * a_53^2 * a_65 * b_6 + - 24 * a_53 * a_54 * a_65 * b_6 + - 12 * a_54^2 * a_65 * b_6 - 1, - 8 * a_21 * a_31 * a_32 * b_3 + - 8 * a_21 * a_32^2 * b_3 + - 8 * a_21 * a_41 * a_42 * b_4 + - 8 * a_21 * a_42^2 * b_4 + - 8 * a_21 * a_42 * a_43 * b_4 + - 8 * a_21 * a_51 * a_52 * b_5 + - 8 * a_21 * a_52^2 * b_5 + - 8 * a_21 * a_52 * a_53 * b_5 + - 8 * a_21 * a_52 * a_54 * b_5 + - 8 * a_21 * a_61 * a_62 * b_6 + - 8 * a_21 * a_62^2 * b_6 + - 8 * a_21 * a_62 * a_63 * b_6 + - 8 * a_21 * a_62 * a_64 * b_6 + - 8 * a_21 * a_62 * a_65 * b_6 + - 8 * a_31 * a_41 * a_43 * b_4 + - 8 * a_31 * a_42 * a_43 * b_4 + - 8 * a_31 * a_43^2 * b_4 + - 8 * a_31 * a_51 * a_53 * b_5 + - 8 * a_31 * a_52 * a_53 * b_5 + - 8 * a_31 * a_53^2 * b_5 + - 8 * a_31 * a_53 * a_54 * b_5 + - 8 * a_31 * a_61 * a_63 * b_6 + - 8 * a_31 * a_62 * a_63 * b_6 + - 8 * a_31 * a_63^2 * b_6 + - 8 * a_31 * a_63 * a_64 * b_6 + - 8 * a_31 * a_63 * a_65 * b_6 + - 8 * a_32 * a_41 * a_43 * b_4 + - 8 * a_32 * a_42 * a_43 * b_4 + - 8 * a_32 * a_43^2 * b_4 + - 8 * a_32 * a_51 * a_53 * b_5 + - 8 * a_32 * a_52 * a_53 * b_5 + - 8 * a_32 * a_53^2 * b_5 + - 8 * a_32 * a_53 * a_54 * b_5 + - 8 * a_32 * a_61 * a_63 * b_6 + - 8 * a_32 * a_62 * a_63 * b_6 + - 8 * a_32 * a_63^2 * b_6 + - 8 * a_32 * a_63 * a_64 * b_6 + - 8 * a_32 * a_63 * a_65 * b_6 + - 8 * a_41 * a_51 * a_54 * b_5 + - 8 * a_41 * a_52 * a_54 * b_5 + - 8 * a_41 * a_53 * a_54 * b_5 + - 8 * a_41 * a_54^2 * b_5 + - 8 * a_41 * a_61 * a_64 * b_6 + - 8 * a_41 * a_62 * a_64 * b_6 + - 8 * a_41 * a_63 * a_64 * b_6 + - 8 * a_41 * a_64^2 * b_6 + - 8 * a_41 * a_64 * a_65 * b_6 + - 8 * a_42 * a_51 * a_54 * b_5 + - 8 * a_42 * a_52 * a_54 * b_5 + - 8 * a_42 * a_53 * a_54 * b_5 + - 8 * a_42 * a_54^2 * b_5 + - 8 * a_42 * a_61 * a_64 * b_6 + - 8 * a_42 * a_62 * a_64 * b_6 + - 8 * a_42 * a_63 * a_64 * b_6 + - 8 * a_42 * a_64^2 * b_6 + - 8 * a_42 * a_64 * a_65 * b_6 + - 8 * a_43 * a_51 * a_54 * b_5 + - 8 * a_43 * a_52 * a_54 * b_5 + - 8 * a_43 * a_53 * a_54 * b_5 + - 8 * a_43 * a_54^2 * b_5 + - 8 * a_43 * a_61 * a_64 * b_6 + - 8 * a_43 * a_62 * a_64 * b_6 + - 8 * a_43 * a_63 * a_64 * b_6 + - 8 * a_43 * a_64^2 * b_6 + - 8 * a_43 * a_64 * a_65 * b_6 + - 8 * a_51 * a_61 * a_65 * b_6 + - 8 * a_51 * a_62 * a_65 * b_6 + - 8 * a_51 * a_63 * a_65 * b_6 + - 8 * a_51 * a_64 * a_65 * b_6 + - 8 * a_51 * a_65^2 * b_6 + - 8 * a_52 * a_61 * a_65 * b_6 + - 8 * a_52 * a_62 * a_65 * b_6 + - 8 * a_52 * a_63 * a_65 * b_6 + - 8 * a_52 * a_64 * a_65 * b_6 + - 8 * a_52 * a_65^2 * b_6 + - 8 * a_53 * a_61 * a_65 * b_6 + - 8 * a_53 * a_62 * a_65 * b_6 + - 8 * a_53 * a_63 * a_65 * b_6 + - 8 * a_53 * a_64 * a_65 * b_6 + - 8 * a_53 * a_65^2 * b_6 + - 8 * a_54 * a_61 * a_65 * b_6 + - 8 * a_54 * a_62 * a_65 * b_6 + - 8 * a_54 * a_63 * a_65 * b_6 + - 8 * a_54 * a_64 * a_65 * b_6 + - 8 * a_54 * a_65^2 * b_6 - 1, - 4 * a_21^3 * b_2 + - 4 * a_31^3 * b_3 + - 12 * a_31^2 * a_32 * b_3 + - 12 * a_31 * a_32^2 * b_3 + - 4 * a_32^3 * b_3 + - 4 * a_41^3 * b_4 + - 12 * a_41^2 * a_42 * b_4 + - 12 * a_41^2 * a_43 * b_4 + - 12 * a_41 * a_42^2 * b_4 + - 24 * a_41 * a_42 * a_43 * b_4 + - 12 * a_41 * a_43^2 * b_4 + - 4 * a_42^3 * b_4 + - 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30 * a_21 * a_42 * a_51 * a_54 * b_5 + - 30 * a_21 * a_42 * a_52 * a_54 * b_5 + - 30 * a_21 * a_42 * a_53 * a_54 * b_5 + - 30 * a_21 * a_42 * a_54^2 * b_5 + - 30 * a_21 * a_42 * a_61 * a_64 * b_6 + - 30 * a_21 * a_42 * a_62 * a_64 * b_6 + - 30 * a_21 * a_42 * a_63 * a_64 * b_6 + - 30 * a_21 * a_42 * a_64^2 * b_6 + - 30 * a_21 * a_42 * a_64 * a_65 * b_6 + - 30 * a_21 * a_52 * a_61 * a_65 * b_6 + - 30 * a_21 * a_52 * a_62 * a_65 * b_6 + - 30 * a_21 * a_52 * a_63 * a_65 * b_6 + - 30 * a_21 * a_52 * a_64 * a_65 * b_6 + - 30 * a_21 * a_52 * a_65^2 * b_6 + - 30 * a_31 * a_43 * a_51 * a_54 * b_5 + - 30 * a_31 * a_43 * a_52 * a_54 * b_5 + - 30 * a_31 * a_43 * a_53 * a_54 * b_5 + - 30 * a_31 * a_43 * a_54^2 * b_5 + - 30 * a_31 * a_43 * a_61 * a_64 * b_6 + - 30 * a_31 * a_43 * a_62 * a_64 * b_6 + - 30 * a_31 * a_43 * a_63 * a_64 * b_6 + - 30 * a_31 * a_43 * a_64^2 * b_6 + - 30 * a_31 * a_43 * a_64 * a_65 * b_6 + - 30 * a_31 * a_53 * a_61 * a_65 * b_6 + - 30 * a_31 * a_53 * a_62 * a_65 * b_6 + - 30 * a_31 * a_53 * a_63 * a_65 * b_6 + - 30 * a_31 * a_53 * a_64 * a_65 * b_6 + - 30 * a_31 * a_53 * a_65^2 * b_6 + - 30 * a_32 * a_43 * a_51 * a_54 * b_5 + - 30 * a_32 * a_43 * a_52 * a_54 * b_5 + - 30 * a_32 * a_43 * a_53 * a_54 * b_5 + - 30 * a_32 * a_43 * a_54^2 * b_5 + - 30 * a_32 * a_43 * a_61 * a_64 * b_6 + - 30 * a_32 * a_43 * a_62 * a_64 * b_6 + - 30 * a_32 * a_43 * a_63 * a_64 * b_6 + - 30 * a_32 * a_43 * a_64^2 * b_6 + - 30 * a_32 * a_43 * a_64 * a_65 * b_6 + - 30 * a_32 * a_53 * a_61 * a_65 * b_6 + - 30 * a_32 * a_53 * a_62 * a_65 * b_6 + - 30 * a_32 * a_53 * a_63 * a_65 * b_6 + - 30 * a_32 * a_53 * a_64 * a_65 * b_6 + - 30 * a_32 * a_53 * a_65^2 * b_6 + - 30 * a_41 * a_54 * a_61 * a_65 * b_6 + - 30 * a_41 * a_54 * a_62 * a_65 * b_6 + - 30 * a_41 * a_54 * a_63 * a_65 * b_6 + - 30 * a_41 * a_54 * a_64 * a_65 * b_6 + - 30 * a_41 * a_54 * a_65^2 * b_6 + - 30 * a_42 * a_54 * a_61 * a_65 * b_6 + - 30 * a_42 * a_54 * a_62 * a_65 * b_6 + - 30 * a_42 * a_54 * a_63 * a_65 * b_6 + - 30 * a_42 * a_54 * a_64 * a_65 * b_6 + - 30 * a_42 * a_54 * a_65^2 * b_6 + - 30 * a_43 * a_54 * a_61 * a_65 * b_6 + - 30 * a_43 * a_54 * a_62 * a_65 * b_6 + - 30 * a_43 * a_54 * a_63 * a_65 * b_6 + - 30 * a_43 * a_54 * a_64 * a_65 * b_6 + - 30 * a_43 * a_54 * a_65^2 * b_6 - 1, - 20 * a_21^3 * a_32 * b_3 + - 20 * a_21^3 * a_42 * b_4 + - 20 * a_21^3 * a_52 * b_5 + - 20 * a_21^3 * a_62 * b_6 + - 20 * a_31^3 * a_43 * b_4 + - 20 * a_31^3 * a_53 * b_5 + - 20 * a_31^3 * a_63 * b_6 + - 60 * a_31^2 * a_32 * a_43 * b_4 + - 60 * a_31^2 * a_32 * a_53 * b_5 + - 60 * a_31^2 * a_32 * a_63 * b_6 + - 60 * a_31 * a_32^2 * a_43 * b_4 + - 60 * a_31 * a_32^2 * a_53 * b_5 + - 60 * a_31 * a_32^2 * a_63 * b_6 + - 20 * a_32^3 * a_43 * b_4 + - 20 * a_32^3 * a_53 * b_5 + - 20 * a_32^3 * a_63 * b_6 + - 20 * a_41^3 * a_54 * b_5 + - 20 * a_41^3 * a_64 * b_6 + - 60 * a_41^2 * a_42 * a_54 * b_5 + - 60 * a_41^2 * a_42 * a_64 * b_6 + - 60 * a_41^2 * a_43 * a_54 * b_5 + - 60 * a_41^2 * a_43 * a_64 * b_6 + - 60 * a_41 * a_42^2 * a_54 * b_5 + - 60 * a_41 * a_42^2 * a_64 * b_6 + - 120 * a_41 * a_42 * a_43 * a_54 * b_5 + - 120 * a_41 * a_42 * a_43 * a_64 * b_6 + - 60 * a_41 * a_43^2 * a_54 * b_5 + - 60 * a_41 * a_43^2 * a_64 * b_6 + - 20 * a_42^3 * a_54 * b_5 + - 20 * a_42^3 * a_64 * b_6 + - 60 * a_42^2 * a_43 * a_54 * b_5 + - 60 * a_42^2 * a_43 * a_64 * b_6 + - 60 * a_42 * a_43^2 * a_54 * b_5 + - 60 * a_42 * a_43^2 * a_64 * b_6 + - 20 * a_43^3 * a_54 * b_5 + - 20 * a_43^3 * a_64 * b_6 + - 20 * a_51^3 * a_65 * b_6 + - 60 * a_51^2 * a_52 * a_65 * b_6 + - 60 * a_51^2 * a_53 * a_65 * b_6 + - 60 * a_51^2 * a_54 * a_65 * b_6 + - 60 * a_51 * a_52^2 * a_65 * b_6 + - 120 * a_51 * a_52 * a_53 * a_65 * b_6 + - 120 * a_51 * a_52 * a_54 * a_65 * b_6 + - 60 * a_51 * a_53^2 * a_65 * b_6 + - 120 * a_51 * a_53 * a_54 * a_65 * b_6 + - 60 * a_51 * a_54^2 * a_65 * b_6 + - 20 * a_52^3 * a_65 * b_6 + - 60 * a_52^2 * a_53 * a_65 * b_6 + - 60 * a_52^2 * a_54 * a_65 * b_6 + - 60 * a_52 * a_53^2 * a_65 * b_6 + - 120 * a_52 * a_53 * a_54 * a_65 * b_6 + - 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30 * a_51^2 * a_53^2 * b_5 + - 60 * a_51^2 * a_53 * a_54 * b_5 + - 30 * a_51^2 * a_54^2 * b_5 + - 20 * a_51 * a_52^3 * b_5 + - 60 * a_51 * a_52^2 * a_53 * b_5 + - 60 * a_51 * a_52^2 * a_54 * b_5 + - 60 * a_51 * a_52 * a_53^2 * b_5 + - 120 * a_51 * a_52 * a_53 * a_54 * b_5 + - 60 * a_51 * a_52 * a_54^2 * b_5 + - 20 * a_51 * a_53^3 * b_5 + - 60 * a_51 * a_53^2 * a_54 * b_5 + - 60 * a_51 * a_53 * a_54^2 * b_5 + - 20 * a_51 * a_54^3 * b_5 + - 5 * a_52^4 * b_5 + - 20 * a_52^3 * a_53 * b_5 + - 20 * a_52^3 * a_54 * b_5 + - 30 * a_52^2 * a_53^2 * b_5 + - 60 * a_52^2 * a_53 * a_54 * b_5 + - 30 * a_52^2 * a_54^2 * b_5 + - 20 * a_52 * a_53^3 * b_5 + - 60 * a_52 * a_53^2 * a_54 * b_5 + - 60 * a_52 * a_53 * a_54^2 * b_5 + - 20 * a_52 * a_54^3 * b_5 + - 5 * a_53^4 * b_5 + - 20 * a_53^3 * a_54 * b_5 + - 30 * a_53^2 * a_54^2 * b_5 + - 20 * a_53 * a_54^3 * b_5 + - 5 * a_54^4 * b_5 + - 5 * a_61^4 * b_6 + - 20 * a_61^3 * a_62 * b_6 + - 20 * a_61^3 * a_63 * b_6 + - 20 * a_61^3 * a_64 * b_6 + - 20 * a_61^3 * a_65 * b_6 + - 30 * a_61^2 * a_62^2 * b_6 + - 60 * a_61^2 * a_62 * a_63 * b_6 + - 60 * a_61^2 * a_62 * a_64 * b_6 + - 60 * a_61^2 * a_62 * a_65 * b_6 + - 30 * a_61^2 * a_63^2 * b_6 + - 60 * a_61^2 * a_63 * a_64 * b_6 + - 60 * a_61^2 * a_63 * a_65 * b_6 + - 30 * a_61^2 * a_64^2 * b_6 + - 60 * a_61^2 * a_64 * a_65 * b_6 + - 30 * a_61^2 * a_65^2 * b_6 + - 20 * a_61 * a_62^3 * b_6 + - 60 * a_61 * a_62^2 * a_63 * b_6 + - 60 * a_61 * a_62^2 * a_64 * b_6 + - 60 * a_61 * a_62^2 * a_65 * b_6 + - 60 * a_61 * a_62 * a_63^2 * b_6 + - 120 * a_61 * a_62 * a_63 * a_64 * b_6 + - 120 * a_61 * a_62 * a_63 * a_65 * b_6 + - 60 * a_61 * a_62 * a_64^2 * b_6 + - 120 * a_61 * a_62 * a_64 * a_65 * b_6 + - 60 * a_61 * a_62 * a_65^2 * b_6 + - 20 * a_61 * a_63^3 * b_6 + - 60 * a_61 * a_63^2 * a_64 * b_6 + - 60 * a_61 * a_63^2 * a_65 * b_6 + - 60 * a_61 * a_63 * a_64^2 * b_6 + - 120 * a_61 * a_63 * a_64 * a_65 * b_6 + - 60 * a_61 * a_63 * a_65^2 * b_6 + - 20 * a_61 * a_64^3 * b_6 + - 60 * a_61 * a_64^2 * a_65 * b_6 + - 60 * a_61 * a_64 * a_65^2 * b_6 + - 20 * a_61 * a_65^3 * b_6 + - 5 * a_62^4 * b_6 + - 20 * a_62^3 * a_63 * b_6 + - 20 * a_62^3 * a_64 * b_6 + - 20 * a_62^3 * a_65 * b_6 + - 30 * a_62^2 * a_63^2 * b_6 + - 60 * a_62^2 * a_63 * a_64 * b_6 + - 60 * a_62^2 * a_63 * a_65 * b_6 + - 30 * a_62^2 * a_64^2 * b_6 + - 60 * a_62^2 * a_64 * a_65 * b_6 + - 30 * a_62^2 * a_65^2 * b_6 + - 20 * a_62 * a_63^3 * b_6 + - 60 * a_62 * a_63^2 * a_64 * b_6 + - 60 * a_62 * a_63^2 * a_65 * b_6 + - 60 * a_62 * a_63 * a_64^2 * b_6 + - 120 * a_62 * a_63 * a_64 * a_65 * b_6 + - 60 * a_62 * a_63 * a_65^2 * b_6 + - 20 * a_62 * a_64^3 * b_6 + - 60 * a_62 * a_64^2 * a_65 * b_6 + - 60 * a_62 * a_64 * a_65^2 * b_6 + - 20 * a_62 * a_65^3 * b_6 + - 5 * a_63^4 * b_6 + - 20 * a_63^3 * a_64 * b_6 + - 20 * a_63^3 * a_65 * b_6 + - 30 * a_63^2 * a_64^2 * b_6 + - 60 * a_63^2 * a_64 * a_65 * b_6 + - 30 * a_63^2 * a_65^2 * b_6 + - 20 * a_63 * a_64^3 * b_6 + - 60 * a_63 * a_64^2 * a_65 * b_6 + - 60 * a_63 * a_64 * a_65^2 * b_6 + - 20 * a_63 * a_65^3 * b_6 + - 5 * a_64^4 * b_6 + - 20 * a_64^3 * a_65 * b_6 + - 30 * a_64^2 * a_65^2 * b_6 + - 20 * a_64 * a_65^3 * b_6 + - 5 * a_65^4 * b_6 - 1, - 720 * a_21 * a_32 * a_43 * a_54 * a_65 * b_6 - 1, - 360 * a_21^2 * a_32 * a_43 * a_54 * b_5 + - 360 * a_21^2 * a_32 * a_43 * a_64 * b_6 + - 360 * a_21^2 * a_32 * a_53 * a_65 * b_6 + - 360 * a_21^2 * a_42 * a_54 * a_65 * b_6 + - 360 * a_31^2 * a_43 * a_54 * a_65 * b_6 + - 720 * a_31 * a_32 * a_43 * a_54 * a_65 * b_6 + - 360 * a_32^2 * a_43 * a_54 * a_65 * b_6 - 1, - 240 * a_21 * a_31 * a_32 * a_43 * a_54 * b_5 + - 240 * a_21 * a_31 * a_32 * a_43 * a_64 * b_6 + - 240 * a_21 * a_31 * a_32 * a_53 * a_65 * b_6 + - 240 * a_21 * a_32^2 * a_43 * a_54 * b_5 + - 240 * a_21 * a_32^2 * a_43 * a_64 * b_6 + - 240 * a_21 * a_32^2 * a_53 * a_65 * b_6 + - 240 * a_21 * a_41 * a_42 * a_54 * a_65 * b_6 + - 240 * a_21 * a_42^2 * a_54 * a_65 * b_6 + - 240 * a_21 * a_42 * a_43 * a_54 * a_65 * b_6 + - 240 * a_31 * a_41 * a_43 * a_54 * a_65 * b_6 + - 240 * a_31 * a_42 * a_43 * a_54 * a_65 * b_6 + - 240 * a_31 * a_43^2 * a_54 * a_65 * b_6 + - 240 * a_32 * a_41 * a_43 * a_54 * a_65 * b_6 + - 240 * a_32 * a_42 * a_43 * a_54 * a_65 * b_6 + - 240 * a_32 * a_43^2 * a_54 * a_65 * b_6 - 1, - 180 * a_21 * a_32 * a_41 * a_43 * a_54 * b_5 + - 180 * a_21 * a_32 * a_41 * a_43 * a_64 * b_6 + - 180 * a_21 * a_32 * a_42 * a_43 * a_54 * b_5 + - 180 * a_21 * a_32 * a_42 * a_43 * a_64 * b_6 + - 180 * a_21 * a_32 * a_43^2 * a_54 * b_5 + - 180 * a_21 * a_32 * a_43^2 * a_64 * b_6 + - 180 * a_21 * a_32 * a_51 * a_53 * a_65 * b_6 + - 180 * a_21 * a_32 * a_52 * a_53 * a_65 * b_6 + - 180 * a_21 * a_32 * a_53^2 * a_65 * b_6 + - 180 * a_21 * a_32 * a_53 * a_54 * a_65 * b_6 + - 180 * a_21 * a_42 * a_51 * a_54 * a_65 * b_6 + - 180 * a_21 * a_42 * a_52 * a_54 * a_65 * b_6 + - 180 * a_21 * a_42 * a_53 * a_54 * a_65 * b_6 + - 180 * a_21 * a_42 * a_54^2 * a_65 * b_6 + - 180 * a_31 * a_43 * a_51 * a_54 * a_65 * b_6 + - 180 * a_31 * a_43 * a_52 * a_54 * a_65 * b_6 + - 180 * a_31 * a_43 * a_53 * a_54 * a_65 * b_6 + - 180 * a_31 * a_43 * a_54^2 * a_65 * b_6 + - 180 * a_32 * a_43 * a_51 * a_54 * a_65 * b_6 + - 180 * a_32 * a_43 * a_52 * a_54 * a_65 * b_6 + - 180 * a_32 * a_43 * a_53 * a_54 * a_65 * b_6 + - 180 * a_32 * a_43 * a_54^2 * a_65 * b_6 - 1, - 144 * a_21 * a_32 * a_43 * a_51 * a_54 * b_5 + - 144 * a_21 * a_32 * a_43 * a_52 * a_54 * b_5 + - 144 * a_21 * a_32 * a_43 * a_53 * a_54 * b_5 + - 144 * a_21 * a_32 * a_43 * a_54^2 * b_5 + - 144 * a_21 * a_32 * a_43 * a_61 * a_64 * b_6 + - 144 * a_21 * a_32 * a_43 * a_62 * a_64 * b_6 + - 144 * a_21 * a_32 * a_43 * a_63 * a_64 * b_6 + - 144 * a_21 * a_32 * a_43 * a_64^2 * b_6 + - 144 * a_21 * a_32 * a_43 * a_64 * a_65 * b_6 + - 144 * a_21 * a_32 * a_53 * a_61 * a_65 * b_6 + - 144 * a_21 * a_32 * a_53 * a_62 * a_65 * b_6 + - 144 * a_21 * a_32 * a_53 * a_63 * a_65 * b_6 + - 144 * a_21 * a_32 * a_53 * a_64 * a_65 * b_6 + - 144 * a_21 * a_32 * a_53 * a_65^2 * b_6 + - 144 * a_21 * a_42 * a_54 * a_61 * a_65 * b_6 + - 144 * a_21 * a_42 * a_54 * a_62 * a_65 * b_6 + - 144 * a_21 * a_42 * a_54 * a_63 * a_65 * b_6 + - 144 * a_21 * a_42 * a_54 * a_64 * a_65 * b_6 + - 144 * a_21 * a_42 * a_54 * a_65^2 * b_6 + - 144 * a_31 * a_43 * a_54 * a_61 * a_65 * b_6 + - 144 * a_31 * a_43 * a_54 * a_62 * a_65 * b_6 + - 144 * a_31 * a_43 * a_54 * a_63 * a_65 * b_6 + - 144 * a_31 * a_43 * a_54 * a_64 * a_65 * b_6 + - 144 * a_31 * a_43 * a_54 * a_65^2 * b_6 + - 144 * a_32 * a_43 * a_54 * a_61 * a_65 * b_6 + - 144 * a_32 * a_43 * a_54 * a_62 * a_65 * b_6 + - 144 * a_32 * a_43 * a_54 * a_63 * a_65 * b_6 + - 144 * a_32 * a_43 * a_54 * a_64 * a_65 * b_6 + - 144 * a_32 * a_43 * a_54 * a_65^2 * b_6 - 1, - 120 * a_21^3 * a_32 * a_43 * b_4 + - 120 * a_21^3 * a_32 * a_53 * b_5 + - 120 * a_21^3 * a_32 * a_63 * b_6 + - 120 * a_21^3 * a_42 * a_54 * b_5 + - 120 * a_21^3 * a_42 * a_64 * b_6 + - 120 * a_21^3 * a_52 * a_65 * b_6 + - 120 * a_31^3 * a_43 * a_54 * b_5 + - 120 * a_31^3 * a_43 * a_64 * b_6 + - 120 * a_31^3 * a_53 * a_65 * b_6 + - 360 * a_31^2 * a_32 * a_43 * a_54 * b_5 + - 360 * a_31^2 * a_32 * a_43 * a_64 * b_6 + - 360 * a_31^2 * a_32 * a_53 * a_65 * b_6 + - 360 * a_31 * a_32^2 * a_43 * a_54 * b_5 + - 360 * a_31 * a_32^2 * a_43 * a_64 * b_6 + - 360 * a_31 * a_32^2 * a_53 * a_65 * b_6 + - 120 * a_32^3 * a_43 * a_54 * b_5 + - 120 * a_32^3 * a_43 * a_64 * b_6 + - 120 * a_32^3 * a_53 * a_65 * b_6 + - 120 * a_41^3 * a_54 * a_65 * b_6 + - 360 * a_41^2 * a_42 * a_54 * a_65 * b_6 + - 360 * a_41^2 * a_43 * a_54 * a_65 * b_6 + - 360 * a_41 * a_42^2 * a_54 * a_65 * b_6 + - 720 * a_41 * a_42 * a_43 * a_54 * a_65 * b_6 + - 360 * a_41 * a_43^2 * a_54 * a_65 * b_6 + - 120 * a_42^3 * a_54 * a_65 * b_6 + - 360 * a_42^2 * a_43 * a_54 * a_65 * b_6 + - 360 * a_42 * a_43^2 * a_54 * a_65 * b_6 + - 120 * a_43^3 * a_54 * a_65 * b_6 - 1, - 90 * a_21^2 * a_31 * a_32 * a_43 * b_4 + - 90 * a_21^2 * a_31 * a_32 * a_53 * b_5 + - 90 * a_21^2 * a_31 * a_32 * a_63 * b_6 + - 90 * a_21^2 * a_32^2 * a_43 * b_4 + - 90 * a_21^2 * a_32^2 * a_53 * b_5 + - 90 * a_21^2 * a_32^2 * a_63 * b_6 + - 90 * a_21^2 * a_41 * a_42 * a_54 * b_5 + - 90 * a_21^2 * a_41 * a_42 * a_64 * b_6 + - 90 * a_21^2 * a_42^2 * a_54 * b_5 + - 90 * a_21^2 * a_42^2 * a_64 * b_6 + - 90 * a_21^2 * a_42 * a_43 * a_54 * b_5 + - 90 * a_21^2 * a_42 * a_43 * a_64 * b_6 + - 90 * a_21^2 * a_51 * a_52 * a_65 * b_6 + - 90 * a_21^2 * a_52^2 * a_65 * b_6 + - 90 * a_21^2 * a_52 * a_53 * a_65 * b_6 + - 90 * a_21^2 * a_52 * a_54 * a_65 * b_6 + - 90 * a_31^2 * a_41 * a_43 * a_54 * b_5 + - 90 * a_31^2 * a_41 * a_43 * a_64 * b_6 + - 90 * a_31^2 * a_42 * a_43 * a_54 * b_5 + - 90 * a_31^2 * a_42 * a_43 * a_64 * b_6 + - 90 * a_31^2 * a_43^2 * a_54 * b_5 + - 90 * a_31^2 * a_43^2 * a_64 * b_6 + - 90 * a_31^2 * a_51 * a_53 * a_65 * b_6 + - 90 * a_31^2 * a_52 * a_53 * a_65 * b_6 + - 90 * a_31^2 * a_53^2 * a_65 * b_6 + - 90 * a_31^2 * a_53 * a_54 * a_65 * b_6 + - 180 * a_31 * a_32 * a_41 * a_43 * a_54 * b_5 + - 180 * a_31 * a_32 * a_41 * a_43 * a_64 * b_6 + - 180 * a_31 * a_32 * a_42 * a_43 * a_54 * b_5 + - 180 * a_31 * a_32 * a_42 * a_43 * a_64 * b_6 + - 180 * a_31 * a_32 * a_43^2 * a_54 * b_5 + - 180 * a_31 * a_32 * a_43^2 * a_64 * b_6 + - 180 * a_31 * a_32 * a_51 * a_53 * a_65 * b_6 + - 180 * a_31 * a_32 * a_52 * a_53 * a_65 * b_6 + - 180 * a_31 * a_32 * a_53^2 * a_65 * b_6 + - 180 * a_31 * a_32 * a_53 * a_54 * a_65 * b_6 + - 90 * a_32^2 * a_41 * a_43 * a_54 * b_5 + - 90 * a_32^2 * a_41 * a_43 * a_64 * b_6 + - 90 * a_32^2 * a_42 * a_43 * a_54 * b_5 + - 90 * a_32^2 * a_42 * a_43 * a_64 * b_6 + - 90 * a_32^2 * a_43^2 * a_54 * b_5 + - 90 * a_32^2 * a_43^2 * a_64 * b_6 + - 90 * a_32^2 * a_51 * a_53 * a_65 * b_6 + - 90 * a_32^2 * a_52 * a_53 * a_65 * b_6 + - 90 * a_32^2 * a_53^2 * a_65 * b_6 + - 90 * a_32^2 * a_53 * a_54 * a_65 * b_6 + - 90 * a_41^2 * a_51 * a_54 * a_65 * b_6 + - 90 * a_41^2 * a_52 * a_54 * a_65 * b_6 + - 90 * a_41^2 * a_53 * a_54 * a_65 * b_6 + - 90 * a_41^2 * a_54^2 * a_65 * b_6 + - 180 * a_41 * a_42 * a_51 * a_54 * a_65 * b_6 + - 180 * a_41 * a_42 * a_52 * a_54 * a_65 * b_6 + - 180 * a_41 * a_42 * a_53 * a_54 * a_65 * b_6 + - 180 * a_41 * a_42 * a_54^2 * a_65 * b_6 + - 180 * a_41 * a_43 * a_51 * a_54 * a_65 * b_6 + - 180 * a_41 * a_43 * a_52 * a_54 * a_65 * b_6 + - 180 * a_41 * a_43 * a_53 * a_54 * a_65 * b_6 + - 180 * a_41 * a_43 * a_54^2 * a_65 * b_6 + - 90 * a_42^2 * a_51 * a_54 * a_65 * b_6 + - 90 * a_42^2 * a_52 * a_54 * a_65 * b_6 + - 90 * a_42^2 * a_53 * a_54 * a_65 * b_6 + - 90 * a_42^2 * a_54^2 * a_65 * b_6 + - 180 * a_42 * a_43 * a_51 * a_54 * a_65 * b_6 + - 180 * a_42 * a_43 * a_52 * a_54 * a_65 * b_6 + - 180 * a_42 * a_43 * a_53 * a_54 * a_65 * b_6 + - 180 * a_42 * a_43 * a_54^2 * a_65 * b_6 + - 90 * a_43^2 * a_51 * a_54 * a_65 * b_6 + - 90 * a_43^2 * a_52 * a_54 * a_65 * b_6 + - 90 * a_43^2 * a_53 * a_54 * a_65 * b_6 + - 90 * a_43^2 * a_54^2 * a_65 * b_6 - 1, - 72 * a_21^2 * a_32 * a_41 * a_43 * b_4 + - 72 * a_21^2 * a_32 * a_42 * a_43 * b_4 + - 72 * a_21^2 * a_32 * a_43^2 * b_4 + - 72 * a_21^2 * a_32 * a_51 * a_53 * b_5 + - 72 * a_21^2 * a_32 * a_52 * a_53 * b_5 + - 72 * a_21^2 * a_32 * a_53^2 * b_5 + - 72 * a_21^2 * a_32 * a_53 * a_54 * b_5 + - 72 * a_21^2 * a_32 * a_61 * a_63 * b_6 + - 72 * a_21^2 * a_32 * a_62 * a_63 * b_6 + - 72 * a_21^2 * a_32 * a_63^2 * b_6 + - 72 * a_21^2 * a_32 * a_63 * a_64 * b_6 + - 72 * a_21^2 * a_32 * a_63 * a_65 * b_6 + - 72 * a_21^2 * a_42 * a_51 * a_54 * b_5 + - 72 * a_21^2 * a_42 * a_52 * a_54 * b_5 + - 72 * a_21^2 * a_42 * a_53 * a_54 * b_5 + - 72 * a_21^2 * a_42 * a_54^2 * b_5 + - 72 * a_21^2 * a_42 * a_61 * a_64 * b_6 + - 72 * a_21^2 * a_42 * a_62 * a_64 * b_6 + - 72 * a_21^2 * a_42 * a_63 * a_64 * b_6 + - 72 * a_21^2 * a_42 * a_64^2 * b_6 + - 72 * a_21^2 * a_42 * a_64 * a_65 * b_6 + - 72 * a_21^2 * a_52 * a_61 * a_65 * b_6 + - 72 * a_21^2 * a_52 * a_62 * a_65 * b_6 + - 72 * a_21^2 * a_52 * a_63 * a_65 * b_6 + - 72 * a_21^2 * a_52 * a_64 * a_65 * b_6 + - 72 * a_21^2 * a_52 * a_65^2 * b_6 + - 72 * a_31^2 * a_43 * a_51 * a_54 * b_5 + - 72 * a_31^2 * a_43 * a_52 * a_54 * b_5 + - 72 * a_31^2 * a_43 * a_53 * a_54 * b_5 + - 72 * a_31^2 * a_43 * a_54^2 * b_5 + - 72 * a_31^2 * a_43 * a_61 * a_64 * b_6 + - 72 * a_31^2 * a_43 * a_62 * a_64 * b_6 + - 72 * a_31^2 * a_43 * a_63 * a_64 * b_6 + - 72 * a_31^2 * a_43 * a_64^2 * b_6 + - 72 * a_31^2 * a_43 * a_64 * a_65 * b_6 + - 72 * a_31^2 * a_53 * a_61 * a_65 * b_6 + - 72 * a_31^2 * a_53 * a_62 * a_65 * b_6 + - 72 * a_31^2 * a_53 * a_63 * a_65 * b_6 + - 72 * a_31^2 * a_53 * a_64 * a_65 * b_6 + - 72 * a_31^2 * a_53 * a_65^2 * b_6 + - 144 * a_31 * a_32 * a_43 * a_51 * a_54 * b_5 + - 144 * a_31 * a_32 * a_43 * a_52 * a_54 * b_5 + - 144 * a_31 * a_32 * a_43 * a_53 * a_54 * b_5 + - 144 * a_31 * a_32 * a_43 * a_54^2 * b_5 + - 144 * a_31 * a_32 * a_43 * a_61 * a_64 * b_6 + - 144 * a_31 * a_32 * a_43 * a_62 * a_64 * b_6 + - 144 * a_31 * a_32 * a_43 * a_63 * a_64 * b_6 + - 144 * a_31 * a_32 * a_43 * a_64^2 * b_6 + - 144 * a_31 * a_32 * a_43 * a_64 * a_65 * b_6 + - 144 * a_31 * a_32 * a_53 * a_61 * a_65 * b_6 + - 144 * a_31 * a_32 * a_53 * a_62 * a_65 * b_6 + - 144 * a_31 * a_32 * a_53 * a_63 * a_65 * b_6 + - 144 * a_31 * a_32 * a_53 * a_64 * a_65 * b_6 + - 144 * a_31 * a_32 * a_53 * a_65^2 * b_6 + - 72 * a_32^2 * a_43 * a_51 * a_54 * b_5 + - 72 * a_32^2 * a_43 * a_52 * a_54 * b_5 + - 72 * a_32^2 * a_43 * a_53 * a_54 * b_5 + - 72 * a_32^2 * a_43 * a_54^2 * b_5 + - 72 * a_32^2 * a_43 * a_61 * a_64 * b_6 + - 72 * a_32^2 * a_43 * a_62 * a_64 * b_6 + - 72 * a_32^2 * a_43 * a_63 * a_64 * b_6 + - 72 * a_32^2 * a_43 * a_64^2 * b_6 + - 72 * a_32^2 * a_43 * a_64 * a_65 * b_6 + - 72 * a_32^2 * a_53 * a_61 * a_65 * b_6 + - 72 * a_32^2 * a_53 * a_62 * a_65 * b_6 + - 72 * a_32^2 * a_53 * a_63 * a_65 * b_6 + - 72 * a_32^2 * a_53 * a_64 * a_65 * b_6 + - 72 * a_32^2 * a_53 * a_65^2 * b_6 + - 72 * a_41^2 * a_54 * a_61 * a_65 * b_6 + - 72 * a_41^2 * a_54 * a_62 * a_65 * b_6 + - 72 * a_41^2 * a_54 * a_63 * a_65 * b_6 + - 72 * a_41^2 * a_54 * a_64 * a_65 * b_6 + - 72 * a_41^2 * a_54 * a_65^2 * b_6 + - 144 * a_41 * a_42 * a_54 * a_61 * a_65 * b_6 + - 144 * a_41 * a_42 * a_54 * a_62 * a_65 * b_6 + - 144 * a_41 * a_42 * a_54 * a_63 * a_65 * b_6 + - 144 * a_41 * a_42 * a_54 * a_64 * a_65 * b_6 + - 144 * a_41 * a_42 * a_54 * a_65^2 * b_6 + - 144 * a_41 * a_43 * a_54 * a_61 * a_65 * b_6 + - 144 * a_41 * a_43 * a_54 * a_62 * a_65 * b_6 + - 144 * a_41 * a_43 * a_54 * a_63 * a_65 * b_6 + - 144 * a_41 * a_43 * a_54 * a_64 * a_65 * b_6 + - 144 * a_41 * a_43 * a_54 * a_65^2 * b_6 + - 72 * a_42^2 * a_54 * a_61 * a_65 * b_6 + - 72 * a_42^2 * a_54 * a_62 * a_65 * b_6 + - 72 * a_42^2 * a_54 * a_63 * a_65 * b_6 + - 72 * a_42^2 * a_54 * a_64 * a_65 * b_6 + - 72 * a_42^2 * a_54 * a_65^2 * b_6 + - 144 * a_42 * a_43 * a_54 * a_61 * a_65 * b_6 + - 144 * a_42 * a_43 * a_54 * a_62 * a_65 * b_6 + - 144 * a_42 * a_43 * a_54 * a_63 * a_65 * b_6 + - 144 * a_42 * a_43 * a_54 * a_64 * a_65 * b_6 + - 144 * a_42 * a_43 * a_54 * a_65^2 * b_6 + - 72 * a_43^2 * a_54 * a_61 * a_65 * b_6 + - 72 * a_43^2 * a_54 * a_62 * a_65 * b_6 + - 72 * a_43^2 * a_54 * a_63 * a_65 * b_6 + - 72 * a_43^2 * a_54 * a_64 * a_65 * b_6 + - 72 * a_43^2 * a_54 * a_65^2 * b_6 - 1, - 120 * a_21^2 * a_32^2 * a_43 * b_4 + - 120 * a_21^2 * a_32^2 * a_53 * b_5 + - 120 * a_21^2 * a_32^2 * a_63 * b_6 + - 120 * a_21^2 * a_42^2 * a_54 * b_5 + - 120 * a_21^2 * a_42^2 * a_64 * b_6 + - 120 * a_21^2 * a_52^2 * a_65 * b_6 + - 240 * a_21 * a_31 * a_42 * a_43 * a_54 * b_5 + - 240 * a_21 * a_31 * a_42 * a_43 * a_64 * b_6 + - 240 * a_21 * a_31 * a_52 * a_53 * a_65 * b_6 + - 240 * a_21 * a_32 * a_42 * a_43 * a_54 * b_5 + - 240 * a_21 * a_32 * a_42 * a_43 * a_64 * b_6 + - 240 * a_21 * a_32 * a_52 * a_53 * a_65 * b_6 + - 240 * a_21 * a_41 * a_52 * a_54 * a_65 * b_6 + - 240 * a_21 * a_42 * a_52 * a_54 * a_65 * b_6 + - 240 * a_21 * a_43 * a_52 * a_54 * a_65 * b_6 + - 120 * a_31^2 * a_43^2 * a_54 * b_5 + - 120 * a_31^2 * a_43^2 * a_64 * b_6 + - 120 * a_31^2 * a_53^2 * a_65 * b_6 + - 240 * a_31 * a_32 * a_43^2 * a_54 * b_5 + - 240 * a_31 * a_32 * a_43^2 * a_64 * b_6 + - 240 * a_31 * a_32 * a_53^2 * a_65 * b_6 + - 240 * a_31 * a_41 * a_53 * a_54 * a_65 * b_6 + - 240 * a_31 * a_42 * a_53 * a_54 * a_65 * b_6 + - 240 * a_31 * a_43 * a_53 * a_54 * a_65 * b_6 + - 120 * a_32^2 * a_43^2 * a_54 * b_5 + - 120 * a_32^2 * a_43^2 * a_64 * b_6 + - 120 * a_32^2 * a_53^2 * a_65 * b_6 + - 240 * a_32 * a_41 * a_53 * a_54 * a_65 * b_6 + - 240 * a_32 * a_42 * a_53 * a_54 * a_65 * b_6 + - 240 * a_32 * a_43 * a_53 * a_54 * a_65 * b_6 + - 120 * a_41^2 * a_54^2 * a_65 * b_6 + - 240 * a_41 * a_42 * a_54^2 * a_65 * b_6 + - 240 * a_41 * a_43 * a_54^2 * a_65 * b_6 + - 120 * a_42^2 * a_54^2 * a_65 * b_6 + - 240 * a_42 * a_43 * a_54^2 * a_65 * b_6 + - 120 * a_43^2 * a_54^2 * a_65 * b_6 - 1, - 60 * a_21 * a_31^2 * a_32 * a_43 * b_4 + - 60 * a_21 * a_31^2 * a_32 * a_53 * b_5 + - 60 * a_21 * a_31^2 * a_32 * a_63 * b_6 + - 120 * a_21 * a_31 * a_32^2 * a_43 * b_4 + - 120 * a_21 * a_31 * a_32^2 * a_53 * b_5 + - 120 * a_21 * a_31 * a_32^2 * a_63 * b_6 + - 60 * a_21 * a_32^3 * a_43 * b_4 + - 60 * a_21 * a_32^3 * a_53 * b_5 + - 60 * a_21 * a_32^3 * a_63 * b_6 + - 60 * a_21 * a_41^2 * a_42 * a_54 * b_5 + - 60 * a_21 * a_41^2 * a_42 * a_64 * b_6 + - 120 * a_21 * a_41 * a_42^2 * a_54 * b_5 + - 120 * a_21 * a_41 * a_42^2 * a_64 * b_6 + - 120 * a_21 * a_41 * a_42 * a_43 * a_54 * b_5 + - 120 * a_21 * a_41 * a_42 * a_43 * a_64 * b_6 + - 60 * a_21 * a_42^3 * a_54 * b_5 + - 60 * a_21 * a_42^3 * a_64 * b_6 + - 120 * a_21 * a_42^2 * a_43 * a_54 * b_5 + - 120 * a_21 * a_42^2 * a_43 * a_64 * b_6 + - 60 * a_21 * a_42 * a_43^2 * a_54 * b_5 + - 60 * a_21 * a_42 * a_43^2 * a_64 * b_6 + - 60 * a_21 * a_51^2 * a_52 * a_65 * b_6 + - 120 * a_21 * a_51 * a_52^2 * a_65 * b_6 + - 120 * a_21 * a_51 * a_52 * a_53 * a_65 * b_6 + - 120 * a_21 * a_51 * a_52 * a_54 * a_65 * b_6 + - 60 * a_21 * a_52^3 * a_65 * b_6 + - 120 * a_21 * a_52^2 * a_53 * a_65 * b_6 + - 120 * a_21 * a_52^2 * a_54 * a_65 * b_6 + - 60 * a_21 * a_52 * a_53^2 * a_65 * b_6 + - 120 * a_21 * a_52 * a_53 * a_54 * a_65 * b_6 + - 60 * a_21 * a_52 * a_54^2 * a_65 * b_6 + - 60 * a_31 * a_41^2 * a_43 * a_54 * b_5 + - 60 * a_31 * a_41^2 * a_43 * a_64 * b_6 + - 120 * a_31 * a_41 * a_42 * a_43 * a_54 * b_5 + - 120 * a_31 * a_41 * a_42 * a_43 * a_64 * b_6 + - 120 * a_31 * a_41 * a_43^2 * a_54 * b_5 + - 120 * a_31 * a_41 * a_43^2 * a_64 * b_6 + - 60 * a_31 * a_42^2 * a_43 * a_54 * b_5 + - 60 * a_31 * a_42^2 * a_43 * a_64 * b_6 + - 120 * a_31 * a_42 * a_43^2 * a_54 * b_5 + - 120 * a_31 * a_42 * a_43^2 * a_64 * b_6 + - 60 * a_31 * a_43^3 * a_54 * b_5 + - 60 * a_31 * a_43^3 * a_64 * b_6 + - 60 * a_31 * a_51^2 * a_53 * a_65 * b_6 + - 120 * a_31 * a_51 * a_52 * a_53 * a_65 * b_6 + - 120 * a_31 * a_51 * a_53^2 * a_65 * b_6 + - 120 * a_31 * a_51 * a_53 * a_54 * a_65 * b_6 + - 60 * a_31 * a_52^2 * a_53 * a_65 * b_6 + - 120 * a_31 * a_52 * a_53^2 * a_65 * b_6 + - 120 * a_31 * a_52 * a_53 * a_54 * a_65 * b_6 + - 60 * a_31 * a_53^3 * a_65 * b_6 + - 120 * a_31 * a_53^2 * a_54 * a_65 * b_6 + - 60 * a_31 * a_53 * a_54^2 * a_65 * b_6 + - 60 * a_32 * a_41^2 * a_43 * a_54 * b_5 + - 60 * a_32 * a_41^2 * a_43 * a_64 * b_6 + - 120 * a_32 * a_41 * a_42 * a_43 * a_54 * b_5 + - 120 * a_32 * a_41 * a_42 * a_43 * a_64 * b_6 + - 120 * a_32 * a_41 * a_43^2 * a_54 * b_5 + - 120 * a_32 * a_41 * a_43^2 * a_64 * b_6 + - 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48 * a_43 * a_54^2 * a_65^2 * b_6 - 1, - 72 * a_21^2 * a_32 * a_42 * a_43 * b_4 + - 72 * a_21^2 * a_32 * a_52 * a_53 * b_5 + - 72 * a_21^2 * a_32 * a_62 * a_63 * b_6 + - 72 * a_21^2 * a_42 * a_52 * a_54 * b_5 + - 72 * a_21^2 * a_42 * a_62 * a_64 * b_6 + - 72 * a_21^2 * a_52 * a_62 * a_65 * b_6 + - 72 * a_21 * a_31 * a_32 * a_43^2 * b_4 + - 72 * a_21 * a_31 * a_32 * a_53^2 * b_5 + - 72 * a_21 * a_31 * a_32 * a_63^2 * b_6 + - 72 * a_21 * a_31 * a_42 * a_53 * a_54 * b_5 + - 72 * a_21 * a_31 * a_42 * a_63 * a_64 * b_6 + - 72 * a_21 * a_31 * a_43 * a_52 * a_54 * b_5 + - 72 * a_21 * a_31 * a_43 * a_62 * a_64 * b_6 + - 72 * a_21 * a_31 * a_52 * a_63 * a_65 * b_6 + - 72 * a_21 * a_31 * a_53 * a_62 * a_65 * b_6 + - 72 * a_21 * a_32^2 * a_43^2 * b_4 + - 72 * a_21 * a_32^2 * a_53^2 * b_5 + - 72 * a_21 * a_32^2 * a_63^2 * b_6 + - 72 * a_21 * a_32 * a_41 * a_53 * a_54 * b_5 + - 72 * a_21 * a_32 * a_41 * a_63 * a_64 * b_6 + - 144 * a_21 * a_32 * a_42 * a_53 * a_54 * b_5 + - 144 * a_21 * a_32 * a_42 * a_63 * a_64 * b_6 + - 72 * a_21 * a_32 * a_43 * a_52 * a_54 * b_5 + - 72 * a_21 * a_32 * a_43 * a_53 * a_54 * b_5 + - 72 * a_21 * a_32 * a_43 * a_62 * a_64 * b_6 + - 72 * a_21 * a_32 * a_43 * a_63 * a_64 * b_6 + - 72 * a_21 * a_32 * a_51 * a_63 * a_65 * b_6 + - 144 * a_21 * a_32 * a_52 * a_63 * a_65 * b_6 + - 72 * a_21 * a_32 * a_53 * a_62 * a_65 * b_6 + - 72 * a_21 * a_32 * a_53 * a_63 * a_65 * b_6 + - 72 * a_21 * a_32 * a_54 * a_63 * a_65 * b_6 + - 72 * a_21 * a_41 * a_42 * a_54^2 * b_5 + - 72 * a_21 * a_41 * a_42 * a_64^2 * b_6 + - 72 * a_21 * a_41 * a_52 * a_64 * a_65 * b_6 + - 72 * a_21 * a_41 * a_54 * a_62 * a_65 * b_6 + - 72 * a_21 * a_42^2 * a_54^2 * b_5 + - 72 * a_21 * a_42^2 * a_64^2 * b_6 + - 72 * a_21 * a_42 * a_43 * a_54^2 * b_5 + - 72 * a_21 * a_42 * a_43 * a_64^2 * b_6 + - 72 * a_21 * a_42 * a_51 * a_64 * a_65 * b_6 + - 144 * a_21 * a_42 * a_52 * a_64 * a_65 * b_6 + - 72 * a_21 * a_42 * a_53 * a_64 * a_65 * b_6 + - 72 * a_21 * a_42 * a_54 * a_62 * a_65 * b_6 + - 72 * a_21 * a_42 * a_54 * a_64 * a_65 * b_6 + - 72 * a_21 * a_43 * a_52 * a_64 * a_65 * b_6 + - 72 * a_21 * a_43 * a_54 * a_62 * a_65 * b_6 + - 72 * a_21 * a_51 * a_52 * a_65^2 * b_6 + - 72 * a_21 * a_52^2 * a_65^2 * b_6 + - 72 * a_21 * a_52 * a_53 * a_65^2 * b_6 + - 72 * a_21 * a_52 * a_54 * a_65^2 * b_6 + - 72 * a_31^2 * a_43 * a_53 * a_54 * b_5 + - 72 * a_31^2 * a_43 * a_63 * a_64 * b_6 + - 72 * a_31^2 * a_53 * a_63 * a_65 * b_6 + - 144 * a_31 * a_32 * a_43 * a_53 * a_54 * b_5 + - 144 * a_31 * a_32 * a_43 * a_63 * a_64 * b_6 + - 144 * a_31 * a_32 * a_53 * a_63 * a_65 * b_6 + - 72 * a_31 * a_41 * a_43 * a_54^2 * b_5 + - 72 * a_31 * a_41 * a_43 * a_64^2 * b_6 + - 72 * a_31 * a_41 * a_53 * a_64 * a_65 * b_6 + - 72 * a_31 * a_41 * a_54 * a_63 * a_65 * b_6 + - 72 * a_31 * a_42 * a_43 * a_54^2 * b_5 + - 72 * a_31 * a_42 * a_43 * a_64^2 * b_6 + - 72 * a_31 * a_42 * a_53 * a_64 * a_65 * b_6 + - 72 * a_31 * a_42 * a_54 * a_63 * a_65 * b_6 + - 72 * a_31 * a_43^2 * a_54^2 * b_5 + - 72 * a_31 * a_43^2 * a_64^2 * b_6 + - 72 * a_31 * a_43 * a_51 * a_64 * a_65 * b_6 + - 72 * a_31 * a_43 * a_52 * a_64 * a_65 * b_6 + - 144 * a_31 * a_43 * a_53 * a_64 * a_65 * b_6 + - 72 * a_31 * a_43 * a_54 * a_63 * a_65 * b_6 + - 72 * a_31 * a_43 * a_54 * a_64 * a_65 * b_6 + - 72 * a_31 * a_51 * a_53 * a_65^2 * b_6 + - 72 * a_31 * a_52 * a_53 * a_65^2 * b_6 + - 72 * a_31 * a_53^2 * a_65^2 * b_6 + - 72 * a_31 * a_53 * a_54 * a_65^2 * b_6 + - 72 * a_32^2 * a_43 * a_53 * a_54 * b_5 + - 72 * a_32^2 * a_43 * a_63 * a_64 * b_6 + - 72 * a_32^2 * a_53 * a_63 * a_65 * b_6 + - 72 * a_32 * a_41 * a_43 * a_54^2 * b_5 + - 72 * a_32 * a_41 * a_43 * a_64^2 * b_6 + - 72 * a_32 * a_41 * a_53 * a_64 * a_65 * b_6 + - 72 * a_32 * a_41 * a_54 * a_63 * a_65 * b_6 + - 72 * a_32 * a_42 * a_43 * a_54^2 * b_5 + - 72 * a_32 * a_42 * a_43 * a_64^2 * b_6 + - 72 * a_32 * a_42 * a_53 * a_64 * a_65 * b_6 + - 72 * a_32 * a_42 * a_54 * a_63 * a_65 * b_6 + - 72 * a_32 * a_43^2 * a_54^2 * b_5 + - 72 * a_32 * a_43^2 * a_64^2 * b_6 + - 72 * a_32 * a_43 * a_51 * a_64 * a_65 * b_6 + - 72 * a_32 * a_43 * a_52 * a_64 * a_65 * b_6 + - 144 * a_32 * a_43 * a_53 * a_64 * a_65 * b_6 + - 72 * a_32 * a_43 * a_54 * a_63 * a_65 * b_6 + - 72 * a_32 * a_43 * a_54 * a_64 * a_65 * b_6 + - 72 * a_32 * a_51 * a_53 * a_65^2 * b_6 + - 72 * a_32 * a_52 * a_53 * a_65^2 * b_6 + - 72 * a_32 * a_53^2 * a_65^2 * b_6 + - 72 * a_32 * a_53 * a_54 * a_65^2 * b_6 + - 72 * a_41^2 * a_54 * a_64 * a_65 * b_6 + - 144 * a_41 * a_42 * a_54 * a_64 * a_65 * b_6 + - 144 * a_41 * a_43 * a_54 * a_64 * a_65 * b_6 + - 72 * a_41 * a_51 * a_54 * a_65^2 * b_6 + - 72 * a_41 * a_52 * a_54 * a_65^2 * b_6 + - 72 * a_41 * a_53 * a_54 * a_65^2 * b_6 + - 72 * a_41 * a_54^2 * a_65^2 * b_6 + - 72 * a_42^2 * a_54 * a_64 * a_65 * b_6 + - 144 * a_42 * a_43 * a_54 * a_64 * a_65 * b_6 + - 72 * a_42 * a_51 * a_54 * a_65^2 * b_6 + - 72 * a_42 * a_52 * a_54 * a_65^2 * b_6 + - 72 * a_42 * a_53 * a_54 * a_65^2 * b_6 + - 72 * a_42 * a_54^2 * a_65^2 * b_6 + - 72 * a_43^2 * a_54 * a_64 * a_65 * b_6 + - 72 * a_43 * a_51 * a_54 * a_65^2 * b_6 + - 72 * a_43 * a_52 * a_54 * a_65^2 * b_6 + - 72 * a_43 * a_53 * a_54 * a_65^2 * b_6 + - 72 * a_43 * a_54^2 * a_65^2 * b_6 - 1, - 36 * a_21 * a_32 * a_41^2 * a_43 * b_4 + - 72 * a_21 * a_32 * a_41 * a_42 * a_43 * b_4 + - 72 * a_21 * a_32 * a_41 * a_43^2 * b_4 + - 36 * a_21 * a_32 * a_42^2 * a_43 * b_4 + - 72 * a_21 * a_32 * a_42 * a_43^2 * b_4 + - 36 * a_21 * a_32 * a_43^3 * b_4 + - 36 * a_21 * a_32 * a_51^2 * a_53 * b_5 + - 72 * a_21 * a_32 * a_51 * a_52 * a_53 * b_5 + - 72 * a_21 * a_32 * a_51 * a_53^2 * b_5 + - 72 * a_21 * a_32 * a_51 * a_53 * a_54 * b_5 + - 36 * a_21 * a_32 * a_52^2 * a_53 * b_5 + - 72 * a_21 * a_32 * a_52 * a_53^2 * b_5 + - 72 * a_21 * a_32 * a_52 * a_53 * a_54 * b_5 + - 36 * a_21 * a_32 * a_53^3 * b_5 + - 72 * a_21 * a_32 * a_53^2 * a_54 * b_5 + - 36 * a_21 * a_32 * a_53 * a_54^2 * b_5 + - 36 * a_21 * a_32 * a_61^2 * a_63 * b_6 + - 72 * a_21 * a_32 * a_61 * a_62 * a_63 * b_6 + - 72 * a_21 * a_32 * a_61 * a_63^2 * b_6 + - 72 * a_21 * a_32 * a_61 * a_63 * a_64 * b_6 + - 72 * a_21 * a_32 * a_61 * a_63 * a_65 * b_6 + - 36 * a_21 * a_32 * a_62^2 * a_63 * b_6 + - 72 * a_21 * a_32 * a_62 * a_63^2 * b_6 + - 72 * a_21 * a_32 * a_62 * a_63 * a_64 * b_6 + - 72 * a_21 * a_32 * a_62 * a_63 * a_65 * b_6 + - 36 * a_21 * a_32 * a_63^3 * b_6 + - 72 * a_21 * a_32 * a_63^2 * a_64 * b_6 + - 72 * a_21 * a_32 * a_63^2 * a_65 * b_6 + - 36 * a_21 * a_32 * a_63 * a_64^2 * b_6 + - 72 * a_21 * a_32 * a_63 * a_64 * a_65 * b_6 + - 36 * a_21 * a_32 * a_63 * a_65^2 * b_6 + - 36 * a_21 * a_42 * a_51^2 * a_54 * b_5 + - 72 * a_21 * a_42 * a_51 * a_52 * a_54 * b_5 + - 72 * a_21 * a_42 * a_51 * a_53 * a_54 * b_5 + - 72 * a_21 * a_42 * a_51 * a_54^2 * b_5 + - 36 * a_21 * a_42 * a_52^2 * a_54 * b_5 + - 72 * a_21 * a_42 * a_52 * a_53 * a_54 * b_5 + - 72 * a_21 * a_42 * a_52 * a_54^2 * b_5 + - 36 * a_21 * a_42 * a_53^2 * a_54 * b_5 + - 72 * a_21 * a_42 * a_53 * a_54^2 * b_5 + - 36 * a_21 * a_42 * a_54^3 * b_5 + - 36 * a_21 * a_42 * a_61^2 * a_64 * b_6 + - 72 * a_21 * a_42 * a_61 * a_62 * a_64 * b_6 + - 72 * a_21 * a_42 * a_61 * a_63 * a_64 * b_6 + - 72 * a_21 * a_42 * a_61 * a_64^2 * b_6 + - 72 * a_21 * a_42 * a_61 * a_64 * a_65 * b_6 + - 36 * a_21 * a_42 * a_62^2 * a_64 * b_6 + - 72 * a_21 * a_42 * a_62 * a_63 * a_64 * b_6 + - 72 * a_21 * a_42 * a_62 * a_64^2 * b_6 + - 72 * a_21 * a_42 * a_62 * a_64 * a_65 * b_6 + - 36 * a_21 * a_42 * a_63^2 * a_64 * b_6 + - 72 * a_21 * a_42 * a_63 * a_64^2 * b_6 + - 72 * a_21 * a_42 * a_63 * a_64 * a_65 * b_6 + - 36 * a_21 * a_42 * a_64^3 * b_6 + - 72 * a_21 * a_42 * a_64^2 * a_65 * b_6 + - 36 * a_21 * a_42 * a_64 * a_65^2 * b_6 + - 36 * a_21 * a_52 * a_61^2 * a_65 * b_6 + - 72 * a_21 * a_52 * a_61 * a_62 * a_65 * b_6 + - 72 * a_21 * a_52 * a_61 * a_63 * a_65 * b_6 + - 72 * a_21 * a_52 * a_61 * a_64 * a_65 * b_6 + - 72 * a_21 * a_52 * a_61 * a_65^2 * b_6 + - 36 * a_21 * a_52 * a_62^2 * a_65 * b_6 + - 72 * a_21 * a_52 * a_62 * a_63 * a_65 * b_6 + - 72 * a_21 * a_52 * a_62 * a_64 * a_65 * b_6 + - 72 * a_21 * a_52 * a_62 * a_65^2 * b_6 + - 36 * a_21 * a_52 * a_63^2 * a_65 * b_6 + - 72 * a_21 * a_52 * a_63 * a_64 * a_65 * b_6 + - 72 * a_21 * a_52 * a_63 * a_65^2 * b_6 + - 36 * a_21 * a_52 * a_64^2 * a_65 * b_6 + - 72 * a_21 * a_52 * a_64 * a_65^2 * b_6 + - 36 * a_21 * a_52 * a_65^3 * b_6 + - 36 * a_31 * a_43 * a_51^2 * a_54 * b_5 + - 72 * a_31 * a_43 * a_51 * a_52 * a_54 * b_5 + - 72 * a_31 * a_43 * a_51 * a_53 * a_54 * b_5 + - 72 * a_31 * a_43 * a_51 * a_54^2 * b_5 + - 36 * a_31 * a_43 * a_52^2 * a_54 * b_5 + - 72 * a_31 * a_43 * a_52 * a_53 * a_54 * b_5 + - 72 * a_31 * a_43 * a_52 * a_54^2 * b_5 + - 36 * a_31 * a_43 * a_53^2 * a_54 * b_5 + - 72 * a_31 * a_43 * a_53 * a_54^2 * b_5 + - 36 * a_31 * a_43 * a_54^3 * b_5 + - 36 * a_31 * a_43 * a_61^2 * a_64 * b_6 + - 72 * a_31 * a_43 * a_61 * a_62 * a_64 * b_6 + - 72 * a_31 * a_43 * a_61 * a_63 * a_64 * b_6 + - 72 * a_31 * a_43 * a_61 * a_64^2 * b_6 + - 72 * a_31 * a_43 * a_61 * a_64 * a_65 * b_6 + - 36 * a_31 * a_43 * a_62^2 * a_64 * b_6 + - 72 * a_31 * a_43 * a_62 * a_63 * a_64 * b_6 + - 72 * a_31 * a_43 * a_62 * a_64^2 * b_6 + - 72 * a_31 * a_43 * a_62 * a_64 * a_65 * b_6 + - 36 * a_31 * a_43 * a_63^2 * a_64 * b_6 + - 72 * a_31 * a_43 * a_63 * a_64^2 * b_6 + - 72 * a_31 * a_43 * a_63 * a_64 * a_65 * b_6 + - 36 * a_31 * a_43 * a_64^3 * b_6 + - 72 * a_31 * a_43 * a_64^2 * a_65 * b_6 + - 36 * a_31 * a_43 * a_64 * a_65^2 * b_6 + - 36 * a_31 * a_53 * a_61^2 * a_65 * b_6 + - 72 * a_31 * a_53 * a_61 * a_62 * a_65 * b_6 + - 72 * a_31 * a_53 * a_61 * a_63 * a_65 * b_6 + - 72 * a_31 * a_53 * a_61 * a_64 * a_65 * b_6 + - 72 * a_31 * a_53 * a_61 * a_65^2 * b_6 + - 36 * a_31 * a_53 * a_62^2 * a_65 * b_6 + - 72 * a_31 * a_53 * a_62 * a_63 * a_65 * b_6 + - 72 * a_31 * a_53 * a_62 * a_64 * a_65 * b_6 + - 72 * a_31 * a_53 * a_62 * a_65^2 * b_6 + - 36 * a_31 * a_53 * a_63^2 * a_65 * b_6 + - 72 * a_31 * a_53 * a_63 * a_64 * a_65 * b_6 + - 72 * a_31 * a_53 * a_63 * a_65^2 * b_6 + - 36 * a_31 * a_53 * a_64^2 * a_65 * b_6 + - 72 * a_31 * a_53 * a_64 * a_65^2 * b_6 + - 36 * a_31 * a_53 * a_65^3 * b_6 + - 36 * a_32 * a_43 * a_51^2 * a_54 * b_5 + - 72 * a_32 * a_43 * a_51 * a_52 * a_54 * b_5 + - 72 * a_32 * a_43 * a_51 * a_53 * a_54 * b_5 + - 72 * a_32 * a_43 * a_51 * a_54^2 * b_5 + - 36 * a_32 * a_43 * a_52^2 * a_54 * b_5 + - 72 * a_32 * a_43 * a_52 * a_53 * a_54 * b_5 + - 72 * a_32 * a_43 * a_52 * a_54^2 * b_5 + - 36 * a_32 * a_43 * a_53^2 * a_54 * b_5 + - 72 * a_32 * a_43 * a_53 * a_54^2 * b_5 + - 36 * a_32 * a_43 * a_54^3 * b_5 + - 36 * a_32 * a_43 * a_61^2 * a_64 * b_6 + - 72 * a_32 * a_43 * a_61 * a_62 * a_64 * b_6 + - 72 * a_32 * a_43 * a_61 * a_63 * a_64 * b_6 + - 72 * a_32 * a_43 * a_61 * a_64^2 * b_6 + - 72 * a_32 * a_43 * a_61 * a_64 * a_65 * b_6 + - 36 * a_32 * a_43 * a_62^2 * a_64 * b_6 + - 72 * a_32 * a_43 * a_62 * a_63 * a_64 * b_6 + - 72 * a_32 * a_43 * a_62 * a_64^2 * b_6 + - 72 * a_32 * a_43 * a_62 * a_64 * a_65 * b_6 + - 36 * a_32 * a_43 * a_63^2 * a_64 * b_6 + - 72 * a_32 * a_43 * a_63 * a_64^2 * b_6 + - 72 * a_32 * a_43 * a_63 * a_64 * a_65 * b_6 + - 36 * a_32 * a_43 * a_64^3 * b_6 + - 72 * a_32 * a_43 * a_64^2 * a_65 * b_6 + - 36 * a_32 * a_43 * a_64 * a_65^2 * b_6 + - 36 * a_32 * a_53 * a_61^2 * a_65 * b_6 + - 72 * a_32 * a_53 * a_61 * a_62 * a_65 * b_6 + - 72 * a_32 * a_53 * a_61 * a_63 * a_65 * b_6 + - 72 * a_32 * a_53 * a_61 * a_64 * a_65 * b_6 + - 72 * a_32 * a_53 * a_61 * a_65^2 * b_6 + - 36 * a_32 * a_53 * a_62^2 * a_65 * b_6 + - 72 * a_32 * a_53 * a_62 * a_63 * a_65 * b_6 + - 72 * a_32 * a_53 * a_62 * a_64 * a_65 * b_6 + - 72 * a_32 * a_53 * a_62 * a_65^2 * b_6 + - 36 * a_32 * a_53 * a_63^2 * a_65 * b_6 + - 72 * a_32 * a_53 * a_63 * a_64 * a_65 * b_6 + - 72 * a_32 * a_53 * a_63 * a_65^2 * b_6 + - 36 * a_32 * a_53 * a_64^2 * a_65 * b_6 + - 72 * a_32 * a_53 * a_64 * a_65^2 * b_6 + - 36 * a_32 * a_53 * a_65^3 * b_6 + - 36 * a_41 * a_54 * a_61^2 * a_65 * b_6 + - 72 * a_41 * a_54 * a_61 * a_62 * a_65 * b_6 + - 72 * a_41 * a_54 * a_61 * a_63 * a_65 * b_6 + - 72 * a_41 * a_54 * a_61 * a_64 * a_65 * b_6 + - 72 * a_41 * a_54 * a_61 * a_65^2 * b_6 + - 36 * a_41 * a_54 * a_62^2 * a_65 * b_6 + - 72 * a_41 * a_54 * a_62 * a_63 * a_65 * b_6 + - 72 * a_41 * a_54 * a_62 * a_64 * a_65 * b_6 + - 72 * a_41 * a_54 * a_62 * a_65^2 * b_6 + - 36 * a_41 * a_54 * a_63^2 * a_65 * b_6 + - 72 * a_41 * a_54 * a_63 * a_64 * a_65 * b_6 + - 72 * a_41 * a_54 * a_63 * a_65^2 * b_6 + - 36 * a_41 * a_54 * a_64^2 * a_65 * b_6 + - 72 * a_41 * a_54 * a_64 * a_65^2 * b_6 + - 36 * a_41 * a_54 * a_65^3 * b_6 + - 36 * a_42 * a_54 * a_61^2 * a_65 * b_6 + - 72 * a_42 * a_54 * a_61 * a_62 * a_65 * b_6 + - 72 * a_42 * a_54 * a_61 * a_63 * a_65 * b_6 + - 72 * a_42 * a_54 * a_61 * a_64 * a_65 * b_6 + - 72 * a_42 * a_54 * a_61 * a_65^2 * b_6 + - 36 * a_42 * a_54 * a_62^2 * a_65 * b_6 + - 72 * a_42 * a_54 * a_62 * a_63 * a_65 * b_6 + - 72 * a_42 * a_54 * a_62 * a_64 * a_65 * b_6 + - 72 * a_42 * a_54 * a_62 * a_65^2 * b_6 + - 36 * a_42 * a_54 * a_63^2 * a_65 * b_6 + - 72 * a_42 * a_54 * a_63 * a_64 * a_65 * b_6 + - 72 * a_42 * a_54 * a_63 * a_65^2 * b_6 + - 36 * a_42 * a_54 * a_64^2 * a_65 * b_6 + - 72 * a_42 * a_54 * a_64 * a_65^2 * b_6 + - 36 * a_42 * a_54 * a_65^3 * b_6 + - 36 * a_43 * a_54 * a_61^2 * a_65 * b_6 + - 72 * a_43 * a_54 * a_61 * a_62 * a_65 * b_6 + - 72 * a_43 * a_54 * a_61 * a_63 * a_65 * b_6 + - 72 * a_43 * a_54 * a_61 * a_64 * a_65 * b_6 + - 72 * a_43 * a_54 * a_61 * a_65^2 * b_6 + - 36 * a_43 * a_54 * a_62^2 * a_65 * b_6 + - 72 * a_43 * a_54 * a_62 * a_63 * a_65 * b_6 + - 72 * a_43 * a_54 * a_62 * a_64 * a_65 * b_6 + - 72 * a_43 * a_54 * a_62 * a_65^2 * b_6 + - 36 * a_43 * a_54 * a_63^2 * a_65 * b_6 + - 72 * a_43 * a_54 * a_63 * a_64 * a_65 * b_6 + - 72 * a_43 * a_54 * a_63 * a_65^2 * b_6 + - 36 * a_43 * a_54 * a_64^2 * a_65 * b_6 + - 72 * a_43 * a_54 * a_64 * a_65^2 * b_6 + - 36 * a_43 * a_54 * a_65^3 * b_6 - 1, - 30 * a_21^4 * a_32 * b_3 + - 30 * a_21^4 * a_42 * b_4 + - 30 * a_21^4 * a_52 * b_5 + - 30 * a_21^4 * a_62 * b_6 + - 30 * a_31^4 * a_43 * b_4 + - 30 * a_31^4 * a_53 * b_5 + - 30 * a_31^4 * a_63 * b_6 + - 120 * a_31^3 * a_32 * a_43 * b_4 + - 120 * a_31^3 * a_32 * a_53 * b_5 + - 120 * a_31^3 * a_32 * a_63 * b_6 + - 180 * a_31^2 * a_32^2 * a_43 * b_4 + - 180 * a_31^2 * a_32^2 * a_53 * b_5 + - 180 * a_31^2 * a_32^2 * a_63 * b_6 + - 120 * a_31 * a_32^3 * a_43 * b_4 + - 120 * a_31 * a_32^3 * a_53 * b_5 + - 120 * a_31 * a_32^3 * a_63 * b_6 + - 30 * a_32^4 * a_43 * b_4 + - 30 * a_32^4 * a_53 * b_5 + - 30 * a_32^4 * a_63 * b_6 + - 30 * a_41^4 * a_54 * b_5 + - 30 * a_41^4 * a_64 * b_6 + - 120 * a_41^3 * a_42 * a_54 * b_5 + - 120 * a_41^3 * a_42 * a_64 * b_6 + - 120 * a_41^3 * a_43 * a_54 * b_5 + - 120 * a_41^3 * a_43 * a_64 * b_6 + - 180 * a_41^2 * a_42^2 * a_54 * b_5 + - 180 * a_41^2 * a_42^2 * a_64 * b_6 + - 360 * a_41^2 * a_42 * a_43 * a_54 * b_5 + - 360 * a_41^2 * a_42 * a_43 * a_64 * b_6 + - 180 * a_41^2 * a_43^2 * a_54 * b_5 + - 180 * a_41^2 * a_43^2 * a_64 * b_6 + - 120 * a_41 * a_42^3 * a_54 * b_5 + - 120 * a_41 * a_42^3 * a_64 * b_6 + - 360 * a_41 * a_42^2 * a_43 * a_54 * b_5 + - 360 * a_41 * a_42^2 * a_43 * a_64 * b_6 + - 360 * a_41 * a_42 * a_43^2 * a_54 * b_5 + - 360 * a_41 * a_42 * a_43^2 * a_64 * b_6 + - 120 * a_41 * a_43^3 * a_54 * b_5 + - 120 * a_41 * a_43^3 * a_64 * b_6 + - 30 * a_42^4 * a_54 * b_5 + - 30 * a_42^4 * a_64 * b_6 + - 120 * a_42^3 * a_43 * a_54 * b_5 + - 120 * a_42^3 * a_43 * a_64 * b_6 + - 180 * a_42^2 * a_43^2 * a_54 * b_5 + - 180 * a_42^2 * a_43^2 * a_64 * b_6 + - 120 * a_42 * a_43^3 * a_54 * b_5 + - 120 * a_42 * a_43^3 * a_64 * b_6 + - 30 * a_43^4 * a_54 * b_5 + - 30 * a_43^4 * a_64 * b_6 + - 30 * a_51^4 * a_65 * b_6 + - 120 * a_51^3 * a_52 * a_65 * b_6 + - 120 * a_51^3 * a_53 * a_65 * b_6 + - 120 * a_51^3 * a_54 * a_65 * b_6 + - 180 * a_51^2 * a_52^2 * a_65 * b_6 + - 360 * a_51^2 * a_52 * a_53 * a_65 * b_6 + - 360 * a_51^2 * a_52 * a_54 * a_65 * b_6 + - 180 * a_51^2 * a_53^2 * a_65 * b_6 + - 360 * a_51^2 * a_53 * a_54 * a_65 * b_6 + - 180 * a_51^2 * a_54^2 * a_65 * b_6 + - 120 * a_51 * a_52^3 * a_65 * b_6 + - 360 * a_51 * a_52^2 * a_53 * a_65 * b_6 + - 360 * a_51 * a_52^2 * a_54 * a_65 * b_6 + - 360 * a_51 * a_52 * a_53^2 * a_65 * b_6 + - 720 * a_51 * a_52 * a_53 * a_54 * a_65 * b_6 + - 360 * a_51 * a_52 * a_54^2 * a_65 * b_6 + - 120 * a_51 * a_53^3 * a_65 * b_6 + - 360 * a_51 * a_53^2 * a_54 * a_65 * b_6 + - 360 * a_51 * a_53 * a_54^2 * a_65 * b_6 + - 120 * a_51 * a_54^3 * a_65 * b_6 + - 30 * a_52^4 * a_65 * b_6 + - 120 * a_52^3 * a_53 * a_65 * b_6 + - 120 * a_52^3 * a_54 * a_65 * b_6 + - 180 * a_52^2 * a_53^2 * a_65 * b_6 + - 360 * a_52^2 * a_53 * a_54 * a_65 * b_6 + - 180 * a_52^2 * a_54^2 * a_65 * b_6 + - 120 * a_52 * a_53^3 * a_65 * b_6 + - 360 * a_52 * a_53^2 * a_54 * a_65 * b_6 + - 360 * a_52 * a_53 * a_54^2 * a_65 * b_6 + - 120 * a_52 * a_54^3 * a_65 * b_6 + - 30 * a_53^4 * a_65 * b_6 + - 120 * a_53^3 * a_54 * a_65 * b_6 + - 180 * a_53^2 * a_54^2 * a_65 * b_6 + - 120 * a_53 * a_54^3 * a_65 * b_6 + - 30 * a_54^4 * a_65 * b_6 - 1, - 24 * a_21^3 * a_31 * a_32 * b_3 + - 24 * a_21^3 * a_32^2 * b_3 + - 24 * a_21^3 * a_41 * a_42 * b_4 + - 24 * a_21^3 * a_42^2 * b_4 + - 24 * a_21^3 * a_42 * a_43 * b_4 + - 24 * a_21^3 * a_51 * a_52 * b_5 + - 24 * a_21^3 * a_52^2 * b_5 + - 24 * a_21^3 * a_52 * a_53 * b_5 + - 24 * a_21^3 * a_52 * a_54 * b_5 + - 24 * a_21^3 * a_61 * a_62 * b_6 + - 24 * a_21^3 * a_62^2 * b_6 + - 24 * a_21^3 * a_62 * a_63 * b_6 + - 24 * a_21^3 * a_62 * a_64 * b_6 + - 24 * a_21^3 * a_62 * a_65 * b_6 + - 24 * a_31^3 * a_41 * a_43 * b_4 + - 24 * a_31^3 * a_42 * a_43 * b_4 + - 24 * a_31^3 * a_43^2 * b_4 + - 24 * a_31^3 * a_51 * a_53 * b_5 + - 24 * a_31^3 * a_52 * a_53 * b_5 + - 24 * a_31^3 * a_53^2 * b_5 + - 24 * a_31^3 * a_53 * a_54 * b_5 + - 24 * a_31^3 * a_61 * a_63 * b_6 + - 24 * a_31^3 * a_62 * a_63 * b_6 + - 24 * a_31^3 * a_63^2 * b_6 + - 24 * a_31^3 * a_63 * a_64 * b_6 + - 24 * a_31^3 * a_63 * a_65 * b_6 + - 72 * a_31^2 * a_32 * a_41 * a_43 * b_4 + - 72 * a_31^2 * a_32 * a_42 * a_43 * b_4 + - 72 * a_31^2 * a_32 * a_43^2 * b_4 + - 72 * a_31^2 * a_32 * a_51 * a_53 * b_5 + - 72 * a_31^2 * a_32 * a_52 * a_53 * b_5 + - 72 * a_31^2 * a_32 * a_53^2 * b_5 + - 72 * a_31^2 * a_32 * a_53 * a_54 * b_5 + - 72 * a_31^2 * a_32 * a_61 * a_63 * b_6 + - 72 * a_31^2 * a_32 * a_62 * a_63 * b_6 + - 72 * a_31^2 * a_32 * a_63^2 * b_6 + - 72 * a_31^2 * a_32 * a_63 * a_64 * b_6 + - 72 * a_31^2 * a_32 * a_63 * a_65 * b_6 + - 72 * a_31 * a_32^2 * a_41 * a_43 * b_4 + - 72 * a_31 * a_32^2 * a_42 * a_43 * b_4 + - 72 * a_31 * a_32^2 * a_43^2 * b_4 + - 72 * a_31 * a_32^2 * a_51 * a_53 * b_5 + - 72 * a_31 * a_32^2 * a_52 * a_53 * b_5 + - 72 * a_31 * a_32^2 * a_53^2 * b_5 + - 72 * a_31 * a_32^2 * a_53 * a_54 * b_5 + - 72 * a_31 * a_32^2 * a_61 * a_63 * b_6 + - 72 * a_31 * a_32^2 * a_62 * a_63 * b_6 + - 72 * a_31 * a_32^2 * a_63^2 * b_6 + - 72 * a_31 * a_32^2 * a_63 * a_64 * b_6 + - 72 * a_31 * a_32^2 * a_63 * a_65 * b_6 + - 24 * a_32^3 * a_41 * a_43 * b_4 + - 24 * a_32^3 * a_42 * a_43 * b_4 + - 24 * a_32^3 * a_43^2 * b_4 + - 24 * a_32^3 * a_51 * a_53 * b_5 + - 24 * a_32^3 * a_52 * a_53 * b_5 + - 24 * a_32^3 * a_53^2 * b_5 + - 24 * a_32^3 * a_53 * a_54 * b_5 + - 24 * a_32^3 * a_61 * a_63 * b_6 + - 24 * a_32^3 * a_62 * a_63 * b_6 + - 24 * a_32^3 * a_63^2 * b_6 + - 24 * a_32^3 * a_63 * a_64 * b_6 + - 24 * a_32^3 * a_63 * a_65 * b_6 + - 24 * a_41^3 * a_51 * a_54 * b_5 + - 24 * a_41^3 * a_52 * a_54 * b_5 + - 24 * a_41^3 * a_53 * a_54 * b_5 + - 24 * a_41^3 * a_54^2 * b_5 + - 24 * a_41^3 * a_61 * a_64 * b_6 + - 24 * a_41^3 * a_62 * a_64 * b_6 + - 24 * a_41^3 * a_63 * a_64 * b_6 + - 24 * a_41^3 * a_64^2 * b_6 + - 24 * a_41^3 * a_64 * a_65 * b_6 + - 72 * a_41^2 * a_42 * a_51 * a_54 * b_5 + - 72 * a_41^2 * a_42 * a_52 * a_54 * b_5 + - 72 * a_41^2 * a_42 * a_53 * a_54 * b_5 + - 72 * a_41^2 * a_42 * a_54^2 * b_5 + - 72 * a_41^2 * a_42 * a_61 * a_64 * b_6 + - 72 * a_41^2 * a_42 * a_62 * a_64 * b_6 + - 72 * a_41^2 * a_42 * a_63 * a_64 * b_6 + - 72 * a_41^2 * a_42 * a_64^2 * b_6 + - 72 * a_41^2 * a_42 * a_64 * a_65 * b_6 + - 72 * a_41^2 * a_43 * a_51 * a_54 * b_5 + - 72 * a_41^2 * a_43 * a_52 * a_54 * b_5 + - 72 * a_41^2 * a_43 * a_53 * a_54 * b_5 + - 72 * a_41^2 * a_43 * a_54^2 * b_5 + - 72 * a_41^2 * a_43 * a_61 * a_64 * b_6 + - 72 * a_41^2 * a_43 * a_62 * a_64 * b_6 + - 72 * a_41^2 * a_43 * a_63 * a_64 * b_6 + - 72 * a_41^2 * a_43 * a_64^2 * b_6 + - 72 * a_41^2 * a_43 * a_64 * a_65 * b_6 + - 72 * a_41 * a_42^2 * a_51 * a_54 * b_5 + - 72 * a_41 * a_42^2 * a_52 * a_54 * b_5 + - 72 * a_41 * a_42^2 * a_53 * a_54 * b_5 + - 72 * a_41 * a_42^2 * a_54^2 * b_5 + - 72 * a_41 * a_42^2 * a_61 * a_64 * b_6 + - 72 * a_41 * a_42^2 * a_62 * a_64 * b_6 + - 72 * a_41 * a_42^2 * a_63 * a_64 * b_6 + - 72 * a_41 * a_42^2 * a_64^2 * b_6 + - 72 * a_41 * a_42^2 * a_64 * a_65 * b_6 + - 144 * a_41 * a_42 * a_43 * a_51 * a_54 * b_5 + - 144 * a_41 * a_42 * a_43 * a_52 * a_54 * b_5 + - 144 * a_41 * a_42 * a_43 * a_53 * a_54 * b_5 + - 144 * a_41 * a_42 * a_43 * a_54^2 * b_5 + - 144 * a_41 * a_42 * a_43 * a_61 * a_64 * b_6 + - 144 * a_41 * a_42 * a_43 * a_62 * a_64 * b_6 + - 144 * a_41 * a_42 * a_43 * a_63 * a_64 * b_6 + - 144 * a_41 * a_42 * a_43 * a_64^2 * b_6 + - 144 * a_41 * a_42 * a_43 * a_64 * a_65 * b_6 + - 72 * a_41 * a_43^2 * a_51 * a_54 * b_5 + - 72 * a_41 * a_43^2 * a_52 * a_54 * b_5 + - 72 * a_41 * a_43^2 * a_53 * a_54 * b_5 + - 72 * a_41 * a_43^2 * a_54^2 * b_5 + - 72 * a_41 * a_43^2 * a_61 * a_64 * b_6 + - 72 * a_41 * a_43^2 * a_62 * a_64 * b_6 + - 72 * a_41 * a_43^2 * a_63 * a_64 * b_6 + - 72 * a_41 * a_43^2 * a_64^2 * b_6 + - 72 * a_41 * a_43^2 * a_64 * a_65 * b_6 + - 24 * a_42^3 * a_51 * a_54 * b_5 + - 24 * a_42^3 * a_52 * a_54 * b_5 + - 24 * a_42^3 * a_53 * a_54 * b_5 + - 24 * a_42^3 * a_54^2 * b_5 + - 24 * a_42^3 * a_61 * a_64 * b_6 + - 24 * a_42^3 * a_62 * a_64 * b_6 + - 24 * a_42^3 * a_63 * a_64 * b_6 + - 24 * a_42^3 * a_64^2 * b_6 + - 24 * a_42^3 * a_64 * a_65 * b_6 + - 72 * a_42^2 * a_43 * a_51 * a_54 * b_5 + - 72 * a_42^2 * a_43 * a_52 * a_54 * b_5 + - 72 * a_42^2 * a_43 * a_53 * a_54 * b_5 + - 72 * a_42^2 * a_43 * a_54^2 * b_5 + - 72 * a_42^2 * a_43 * a_61 * a_64 * b_6 + - 72 * a_42^2 * a_43 * a_62 * a_64 * b_6 + - 72 * a_42^2 * a_43 * a_63 * a_64 * b_6 + - 72 * a_42^2 * a_43 * a_64^2 * b_6 + - 72 * a_42^2 * a_43 * a_64 * a_65 * b_6 + - 72 * a_42 * a_43^2 * a_51 * a_54 * b_5 + - 72 * a_42 * a_43^2 * a_52 * a_54 * b_5 + - 72 * a_42 * a_43^2 * a_53 * a_54 * b_5 + - 72 * a_42 * a_43^2 * a_54^2 * b_5 + - 72 * a_42 * a_43^2 * a_61 * a_64 * b_6 + - 72 * a_42 * a_43^2 * a_62 * a_64 * b_6 + - 72 * a_42 * a_43^2 * a_63 * a_64 * b_6 + - 72 * a_42 * a_43^2 * a_64^2 * b_6 + - 72 * a_42 * a_43^2 * a_64 * a_65 * b_6 + - 24 * a_43^3 * a_51 * a_54 * b_5 + - 24 * a_43^3 * a_52 * a_54 * b_5 + - 24 * a_43^3 * a_53 * a_54 * b_5 + - 24 * a_43^3 * a_54^2 * b_5 + - 24 * a_43^3 * a_61 * a_64 * b_6 + - 24 * a_43^3 * a_62 * a_64 * b_6 + - 24 * a_43^3 * a_63 * a_64 * b_6 + - 24 * a_43^3 * a_64^2 * b_6 + - 24 * a_43^3 * a_64 * a_65 * b_6 + - 24 * a_51^3 * a_61 * a_65 * b_6 + - 24 * a_51^3 * a_62 * a_65 * b_6 + - 24 * a_51^3 * a_63 * a_65 * b_6 + - 24 * a_51^3 * a_64 * a_65 * b_6 + - 24 * a_51^3 * a_65^2 * b_6 + - 72 * a_51^2 * a_52 * a_61 * a_65 * b_6 + - 72 * a_51^2 * a_52 * a_62 * a_65 * b_6 + - 72 * a_51^2 * a_52 * a_63 * a_65 * b_6 + - 72 * a_51^2 * a_52 * a_64 * a_65 * b_6 + - 72 * a_51^2 * a_52 * a_65^2 * b_6 + - 72 * a_51^2 * a_53 * a_61 * a_65 * b_6 + - 72 * a_51^2 * a_53 * a_62 * a_65 * b_6 + - 72 * a_51^2 * a_53 * a_63 * a_65 * b_6 + - 72 * a_51^2 * a_53 * a_64 * a_65 * b_6 + - 72 * a_51^2 * a_53 * a_65^2 * b_6 + - 72 * a_51^2 * a_54 * a_61 * a_65 * b_6 + - 72 * a_51^2 * a_54 * a_62 * a_65 * b_6 + - 72 * a_51^2 * a_54 * a_63 * a_65 * b_6 + - 72 * a_51^2 * a_54 * a_64 * a_65 * b_6 + - 72 * a_51^2 * a_54 * a_65^2 * b_6 + - 72 * a_51 * a_52^2 * a_61 * a_65 * b_6 + - 72 * a_51 * a_52^2 * a_62 * a_65 * b_6 + - 72 * a_51 * a_52^2 * a_63 * a_65 * b_6 + - 72 * a_51 * a_52^2 * a_64 * a_65 * b_6 + - 72 * a_51 * a_52^2 * a_65^2 * b_6 + - 144 * a_51 * a_52 * a_53 * a_61 * a_65 * b_6 + - 144 * a_51 * a_52 * a_53 * a_62 * a_65 * b_6 + - 144 * a_51 * a_52 * a_53 * a_63 * a_65 * b_6 + - 144 * a_51 * a_52 * a_53 * a_64 * a_65 * b_6 + - 144 * a_51 * a_52 * a_53 * a_65^2 * b_6 + - 144 * a_51 * a_52 * a_54 * a_61 * a_65 * b_6 + - 144 * a_51 * a_52 * a_54 * a_62 * a_65 * b_6 + - 144 * a_51 * a_52 * a_54 * a_63 * a_65 * b_6 + - 144 * a_51 * a_52 * a_54 * a_64 * a_65 * b_6 + - 144 * a_51 * a_52 * a_54 * a_65^2 * b_6 + - 72 * a_51 * a_53^2 * a_61 * a_65 * b_6 + - 72 * a_51 * a_53^2 * a_62 * a_65 * b_6 + - 72 * a_51 * a_53^2 * a_63 * a_65 * b_6 + - 72 * a_51 * a_53^2 * a_64 * a_65 * b_6 + - 72 * a_51 * a_53^2 * a_65^2 * b_6 + - 144 * a_51 * a_53 * a_54 * a_61 * a_65 * b_6 + - 144 * a_51 * a_53 * a_54 * a_62 * a_65 * b_6 + - 144 * a_51 * a_53 * a_54 * a_63 * a_65 * b_6 + - 144 * a_51 * a_53 * a_54 * a_64 * a_65 * b_6 + - 144 * a_51 * a_53 * a_54 * a_65^2 * b_6 + - 72 * a_51 * a_54^2 * a_61 * a_65 * b_6 + - 72 * a_51 * a_54^2 * a_62 * a_65 * b_6 + - 72 * a_51 * a_54^2 * a_63 * a_65 * b_6 + - 72 * a_51 * a_54^2 * a_64 * a_65 * b_6 + - 72 * a_51 * a_54^2 * a_65^2 * b_6 + - 24 * a_52^3 * a_61 * a_65 * b_6 + - 24 * a_52^3 * a_62 * a_65 * b_6 + - 24 * a_52^3 * a_63 * a_65 * b_6 + - 24 * a_52^3 * a_64 * a_65 * b_6 + - 24 * a_52^3 * a_65^2 * b_6 + - 72 * a_52^2 * a_53 * a_61 * a_65 * b_6 + - 72 * a_52^2 * a_53 * a_62 * a_65 * b_6 + - 72 * a_52^2 * a_53 * a_63 * a_65 * b_6 + - 72 * a_52^2 * a_53 * a_64 * a_65 * b_6 + - 72 * a_52^2 * a_53 * a_65^2 * b_6 + - 72 * a_52^2 * a_54 * a_61 * a_65 * b_6 + - 72 * a_52^2 * a_54 * a_62 * a_65 * b_6 + - 72 * a_52^2 * a_54 * a_63 * a_65 * b_6 + - 72 * a_52^2 * a_54 * a_64 * a_65 * b_6 + - 72 * a_52^2 * a_54 * a_65^2 * b_6 + - 72 * a_52 * a_53^2 * a_61 * a_65 * b_6 + - 72 * a_52 * a_53^2 * a_62 * a_65 * b_6 + - 72 * a_52 * a_53^2 * a_63 * a_65 * b_6 + - 72 * a_52 * a_53^2 * a_64 * a_65 * b_6 + - 72 * a_52 * a_53^2 * a_65^2 * b_6 + - 144 * a_52 * a_53 * a_54 * a_61 * a_65 * b_6 + - 144 * a_52 * a_53 * a_54 * a_62 * a_65 * b_6 + - 144 * a_52 * a_53 * a_54 * a_63 * a_65 * b_6 + - 144 * a_52 * a_53 * a_54 * a_64 * a_65 * b_6 + - 144 * a_52 * a_53 * a_54 * a_65^2 * b_6 + - 72 * a_52 * a_54^2 * a_61 * a_65 * b_6 + - 72 * a_52 * a_54^2 * a_62 * a_65 * b_6 + - 72 * a_52 * a_54^2 * a_63 * a_65 * b_6 + - 72 * a_52 * a_54^2 * a_64 * a_65 * b_6 + - 72 * a_52 * a_54^2 * a_65^2 * b_6 + - 24 * a_53^3 * a_61 * a_65 * b_6 + - 24 * a_53^3 * a_62 * a_65 * b_6 + - 24 * a_53^3 * a_63 * a_65 * b_6 + - 24 * a_53^3 * a_64 * a_65 * b_6 + - 24 * a_53^3 * a_65^2 * b_6 + - 72 * a_53^2 * a_54 * a_61 * a_65 * b_6 + - 72 * a_53^2 * a_54 * a_62 * a_65 * b_6 + - 72 * a_53^2 * a_54 * a_63 * a_65 * b_6 + - 72 * a_53^2 * a_54 * a_64 * a_65 * b_6 + - 72 * a_53^2 * a_54 * a_65^2 * b_6 + - 72 * a_53 * a_54^2 * a_61 * a_65 * b_6 + - 72 * a_53 * a_54^2 * a_62 * a_65 * b_6 + - 72 * a_53 * a_54^2 * a_63 * a_65 * b_6 + - 72 * a_53 * a_54^2 * a_64 * a_65 * b_6 + - 72 * a_53 * a_54^2 * a_65^2 * b_6 + - 24 * a_54^3 * a_61 * a_65 * b_6 + - 24 * a_54^3 * a_62 * a_65 * b_6 + - 24 * a_54^3 * a_63 * a_65 * b_6 + - 24 * a_54^3 * a_64 * a_65 * b_6 + - 24 * a_54^3 * a_65^2 * b_6 - 1, - 36 * a_21^3 * a_32^2 * b_3 + - 36 * a_21^3 * a_42^2 * b_4 + - 36 * a_21^3 * a_52^2 * b_5 + - 36 * a_21^3 * a_62^2 * b_6 + - 36 * a_21^2 * a_31 * a_42 * a_43 * b_4 + - 36 * a_21^2 * a_31 * a_52 * a_53 * b_5 + - 36 * a_21^2 * a_31 * a_62 * a_63 * b_6 + - 36 * a_21^2 * a_32 * a_42 * a_43 * b_4 + - 36 * a_21^2 * a_32 * a_52 * a_53 * b_5 + - 36 * a_21^2 * a_32 * a_62 * a_63 * b_6 + - 36 * a_21^2 * a_41 * a_52 * a_54 * b_5 + - 36 * a_21^2 * a_41 * a_62 * a_64 * b_6 + - 36 * a_21^2 * a_42 * a_52 * a_54 * b_5 + - 36 * a_21^2 * a_42 * a_62 * a_64 * b_6 + - 36 * a_21^2 * a_43 * a_52 * a_54 * b_5 + - 36 * a_21^2 * a_43 * a_62 * a_64 * b_6 + - 36 * a_21^2 * a_51 * a_62 * a_65 * b_6 + - 36 * a_21^2 * a_52 * a_62 * a_65 * b_6 + - 36 * a_21^2 * a_53 * a_62 * a_65 * b_6 + - 36 * a_21^2 * a_54 * a_62 * a_65 * b_6 + - 36 * a_21 * a_31^2 * a_42 * a_43 * b_4 + - 36 * a_21 * a_31^2 * a_52 * a_53 * b_5 + - 36 * a_21 * a_31^2 * a_62 * a_63 * b_6 + - 72 * a_21 * a_31 * a_32 * a_42 * a_43 * b_4 + - 72 * a_21 * a_31 * a_32 * a_52 * a_53 * b_5 + - 72 * a_21 * a_31 * a_32 * a_62 * a_63 * b_6 + - 36 * a_21 * a_32^2 * a_42 * a_43 * b_4 + - 36 * a_21 * a_32^2 * a_52 * a_53 * b_5 + - 36 * a_21 * a_32^2 * a_62 * a_63 * b_6 + - 36 * a_21 * a_41^2 * a_52 * a_54 * b_5 + - 36 * a_21 * a_41^2 * a_62 * a_64 * b_6 + - 72 * a_21 * a_41 * a_42 * a_52 * a_54 * b_5 + - 72 * a_21 * a_41 * a_42 * a_62 * a_64 * b_6 + - 72 * a_21 * a_41 * a_43 * a_52 * a_54 * b_5 + - 72 * a_21 * a_41 * a_43 * a_62 * a_64 * b_6 + - 36 * a_21 * a_42^2 * a_52 * a_54 * b_5 + - 36 * a_21 * a_42^2 * a_62 * a_64 * b_6 + - 72 * a_21 * a_42 * a_43 * a_52 * a_54 * b_5 + - 72 * a_21 * a_42 * a_43 * a_62 * a_64 * b_6 + - 36 * a_21 * a_43^2 * a_52 * a_54 * b_5 + - 36 * a_21 * a_43^2 * a_62 * a_64 * b_6 + - 36 * a_21 * a_51^2 * a_62 * a_65 * b_6 + - 72 * a_21 * a_51 * a_52 * a_62 * a_65 * b_6 + - 72 * a_21 * a_51 * a_53 * a_62 * a_65 * b_6 + - 72 * a_21 * a_51 * a_54 * a_62 * a_65 * b_6 + - 36 * a_21 * a_52^2 * a_62 * a_65 * b_6 + - 72 * a_21 * a_52 * a_53 * a_62 * a_65 * b_6 + - 72 * a_21 * a_52 * a_54 * a_62 * a_65 * b_6 + - 36 * a_21 * a_53^2 * a_62 * a_65 * b_6 + - 72 * a_21 * a_53 * a_54 * a_62 * a_65 * b_6 + - 36 * a_21 * a_54^2 * a_62 * a_65 * b_6 + - 36 * a_31^3 * a_43^2 * b_4 + - 36 * a_31^3 * a_53^2 * b_5 + - 36 * a_31^3 * a_63^2 * b_6 + - 108 * a_31^2 * a_32 * a_43^2 * b_4 + - 108 * a_31^2 * a_32 * a_53^2 * b_5 + - 108 * a_31^2 * a_32 * a_63^2 * b_6 + - 36 * a_31^2 * a_41 * a_53 * a_54 * b_5 + - 36 * a_31^2 * a_41 * a_63 * a_64 * b_6 + - 36 * a_31^2 * a_42 * a_53 * a_54 * b_5 + - 36 * a_31^2 * a_42 * a_63 * a_64 * b_6 + - 36 * a_31^2 * a_43 * a_53 * a_54 * b_5 + - 36 * a_31^2 * a_43 * a_63 * a_64 * b_6 + - 36 * a_31^2 * a_51 * a_63 * a_65 * b_6 + - 36 * a_31^2 * a_52 * a_63 * a_65 * b_6 + - 36 * a_31^2 * a_53 * a_63 * a_65 * b_6 + - 36 * a_31^2 * a_54 * a_63 * a_65 * b_6 + - 108 * a_31 * a_32^2 * a_43^2 * b_4 + - 108 * a_31 * a_32^2 * a_53^2 * b_5 + - 108 * a_31 * a_32^2 * a_63^2 * b_6 + - 72 * a_31 * a_32 * a_41 * a_53 * a_54 * b_5 + - 72 * a_31 * a_32 * a_41 * a_63 * a_64 * b_6 + - 72 * a_31 * a_32 * a_42 * a_53 * a_54 * b_5 + - 72 * a_31 * a_32 * a_42 * a_63 * a_64 * b_6 + - 72 * a_31 * a_32 * a_43 * a_53 * a_54 * b_5 + - 72 * a_31 * a_32 * a_43 * a_63 * a_64 * b_6 + - 72 * a_31 * a_32 * a_51 * a_63 * a_65 * b_6 + - 72 * a_31 * a_32 * a_52 * a_63 * a_65 * b_6 + - 72 * a_31 * a_32 * a_53 * a_63 * a_65 * b_6 + - 72 * a_31 * a_32 * a_54 * a_63 * a_65 * b_6 + - 36 * a_31 * a_41^2 * a_53 * a_54 * b_5 + - 36 * a_31 * a_41^2 * a_63 * a_64 * b_6 + - 72 * a_31 * a_41 * a_42 * a_53 * a_54 * b_5 + - 72 * a_31 * a_41 * a_42 * a_63 * a_64 * b_6 + - 72 * a_31 * a_41 * a_43 * a_53 * a_54 * b_5 + - 72 * a_31 * a_41 * a_43 * a_63 * a_64 * b_6 + - 36 * a_31 * a_42^2 * a_53 * a_54 * b_5 + - 36 * a_31 * a_42^2 * a_63 * a_64 * b_6 + - 72 * a_31 * a_42 * a_43 * a_53 * a_54 * b_5 + - 72 * a_31 * a_42 * a_43 * a_63 * a_64 * b_6 + - 36 * a_31 * a_43^2 * a_53 * a_54 * b_5 + - 36 * a_31 * a_43^2 * a_63 * a_64 * b_6 + - 36 * a_31 * a_51^2 * a_63 * a_65 * b_6 + - 72 * a_31 * a_51 * a_52 * a_63 * a_65 * b_6 + - 72 * a_31 * a_51 * a_53 * a_63 * a_65 * b_6 + - 72 * a_31 * a_51 * a_54 * a_63 * a_65 * b_6 + - 36 * a_31 * a_52^2 * a_63 * a_65 * b_6 + - 72 * a_31 * a_52 * a_53 * a_63 * a_65 * b_6 + - 72 * a_31 * a_52 * a_54 * a_63 * a_65 * b_6 + - 36 * a_31 * a_53^2 * a_63 * a_65 * b_6 + - 72 * a_31 * a_53 * a_54 * a_63 * a_65 * b_6 + - 36 * a_31 * a_54^2 * a_63 * a_65 * b_6 + - 36 * a_32^3 * a_43^2 * b_4 + - 36 * a_32^3 * a_53^2 * b_5 + - 36 * a_32^3 * a_63^2 * b_6 + - 36 * a_32^2 * a_41 * a_53 * a_54 * b_5 + - 36 * a_32^2 * a_41 * a_63 * a_64 * b_6 + - 36 * a_32^2 * a_42 * a_53 * a_54 * b_5 + - 36 * a_32^2 * a_42 * a_63 * a_64 * b_6 + - 36 * a_32^2 * a_43 * a_53 * a_54 * b_5 + - 36 * a_32^2 * a_43 * a_63 * a_64 * b_6 + - 36 * a_32^2 * a_51 * a_63 * a_65 * b_6 + - 36 * a_32^2 * a_52 * a_63 * a_65 * b_6 + - 36 * a_32^2 * a_53 * a_63 * a_65 * b_6 + - 36 * a_32^2 * a_54 * a_63 * a_65 * b_6 + - 36 * a_32 * a_41^2 * a_53 * a_54 * b_5 + - 36 * a_32 * a_41^2 * a_63 * a_64 * b_6 + - 72 * a_32 * a_41 * a_42 * a_53 * a_54 * b_5 + - 72 * a_32 * a_41 * a_42 * a_63 * a_64 * b_6 + - 72 * a_32 * a_41 * a_43 * a_53 * a_54 * b_5 + - 72 * a_32 * a_41 * a_43 * a_63 * a_64 * b_6 + - 36 * a_32 * a_42^2 * a_53 * a_54 * b_5 + - 36 * a_32 * a_42^2 * a_63 * a_64 * b_6 + - 72 * a_32 * a_42 * a_43 * a_53 * a_54 * b_5 + - 72 * a_32 * a_42 * a_43 * a_63 * a_64 * b_6 + - 36 * a_32 * a_43^2 * a_53 * a_54 * b_5 + - 36 * a_32 * a_43^2 * a_63 * a_64 * b_6 + - 36 * a_32 * a_51^2 * a_63 * a_65 * b_6 + - 72 * a_32 * a_51 * a_52 * a_63 * a_65 * b_6 + - 72 * a_32 * a_51 * a_53 * a_63 * a_65 * b_6 + - 72 * a_32 * a_51 * a_54 * a_63 * a_65 * b_6 + - 36 * a_32 * a_52^2 * a_63 * a_65 * b_6 + - 72 * a_32 * a_52 * a_53 * a_63 * a_65 * b_6 + - 72 * a_32 * a_52 * a_54 * a_63 * a_65 * b_6 + - 36 * a_32 * a_53^2 * a_63 * a_65 * b_6 + - 72 * a_32 * a_53 * a_54 * a_63 * a_65 * b_6 + - 36 * a_32 * a_54^2 * a_63 * a_65 * b_6 + - 36 * a_41^3 * a_54^2 * b_5 + - 36 * a_41^3 * a_64^2 * b_6 + - 108 * a_41^2 * a_42 * a_54^2 * b_5 + - 108 * a_41^2 * a_42 * a_64^2 * b_6 + - 108 * a_41^2 * a_43 * a_54^2 * b_5 + - 108 * a_41^2 * a_43 * a_64^2 * b_6 + - 36 * a_41^2 * a_51 * a_64 * a_65 * b_6 + - 36 * a_41^2 * a_52 * a_64 * a_65 * b_6 + - 36 * a_41^2 * a_53 * a_64 * a_65 * b_6 + - 36 * a_41^2 * a_54 * a_64 * a_65 * b_6 + - 108 * a_41 * a_42^2 * a_54^2 * b_5 + - 108 * a_41 * a_42^2 * a_64^2 * b_6 + - 216 * a_41 * a_42 * a_43 * a_54^2 * b_5 + - 216 * a_41 * a_42 * a_43 * a_64^2 * b_6 + - 72 * a_41 * a_42 * a_51 * a_64 * a_65 * b_6 + - 72 * a_41 * a_42 * a_52 * a_64 * a_65 * b_6 + - 72 * a_41 * a_42 * a_53 * a_64 * a_65 * b_6 + - 72 * a_41 * a_42 * a_54 * a_64 * a_65 * b_6 + - 108 * a_41 * a_43^2 * a_54^2 * b_5 + - 108 * a_41 * a_43^2 * a_64^2 * b_6 + - 72 * a_41 * a_43 * a_51 * a_64 * a_65 * b_6 + - 72 * a_41 * a_43 * a_52 * a_64 * a_65 * b_6 + - 72 * a_41 * a_43 * a_53 * a_64 * a_65 * b_6 + - 72 * a_41 * a_43 * a_54 * a_64 * a_65 * b_6 + - 36 * a_41 * a_51^2 * a_64 * a_65 * b_6 + - 72 * a_41 * a_51 * a_52 * a_64 * a_65 * b_6 + - 72 * a_41 * a_51 * a_53 * a_64 * a_65 * b_6 + - 72 * a_41 * a_51 * a_54 * a_64 * a_65 * b_6 + - 36 * a_41 * a_52^2 * a_64 * a_65 * b_6 + - 72 * a_41 * a_52 * a_53 * a_64 * a_65 * b_6 + - 72 * a_41 * a_52 * a_54 * a_64 * a_65 * b_6 + - 36 * a_41 * a_53^2 * a_64 * a_65 * b_6 + - 72 * a_41 * a_53 * a_54 * a_64 * a_65 * b_6 + - 36 * a_41 * a_54^2 * a_64 * a_65 * b_6 + - 36 * a_42^3 * a_54^2 * b_5 + - 36 * a_42^3 * a_64^2 * b_6 + - 108 * a_42^2 * a_43 * a_54^2 * b_5 + - 108 * a_42^2 * a_43 * a_64^2 * b_6 + - 36 * a_42^2 * a_51 * a_64 * a_65 * b_6 + - 36 * a_42^2 * a_52 * a_64 * a_65 * b_6 + - 36 * a_42^2 * a_53 * a_64 * a_65 * b_6 + - 36 * a_42^2 * a_54 * a_64 * a_65 * b_6 + - 108 * a_42 * a_43^2 * a_54^2 * b_5 + - 108 * a_42 * a_43^2 * a_64^2 * b_6 + - 72 * a_42 * a_43 * a_51 * a_64 * a_65 * b_6 + - 72 * a_42 * a_43 * a_52 * a_64 * a_65 * b_6 + - 72 * a_42 * a_43 * a_53 * a_64 * a_65 * b_6 + - 72 * a_42 * a_43 * a_54 * a_64 * a_65 * b_6 + - 36 * a_42 * a_51^2 * a_64 * a_65 * b_6 + - 72 * a_42 * a_51 * a_52 * a_64 * a_65 * b_6 + - 72 * a_42 * a_51 * a_53 * a_64 * a_65 * b_6 + - 72 * a_42 * a_51 * a_54 * a_64 * a_65 * b_6 + - 36 * a_42 * a_52^2 * a_64 * a_65 * b_6 + - 72 * a_42 * a_52 * a_53 * a_64 * a_65 * b_6 + - 72 * a_42 * a_52 * a_54 * a_64 * a_65 * b_6 + - 36 * a_42 * a_53^2 * a_64 * a_65 * b_6 + - 72 * a_42 * a_53 * a_54 * a_64 * a_65 * b_6 + - 36 * a_42 * a_54^2 * a_64 * a_65 * b_6 + - 36 * a_43^3 * a_54^2 * b_5 + - 36 * a_43^3 * a_64^2 * b_6 + - 36 * a_43^2 * a_51 * a_64 * a_65 * b_6 + - 36 * a_43^2 * a_52 * a_64 * a_65 * b_6 + - 36 * a_43^2 * a_53 * a_64 * a_65 * b_6 + - 36 * a_43^2 * a_54 * a_64 * a_65 * b_6 + - 36 * a_43 * a_51^2 * a_64 * a_65 * b_6 + - 72 * a_43 * a_51 * a_52 * a_64 * a_65 * b_6 + - 72 * a_43 * a_51 * a_53 * a_64 * a_65 * b_6 + - 72 * a_43 * a_51 * a_54 * a_64 * a_65 * b_6 + - 36 * a_43 * a_52^2 * a_64 * a_65 * b_6 + - 72 * a_43 * a_52 * a_53 * a_64 * a_65 * b_6 + - 72 * a_43 * a_52 * a_54 * a_64 * a_65 * b_6 + - 36 * a_43 * a_53^2 * a_64 * a_65 * b_6 + - 72 * a_43 * a_53 * a_54 * a_64 * a_65 * b_6 + - 36 * a_43 * a_54^2 * a_64 * a_65 * b_6 + - 36 * a_51^3 * a_65^2 * b_6 + - 108 * a_51^2 * a_52 * a_65^2 * b_6 + - 108 * a_51^2 * a_53 * a_65^2 * b_6 + - 108 * a_51^2 * a_54 * a_65^2 * b_6 + - 108 * a_51 * a_52^2 * a_65^2 * b_6 + - 216 * a_51 * a_52 * a_53 * a_65^2 * b_6 + - 216 * a_51 * a_52 * a_54 * a_65^2 * b_6 + - 108 * a_51 * a_53^2 * a_65^2 * b_6 + - 216 * a_51 * a_53 * a_54 * a_65^2 * b_6 + - 108 * a_51 * a_54^2 * a_65^2 * b_6 + - 36 * a_52^3 * a_65^2 * b_6 + - 108 * a_52^2 * a_53 * a_65^2 * b_6 + - 108 * a_52^2 * a_54 * a_65^2 * b_6 + - 108 * a_52 * a_53^2 * a_65^2 * b_6 + - 216 * a_52 * a_53 * a_54 * a_65^2 * b_6 + - 108 * a_52 * a_54^2 * a_65^2 * b_6 + - 36 * a_53^3 * a_65^2 * b_6 + - 108 * a_53^2 * a_54 * a_65^2 * b_6 + - 108 * a_53 * a_54^2 * a_65^2 * b_6 + - 36 * a_54^3 * a_65^2 * b_6 - 1, - 18 * a_21^2 * a_31^2 * a_32 * b_3 + - 36 * a_21^2 * a_31 * a_32^2 * b_3 + - 18 * a_21^2 * a_32^3 * b_3 + - 18 * a_21^2 * a_41^2 * a_42 * b_4 + - 36 * a_21^2 * a_41 * a_42^2 * b_4 + - 36 * a_21^2 * a_41 * a_42 * a_43 * b_4 + - 18 * a_21^2 * a_42^3 * b_4 + - 36 * a_21^2 * a_42^2 * a_43 * b_4 + - 18 * a_21^2 * a_42 * a_43^2 * b_4 + - 18 * a_21^2 * a_51^2 * a_52 * b_5 + - 36 * a_21^2 * a_51 * a_52^2 * b_5 + - 36 * a_21^2 * a_51 * a_52 * a_53 * b_5 + - 36 * a_21^2 * a_51 * a_52 * a_54 * b_5 + - 18 * a_21^2 * a_52^3 * b_5 + - 36 * a_21^2 * a_52^2 * a_53 * b_5 + - 36 * a_21^2 * a_52^2 * a_54 * b_5 + - 18 * a_21^2 * a_52 * a_53^2 * b_5 + - 36 * a_21^2 * a_52 * a_53 * a_54 * b_5 + - 18 * a_21^2 * a_52 * a_54^2 * b_5 + - 18 * a_21^2 * a_61^2 * a_62 * b_6 + - 36 * a_21^2 * a_61 * a_62^2 * b_6 + - 36 * a_21^2 * a_61 * a_62 * a_63 * b_6 + - 36 * a_21^2 * a_61 * a_62 * a_64 * b_6 + - 36 * a_21^2 * a_61 * a_62 * a_65 * b_6 + - 18 * a_21^2 * a_62^3 * b_6 + - 36 * a_21^2 * a_62^2 * a_63 * b_6 + - 36 * a_21^2 * a_62^2 * a_64 * b_6 + - 36 * a_21^2 * a_62^2 * a_65 * b_6 + - 18 * a_21^2 * a_62 * a_63^2 * b_6 + - 36 * a_21^2 * a_62 * a_63 * a_64 * b_6 + - 36 * a_21^2 * a_62 * a_63 * a_65 * b_6 + - 18 * a_21^2 * a_62 * a_64^2 * b_6 + - 36 * a_21^2 * a_62 * a_64 * a_65 * b_6 + - 18 * a_21^2 * a_62 * a_65^2 * b_6 + - 18 * a_31^2 * a_41^2 * a_43 * b_4 + - 36 * a_31^2 * a_41 * a_42 * a_43 * b_4 + - 36 * a_31^2 * a_41 * a_43^2 * b_4 + - 18 * a_31^2 * a_42^2 * a_43 * b_4 + - 36 * a_31^2 * a_42 * a_43^2 * b_4 + - 18 * a_31^2 * a_43^3 * b_4 + - 18 * a_31^2 * a_51^2 * a_53 * b_5 + - 36 * a_31^2 * a_51 * a_52 * a_53 * b_5 + - 36 * a_31^2 * a_51 * a_53^2 * b_5 + - 36 * a_31^2 * a_51 * a_53 * a_54 * b_5 + - 18 * a_31^2 * a_52^2 * a_53 * b_5 + - 36 * a_31^2 * a_52 * a_53^2 * b_5 + - 36 * a_31^2 * a_52 * a_53 * a_54 * b_5 + - 18 * a_31^2 * a_53^3 * b_5 + - 36 * a_31^2 * a_53^2 * a_54 * b_5 + - 18 * a_31^2 * a_53 * a_54^2 * b_5 + - 18 * a_31^2 * a_61^2 * a_63 * b_6 + - 36 * a_31^2 * a_61 * a_62 * a_63 * b_6 + - 36 * a_31^2 * a_61 * a_63^2 * b_6 + - 36 * a_31^2 * a_61 * a_63 * a_64 * b_6 + - 36 * a_31^2 * a_61 * a_63 * a_65 * b_6 + - 18 * a_31^2 * a_62^2 * a_63 * b_6 + - 36 * a_31^2 * a_62 * a_63^2 * b_6 + - 36 * a_31^2 * a_62 * a_63 * a_64 * b_6 + - 36 * a_31^2 * a_62 * a_63 * a_65 * b_6 + - 18 * a_31^2 * a_63^3 * b_6 + - 36 * a_31^2 * a_63^2 * a_64 * b_6 + - 36 * a_31^2 * a_63^2 * a_65 * b_6 + - 18 * a_31^2 * a_63 * a_64^2 * b_6 + - 36 * a_31^2 * a_63 * a_64 * a_65 * b_6 + - 18 * a_31^2 * a_63 * a_65^2 * b_6 + - 36 * a_31 * a_32 * a_41^2 * a_43 * b_4 + - 72 * a_31 * a_32 * a_41 * a_42 * a_43 * b_4 + - 72 * a_31 * a_32 * a_41 * a_43^2 * b_4 + - 36 * a_31 * a_32 * a_42^2 * a_43 * b_4 + - 72 * a_31 * a_32 * a_42 * a_43^2 * b_4 + - 36 * a_31 * a_32 * a_43^3 * b_4 + - 36 * a_31 * a_32 * a_51^2 * a_53 * b_5 + - 72 * a_31 * a_32 * a_51 * a_52 * a_53 * b_5 + - 72 * a_31 * a_32 * a_51 * a_53^2 * b_5 + - 72 * a_31 * a_32 * a_51 * a_53 * a_54 * b_5 + - 36 * a_31 * a_32 * a_52^2 * a_53 * b_5 + - 72 * a_31 * a_32 * a_52 * a_53^2 * b_5 + - 72 * a_31 * a_32 * a_52 * a_53 * a_54 * b_5 + - 36 * a_31 * a_32 * a_53^3 * b_5 + - 72 * a_31 * a_32 * a_53^2 * a_54 * b_5 + - 36 * a_31 * a_32 * a_53 * a_54^2 * b_5 + - 36 * a_31 * a_32 * a_61^2 * a_63 * b_6 + - 72 * a_31 * a_32 * a_61 * a_62 * a_63 * b_6 + - 72 * a_31 * a_32 * a_61 * a_63^2 * b_6 + - 72 * a_31 * a_32 * a_61 * a_63 * a_64 * b_6 + - 72 * a_31 * a_32 * a_61 * a_63 * a_65 * b_6 + - 36 * a_31 * a_32 * a_62^2 * a_63 * b_6 + - 72 * a_31 * a_32 * a_62 * a_63^2 * b_6 + - 72 * a_31 * a_32 * a_62 * a_63 * a_64 * b_6 + - 72 * a_31 * a_32 * a_62 * a_63 * a_65 * b_6 + - 36 * a_31 * a_32 * a_63^3 * b_6 + - 72 * a_31 * a_32 * a_63^2 * a_64 * b_6 + - 72 * a_31 * a_32 * a_63^2 * a_65 * b_6 + - 36 * a_31 * a_32 * a_63 * a_64^2 * b_6 + - 72 * a_31 * a_32 * a_63 * a_64 * a_65 * b_6 + - 36 * a_31 * a_32 * a_63 * a_65^2 * b_6 + - 18 * a_32^2 * a_41^2 * a_43 * b_4 + - 36 * a_32^2 * a_41 * a_42 * a_43 * b_4 + - 36 * a_32^2 * a_41 * a_43^2 * b_4 + - 18 * a_32^2 * a_42^2 * a_43 * b_4 + - 36 * a_32^2 * a_42 * a_43^2 * b_4 + - 18 * a_32^2 * a_43^3 * b_4 + - 18 * a_32^2 * a_51^2 * a_53 * b_5 + - 36 * a_32^2 * a_51 * a_52 * a_53 * b_5 + - 36 * a_32^2 * a_51 * a_53^2 * b_5 + - 36 * a_32^2 * a_51 * a_53 * a_54 * b_5 + - 18 * a_32^2 * a_52^2 * a_53 * b_5 + - 36 * a_32^2 * a_52 * a_53^2 * b_5 + - 36 * a_32^2 * a_52 * a_53 * a_54 * b_5 + - 18 * a_32^2 * a_53^3 * b_5 + - 36 * a_32^2 * a_53^2 * a_54 * b_5 + - 18 * a_32^2 * a_53 * a_54^2 * b_5 + - 18 * a_32^2 * a_61^2 * a_63 * b_6 + - 36 * a_32^2 * a_61 * a_62 * a_63 * b_6 + - 36 * a_32^2 * a_61 * a_63^2 * b_6 + - 36 * a_32^2 * a_61 * a_63 * a_64 * b_6 + - 36 * a_32^2 * a_61 * a_63 * a_65 * b_6 + - 18 * a_32^2 * a_62^2 * a_63 * b_6 + - 36 * a_32^2 * a_62 * a_63^2 * b_6 + - 36 * a_32^2 * a_62 * a_63 * a_64 * b_6 + - 36 * a_32^2 * a_62 * a_63 * a_65 * b_6 + - 18 * a_32^2 * a_63^3 * b_6 + - 36 * a_32^2 * a_63^2 * a_64 * b_6 + - 36 * a_32^2 * a_63^2 * a_65 * b_6 + - 18 * a_32^2 * a_63 * a_64^2 * b_6 + - 36 * a_32^2 * a_63 * a_64 * a_65 * b_6 + - 18 * a_32^2 * a_63 * a_65^2 * b_6 + - 18 * a_41^2 * a_51^2 * a_54 * b_5 + - 36 * a_41^2 * a_51 * a_52 * a_54 * b_5 + - 36 * a_41^2 * a_51 * a_53 * a_54 * b_5 + - 36 * a_41^2 * a_51 * a_54^2 * b_5 + - 18 * a_41^2 * a_52^2 * a_54 * b_5 + - 36 * a_41^2 * a_52 * a_53 * a_54 * b_5 + - 36 * a_41^2 * a_52 * a_54^2 * b_5 + - 18 * a_41^2 * a_53^2 * a_54 * b_5 + - 36 * a_41^2 * a_53 * a_54^2 * b_5 + - 18 * a_41^2 * a_54^3 * b_5 + - 18 * a_41^2 * a_61^2 * a_64 * b_6 + - 36 * a_41^2 * a_61 * a_62 * a_64 * b_6 + - 36 * a_41^2 * a_61 * a_63 * a_64 * b_6 + - 36 * a_41^2 * a_61 * a_64^2 * b_6 + - 36 * a_41^2 * a_61 * a_64 * a_65 * b_6 + - 18 * a_41^2 * a_62^2 * a_64 * b_6 + - 36 * a_41^2 * a_62 * a_63 * a_64 * b_6 + - 36 * a_41^2 * a_62 * a_64^2 * b_6 + - 36 * a_41^2 * a_62 * a_64 * a_65 * b_6 + - 18 * a_41^2 * a_63^2 * a_64 * b_6 + - 36 * a_41^2 * a_63 * a_64^2 * b_6 + - 36 * a_41^2 * a_63 * a_64 * a_65 * b_6 + - 18 * a_41^2 * a_64^3 * b_6 + - 36 * a_41^2 * a_64^2 * a_65 * b_6 + - 18 * a_41^2 * a_64 * a_65^2 * b_6 + - 36 * a_41 * a_42 * a_51^2 * a_54 * b_5 + - 72 * a_41 * a_42 * a_51 * a_52 * a_54 * b_5 + - 72 * a_41 * a_42 * a_51 * a_53 * a_54 * b_5 + - 72 * a_41 * a_42 * a_51 * a_54^2 * b_5 + - 36 * a_41 * a_42 * a_52^2 * a_54 * b_5 + - 72 * a_41 * a_42 * a_52 * a_53 * a_54 * b_5 + - 72 * a_41 * a_42 * a_52 * a_54^2 * b_5 + - 36 * a_41 * a_42 * a_53^2 * a_54 * b_5 + - 72 * a_41 * a_42 * a_53 * a_54^2 * b_5 + - 36 * a_41 * a_42 * a_54^3 * b_5 + - 36 * a_41 * a_42 * a_61^2 * a_64 * b_6 + - 72 * a_41 * a_42 * a_61 * a_62 * a_64 * b_6 + - 72 * a_41 * a_42 * a_61 * a_63 * a_64 * b_6 + - 72 * a_41 * a_42 * a_61 * a_64^2 * b_6 + - 72 * a_41 * a_42 * a_61 * a_64 * a_65 * b_6 + - 36 * a_41 * a_42 * a_62^2 * a_64 * b_6 + - 72 * a_41 * a_42 * a_62 * a_63 * a_64 * b_6 + - 72 * a_41 * a_42 * a_62 * a_64^2 * b_6 + - 72 * a_41 * a_42 * a_62 * a_64 * a_65 * b_6 + - 36 * a_41 * a_42 * a_63^2 * a_64 * b_6 + - 72 * a_41 * a_42 * a_63 * a_64^2 * b_6 + - 72 * a_41 * a_42 * a_63 * a_64 * a_65 * b_6 + - 36 * a_41 * a_42 * a_64^3 * b_6 + - 72 * a_41 * a_42 * a_64^2 * a_65 * b_6 + - 36 * a_41 * a_42 * a_64 * a_65^2 * b_6 + - 36 * a_41 * a_43 * a_51^2 * a_54 * b_5 + - 72 * a_41 * a_43 * a_51 * a_52 * a_54 * b_5 + - 72 * a_41 * a_43 * a_51 * a_53 * a_54 * b_5 + - 72 * a_41 * a_43 * a_51 * a_54^2 * b_5 + - 36 * a_41 * a_43 * a_52^2 * a_54 * b_5 + - 72 * a_41 * a_43 * a_52 * a_53 * a_54 * b_5 + - 72 * a_41 * a_43 * a_52 * a_54^2 * b_5 + - 36 * a_41 * a_43 * a_53^2 * a_54 * b_5 + - 72 * a_41 * a_43 * a_53 * a_54^2 * b_5 + - 36 * a_41 * a_43 * a_54^3 * b_5 + - 36 * a_41 * a_43 * a_61^2 * a_64 * b_6 + - 72 * a_41 * a_43 * a_61 * a_62 * a_64 * b_6 + - 72 * a_41 * a_43 * a_61 * a_63 * a_64 * b_6 + - 72 * a_41 * a_43 * a_61 * a_64^2 * b_6 + - 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24 * a_21^2 * a_52^2 * a_53 * b_5 + - 24 * a_21^2 * a_52^2 * a_54 * b_5 + - 24 * a_21^2 * a_61 * a_62^2 * b_6 + - 24 * a_21^2 * a_62^3 * b_6 + - 24 * a_21^2 * a_62^2 * a_63 * b_6 + - 24 * a_21^2 * a_62^2 * a_64 * b_6 + - 24 * a_21^2 * a_62^2 * a_65 * b_6 + - 48 * a_21 * a_31 * a_41 * a_42 * a_43 * b_4 + - 48 * a_21 * a_31 * a_42^2 * a_43 * b_4 + - 48 * a_21 * a_31 * a_42 * a_43^2 * b_4 + - 48 * a_21 * a_31 * a_51 * a_52 * a_53 * b_5 + - 48 * a_21 * a_31 * a_52^2 * a_53 * b_5 + - 48 * a_21 * a_31 * a_52 * a_53^2 * b_5 + - 48 * a_21 * a_31 * a_52 * a_53 * a_54 * b_5 + - 48 * a_21 * a_31 * a_61 * a_62 * a_63 * b_6 + - 48 * a_21 * a_31 * a_62^2 * a_63 * b_6 + - 48 * a_21 * a_31 * a_62 * a_63^2 * b_6 + - 48 * a_21 * a_31 * a_62 * a_63 * a_64 * b_6 + - 48 * a_21 * a_31 * a_62 * a_63 * a_65 * b_6 + - 48 * a_21 * a_32 * a_41 * a_42 * a_43 * b_4 + - 48 * a_21 * a_32 * a_42^2 * a_43 * b_4 + - 48 * a_21 * a_32 * a_42 * a_43^2 * b_4 + - 48 * a_21 * a_32 * a_51 * a_52 * a_53 * b_5 + - 48 * a_21 * a_32 * a_52^2 * a_53 * b_5 + - 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48 * a_32 * a_43 * a_63^2 * a_64 * b_6 + - 48 * a_32 * a_43 * a_63 * a_64^2 * b_6 + - 48 * a_32 * a_43 * a_63 * a_64 * a_65 * b_6 + - 48 * a_32 * a_51 * a_61 * a_63 * a_65 * b_6 + - 48 * a_32 * a_51 * a_62 * a_63 * a_65 * b_6 + - 48 * a_32 * a_51 * a_63^2 * a_65 * b_6 + - 48 * a_32 * a_51 * a_63 * a_64 * a_65 * b_6 + - 48 * a_32 * a_51 * a_63 * a_65^2 * b_6 + - 48 * a_32 * a_52 * a_61 * a_63 * a_65 * b_6 + - 48 * a_32 * a_52 * a_62 * a_63 * a_65 * b_6 + - 48 * a_32 * a_52 * a_63^2 * a_65 * b_6 + - 48 * a_32 * a_52 * a_63 * a_64 * a_65 * b_6 + - 48 * a_32 * a_52 * a_63 * a_65^2 * b_6 + - 48 * a_32 * a_53 * a_61 * a_63 * a_65 * b_6 + - 48 * a_32 * a_53 * a_62 * a_63 * a_65 * b_6 + - 48 * a_32 * a_53 * a_63^2 * a_65 * b_6 + - 48 * a_32 * a_53 * a_63 * a_64 * a_65 * b_6 + - 48 * a_32 * a_53 * a_63 * a_65^2 * b_6 + - 48 * a_32 * a_54 * a_61 * a_63 * a_65 * b_6 + - 48 * a_32 * a_54 * a_62 * a_63 * a_65 * b_6 + - 48 * a_32 * a_54 * a_63^2 * a_65 * b_6 + - 48 * a_32 * a_54 * a_63 * a_64 * a_65 * b_6 + - 48 * a_32 * a_54 * a_63 * a_65^2 * b_6 + - 24 * a_41^2 * a_51 * a_54^2 * b_5 + - 24 * a_41^2 * a_52 * a_54^2 * b_5 + - 24 * a_41^2 * a_53 * a_54^2 * b_5 + - 24 * a_41^2 * a_54^3 * b_5 + - 24 * a_41^2 * a_61 * a_64^2 * b_6 + - 24 * a_41^2 * a_62 * a_64^2 * b_6 + - 24 * a_41^2 * a_63 * a_64^2 * b_6 + - 24 * a_41^2 * a_64^3 * b_6 + - 24 * a_41^2 * a_64^2 * a_65 * b_6 + - 48 * a_41 * a_42 * a_51 * a_54^2 * b_5 + - 48 * a_41 * a_42 * a_52 * a_54^2 * b_5 + - 48 * a_41 * a_42 * a_53 * a_54^2 * b_5 + - 48 * a_41 * a_42 * a_54^3 * b_5 + - 48 * a_41 * a_42 * a_61 * a_64^2 * b_6 + - 48 * a_41 * a_42 * a_62 * a_64^2 * b_6 + - 48 * a_41 * a_42 * a_63 * a_64^2 * b_6 + - 48 * a_41 * a_42 * a_64^3 * b_6 + - 48 * a_41 * a_42 * a_64^2 * a_65 * b_6 + - 48 * a_41 * a_43 * a_51 * a_54^2 * b_5 + - 48 * a_41 * a_43 * a_52 * a_54^2 * b_5 + - 48 * a_41 * a_43 * a_53 * a_54^2 * b_5 + - 48 * a_41 * a_43 * a_54^3 * b_5 + - 48 * a_41 * a_43 * a_61 * a_64^2 * b_6 + - 48 * a_41 * a_43 * a_62 * a_64^2 * b_6 + - 48 * a_41 * a_43 * a_63 * a_64^2 * b_6 + - 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72 * a_21 * a_41 * a_42^2 * a_43 * b_4 + - 36 * a_21 * a_41 * a_42 * a_43^2 * b_4 + - 12 * a_21 * a_42^4 * b_4 + - 36 * a_21 * a_42^3 * a_43 * b_4 + - 36 * a_21 * a_42^2 * a_43^2 * b_4 + - 12 * a_21 * a_42 * a_43^3 * b_4 + - 12 * a_21 * a_51^3 * a_52 * b_5 + - 36 * a_21 * a_51^2 * a_52^2 * b_5 + - 36 * a_21 * a_51^2 * a_52 * a_53 * b_5 + - 36 * a_21 * a_51^2 * a_52 * a_54 * b_5 + - 36 * a_21 * a_51 * a_52^3 * b_5 + - 72 * a_21 * a_51 * a_52^2 * a_53 * b_5 + - 72 * a_21 * a_51 * a_52^2 * a_54 * b_5 + - 36 * a_21 * a_51 * a_52 * a_53^2 * b_5 + - 72 * a_21 * a_51 * a_52 * a_53 * a_54 * b_5 + - 36 * a_21 * a_51 * a_52 * a_54^2 * b_5 + - 12 * a_21 * a_52^4 * b_5 + - 36 * a_21 * a_52^3 * a_53 * b_5 + - 36 * a_21 * a_52^3 * a_54 * b_5 + - 36 * a_21 * a_52^2 * a_53^2 * b_5 + - 72 * a_21 * a_52^2 * a_53 * a_54 * b_5 + - 36 * a_21 * a_52^2 * a_54^2 * b_5 + - 12 * a_21 * a_52 * a_53^3 * b_5 + - 36 * a_21 * a_52 * a_53^2 * a_54 * b_5 + - 36 * a_21 * a_52 * a_53 * a_54^2 * b_5 + - 12 * a_21 * a_52 * a_54^3 * b_5 + - 12 * a_21 * a_61^3 * a_62 * b_6 + - 36 * a_21 * a_61^2 * a_62^2 * b_6 + - 36 * a_21 * a_61^2 * a_62 * a_63 * b_6 + - 36 * a_21 * a_61^2 * a_62 * a_64 * b_6 + - 36 * a_21 * a_61^2 * a_62 * a_65 * b_6 + - 36 * a_21 * a_61 * a_62^3 * b_6 + - 72 * a_21 * a_61 * a_62^2 * a_63 * b_6 + - 72 * a_21 * a_61 * a_62^2 * a_64 * b_6 + - 72 * a_21 * a_61 * a_62^2 * a_65 * b_6 + - 36 * a_21 * a_61 * a_62 * a_63^2 * b_6 + - 72 * a_21 * a_61 * a_62 * a_63 * a_64 * b_6 + - 72 * a_21 * a_61 * a_62 * a_63 * a_65 * b_6 + - 36 * a_21 * a_61 * a_62 * a_64^2 * b_6 + - 72 * a_21 * a_61 * a_62 * a_64 * a_65 * b_6 + - 36 * a_21 * a_61 * a_62 * a_65^2 * b_6 + - 12 * a_21 * a_62^4 * b_6 + - 36 * a_21 * a_62^3 * a_63 * b_6 + - 36 * a_21 * a_62^3 * a_64 * b_6 + - 36 * a_21 * a_62^3 * a_65 * b_6 + - 36 * a_21 * a_62^2 * a_63^2 * b_6 + - 72 * a_21 * a_62^2 * a_63 * a_64 * b_6 + - 72 * a_21 * a_62^2 * a_63 * a_65 * b_6 + - 36 * a_21 * a_62^2 * a_64^2 * b_6 + - 72 * a_21 * a_62^2 * a_64 * a_65 * b_6 + - 36 * a_21 * a_62^2 * a_65^2 * b_6 + - 12 * a_21 * a_62 * a_63^3 * b_6 + - 36 * a_21 * a_62 * a_63^2 * a_64 * b_6 + - 36 * a_21 * a_62 * a_63^2 * a_65 * b_6 + - 36 * a_21 * a_62 * a_63 * a_64^2 * b_6 + - 72 * a_21 * a_62 * a_63 * a_64 * a_65 * b_6 + - 36 * a_21 * a_62 * a_63 * a_65^2 * b_6 + - 12 * a_21 * a_62 * a_64^3 * b_6 + - 36 * a_21 * a_62 * a_64^2 * a_65 * b_6 + - 36 * a_21 * a_62 * a_64 * a_65^2 * b_6 + - 12 * a_21 * a_62 * a_65^3 * b_6 + - 12 * a_31 * a_41^3 * a_43 * b_4 + - 36 * a_31 * a_41^2 * a_42 * a_43 * b_4 + - 36 * a_31 * a_41^2 * a_43^2 * b_4 + - 36 * a_31 * a_41 * a_42^2 * a_43 * b_4 + - 72 * a_31 * a_41 * a_42 * a_43^2 * b_4 + - 36 * a_31 * a_41 * a_43^3 * b_4 + - 12 * a_31 * a_42^3 * a_43 * b_4 + - 36 * a_31 * a_42^2 * a_43^2 * b_4 + - 36 * a_31 * a_42 * a_43^3 * b_4 + - 12 * a_31 * a_43^4 * b_4 + - 12 * a_31 * a_51^3 * a_53 * b_5 + - 36 * a_31 * a_51^2 * a_52 * a_53 * b_5 + - 36 * a_31 * a_51^2 * a_53^2 * b_5 + - 36 * a_31 * a_51^2 * a_53 * a_54 * b_5 + - 36 * a_31 * a_51 * a_52^2 * a_53 * b_5 + - 72 * a_31 * a_51 * a_52 * a_53^2 * b_5 + - 72 * a_31 * a_51 * a_52 * a_53 * a_54 * b_5 + - 36 * a_31 * a_51 * a_53^3 * b_5 + - 72 * a_31 * a_51 * a_53^2 * a_54 * b_5 + - 36 * a_31 * a_51 * a_53 * a_54^2 * b_5 + - 12 * a_31 * a_52^3 * a_53 * b_5 + - 36 * a_31 * a_52^2 * a_53^2 * b_5 + - 36 * a_31 * a_52^2 * a_53 * a_54 * b_5 + - 36 * a_31 * a_52 * a_53^3 * b_5 + - 72 * a_31 * a_52 * a_53^2 * a_54 * b_5 + - 36 * a_31 * a_52 * a_53 * a_54^2 * b_5 + - 12 * a_31 * a_53^4 * b_5 + - 36 * a_31 * a_53^3 * a_54 * b_5 + - 36 * a_31 * a_53^2 * a_54^2 * b_5 + - 12 * a_31 * a_53 * a_54^3 * b_5 + - 12 * a_31 * a_61^3 * a_63 * b_6 + - 36 * a_31 * a_61^2 * a_62 * a_63 * b_6 + - 36 * a_31 * a_61^2 * a_63^2 * b_6 + - 36 * a_31 * a_61^2 * a_63 * a_64 * b_6 + - 36 * a_31 * a_61^2 * a_63 * a_65 * b_6 + - 36 * a_31 * a_61 * a_62^2 * a_63 * b_6 + - 72 * a_31 * a_61 * a_62 * a_63^2 * b_6 + - 72 * a_31 * a_61 * a_62 * a_63 * a_64 * b_6 + - 72 * a_31 * a_61 * a_62 * a_63 * a_65 * b_6 + - 36 * a_31 * a_61 * a_63^3 * b_6 + - 72 * a_31 * a_61 * a_63^2 * a_64 * b_6 + - 72 * a_31 * a_61 * a_63^2 * a_65 * b_6 + - 36 * a_31 * a_61 * a_63 * a_64^2 * b_6 + - 72 * a_31 * a_61 * a_63 * a_64 * a_65 * b_6 + - 36 * a_31 * a_61 * a_63 * a_65^2 * b_6 + - 12 * a_31 * a_62^3 * a_63 * b_6 + - 36 * a_31 * a_62^2 * a_63^2 * b_6 + - 36 * a_31 * a_62^2 * a_63 * a_64 * b_6 + - 36 * a_31 * a_62^2 * a_63 * a_65 * b_6 + - 36 * a_31 * a_62 * a_63^3 * b_6 + - 72 * a_31 * a_62 * a_63^2 * a_64 * b_6 + - 72 * a_31 * a_62 * a_63^2 * a_65 * b_6 + - 36 * a_31 * a_62 * a_63 * a_64^2 * b_6 + - 72 * a_31 * a_62 * a_63 * a_64 * a_65 * b_6 + - 36 * a_31 * a_62 * a_63 * a_65^2 * b_6 + - 12 * a_31 * a_63^4 * b_6 + - 36 * a_31 * a_63^3 * a_64 * b_6 + - 36 * a_31 * a_63^3 * a_65 * b_6 + - 36 * a_31 * a_63^2 * a_64^2 * b_6 + - 72 * a_31 * a_63^2 * a_64 * a_65 * b_6 + - 36 * a_31 * a_63^2 * a_65^2 * b_6 + - 12 * a_31 * a_63 * a_64^3 * b_6 + - 36 * a_31 * a_63 * a_64^2 * a_65 * b_6 + - 36 * a_31 * a_63 * a_64 * a_65^2 * b_6 + - 12 * a_31 * a_63 * a_65^3 * b_6 + - 12 * a_32 * a_41^3 * a_43 * b_4 + - 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36 * a_52 * a_61 * a_64^2 * a_65 * b_6 + - 72 * a_52 * a_61 * a_64 * a_65^2 * b_6 + - 36 * a_52 * a_61 * a_65^3 * b_6 + - 12 * a_52 * a_62^3 * a_65 * b_6 + - 36 * a_52 * a_62^2 * a_63 * a_65 * b_6 + - 36 * a_52 * a_62^2 * a_64 * a_65 * b_6 + - 36 * a_52 * a_62^2 * a_65^2 * b_6 + - 36 * a_52 * a_62 * a_63^2 * a_65 * b_6 + - 72 * a_52 * a_62 * a_63 * a_64 * a_65 * b_6 + - 72 * a_52 * a_62 * a_63 * a_65^2 * b_6 + - 36 * a_52 * a_62 * a_64^2 * a_65 * b_6 + - 72 * a_52 * a_62 * a_64 * a_65^2 * b_6 + - 36 * a_52 * a_62 * a_65^3 * b_6 + - 12 * a_52 * a_63^3 * a_65 * b_6 + - 36 * a_52 * a_63^2 * a_64 * a_65 * b_6 + - 36 * a_52 * a_63^2 * a_65^2 * b_6 + - 36 * a_52 * a_63 * a_64^2 * a_65 * b_6 + - 72 * a_52 * a_63 * a_64 * a_65^2 * b_6 + - 36 * a_52 * a_63 * a_65^3 * b_6 + - 12 * a_52 * a_64^3 * a_65 * b_6 + - 36 * a_52 * a_64^2 * a_65^2 * b_6 + - 36 * a_52 * a_64 * a_65^3 * b_6 + - 12 * a_52 * a_65^4 * b_6 + - 12 * a_53 * a_61^3 * a_65 * b_6 + - 36 * a_53 * a_61^2 * a_62 * a_65 * b_6 + - 36 * a_53 * a_61^2 * a_63 * a_65 * b_6 + - 36 * a_53 * a_61^2 * a_64 * a_65 * b_6 + - 36 * a_53 * a_61^2 * a_65^2 * b_6 + - 36 * a_53 * a_61 * a_62^2 * a_65 * b_6 + - 72 * a_53 * a_61 * a_62 * a_63 * a_65 * b_6 + - 72 * a_53 * a_61 * a_62 * a_64 * a_65 * b_6 + - 72 * a_53 * a_61 * a_62 * a_65^2 * b_6 + - 36 * a_53 * a_61 * a_63^2 * a_65 * b_6 + - 72 * a_53 * a_61 * a_63 * a_64 * a_65 * b_6 + - 72 * a_53 * a_61 * a_63 * a_65^2 * b_6 + - 36 * a_53 * a_61 * a_64^2 * a_65 * b_6 + - 72 * a_53 * a_61 * a_64 * a_65^2 * b_6 + - 36 * a_53 * a_61 * a_65^3 * b_6 + - 12 * a_53 * a_62^3 * a_65 * b_6 + - 36 * a_53 * a_62^2 * a_63 * a_65 * b_6 + - 36 * a_53 * a_62^2 * a_64 * a_65 * b_6 + - 36 * a_53 * a_62^2 * a_65^2 * b_6 + - 36 * a_53 * a_62 * a_63^2 * a_65 * b_6 + - 72 * a_53 * a_62 * a_63 * a_64 * a_65 * b_6 + - 72 * a_53 * a_62 * a_63 * a_65^2 * b_6 + - 36 * a_53 * a_62 * a_64^2 * a_65 * b_6 + - 72 * a_53 * a_62 * a_64 * a_65^2 * b_6 + - 36 * a_53 * a_62 * a_65^3 * b_6 + - 12 * a_53 * a_63^3 * a_65 * b_6 + - 36 * a_53 * a_63^2 * a_64 * a_65 * b_6 + - 36 * a_53 * a_63^2 * a_65^2 * b_6 + - 36 * a_53 * a_63 * a_64^2 * a_65 * b_6 + - 72 * a_53 * a_63 * a_64 * a_65^2 * b_6 + - 36 * a_53 * a_63 * a_65^3 * b_6 + - 12 * a_53 * a_64^3 * a_65 * b_6 + - 36 * a_53 * a_64^2 * a_65^2 * b_6 + - 36 * a_53 * a_64 * a_65^3 * b_6 + - 12 * a_53 * a_65^4 * b_6 + - 12 * a_54 * a_61^3 * a_65 * b_6 + - 36 * a_54 * a_61^2 * a_62 * a_65 * b_6 + - 36 * a_54 * a_61^2 * a_63 * a_65 * b_6 + - 36 * a_54 * a_61^2 * a_64 * a_65 * b_6 + - 36 * a_54 * a_61^2 * a_65^2 * b_6 + - 36 * a_54 * a_61 * a_62^2 * a_65 * b_6 + - 72 * a_54 * a_61 * a_62 * a_63 * a_65 * b_6 + - 72 * a_54 * a_61 * a_62 * a_64 * a_65 * b_6 + - 72 * a_54 * a_61 * a_62 * a_65^2 * b_6 + - 36 * a_54 * a_61 * a_63^2 * a_65 * b_6 + - 72 * a_54 * a_61 * a_63 * a_64 * a_65 * b_6 + - 72 * a_54 * a_61 * a_63 * a_65^2 * b_6 + - 36 * a_54 * a_61 * a_64^2 * a_65 * b_6 + - 72 * a_54 * a_61 * a_64 * a_65^2 * b_6 + - 36 * a_54 * a_61 * a_65^3 * b_6 + - 12 * a_54 * a_62^3 * a_65 * b_6 + - 36 * a_54 * a_62^2 * a_63 * a_65 * b_6 + - 36 * a_54 * a_62^2 * a_64 * a_65 * b_6 + - 36 * a_54 * a_62^2 * a_65^2 * b_6 + - 36 * a_54 * a_62 * a_63^2 * a_65 * b_6 + - 72 * a_54 * a_62 * a_63 * a_64 * a_65 * b_6 + - 72 * a_54 * a_62 * a_63 * a_65^2 * b_6 + - 36 * a_54 * a_62 * a_64^2 * a_65 * b_6 + - 72 * a_54 * a_62 * a_64 * a_65^2 * b_6 + - 36 * a_54 * a_62 * a_65^3 * b_6 + - 12 * a_54 * a_63^3 * a_65 * b_6 + - 36 * a_54 * a_63^2 * a_64 * a_65 * b_6 + - 36 * a_54 * a_63^2 * a_65^2 * b_6 + - 36 * a_54 * a_63 * a_64^2 * a_65 * b_6 + - 72 * a_54 * a_63 * a_64 * a_65^2 * b_6 + - 36 * a_54 * a_63 * a_65^3 * b_6 + - 12 * a_54 * a_64^3 * a_65 * b_6 + - 36 * a_54 * a_64^2 * a_65^2 * b_6 + - 36 * a_54 * a_64 * a_65^3 * b_6 + - 12 * a_54 * a_65^4 * b_6 - 1, - 6 * a_21^5 * b_2 + - 6 * a_31^5 * b_3 + - 30 * a_31^4 * a_32 * b_3 + - 60 * a_31^3 * a_32^2 * b_3 + - 60 * a_31^2 * a_32^3 * b_3 + - 30 * a_31 * a_32^4 * b_3 + - 6 * a_32^5 * b_3 + - 6 * a_41^5 * b_4 + - 30 * a_41^4 * a_42 * b_4 + - 30 * a_41^4 * a_43 * b_4 + - 60 * a_41^3 * a_42^2 * b_4 + - 120 * a_41^3 * a_42 * a_43 * b_4 + - 60 * a_41^3 * a_43^2 * b_4 + - 60 * a_41^2 * a_42^3 * b_4 + - 180 * a_41^2 * a_42^2 * a_43 * b_4 + - 180 * a_41^2 * a_42 * a_43^2 * b_4 + - 60 * a_41^2 * a_43^3 * b_4 + - 30 * a_41 * a_42^4 * b_4 + - 120 * a_41 * a_42^3 * a_43 * b_4 + - 180 * a_41 * a_42^2 * a_43^2 * b_4 + - 120 * a_41 * a_42 * a_43^3 * b_4 + - 30 * a_41 * a_43^4 * b_4 + - 6 * a_42^5 * b_4 + - 30 * a_42^4 * a_43 * b_4 + - 60 * a_42^3 * a_43^2 * b_4 + - 60 * a_42^2 * a_43^3 * b_4 + - 30 * a_42 * a_43^4 * b_4 + - 6 * a_43^5 * b_4 + - 6 * a_51^5 * b_5 + - 30 * a_51^4 * a_52 * b_5 + - 30 * a_51^4 * a_53 * b_5 + - 30 * a_51^4 * a_54 * b_5 + - 60 * a_51^3 * a_52^2 * b_5 + - 120 * a_51^3 * a_52 * a_53 * b_5 + - 120 * a_51^3 * a_52 * a_54 * b_5 + - 60 * a_51^3 * a_53^2 * b_5 + - 120 * a_51^3 * a_53 * a_54 * b_5 + - 60 * a_51^3 * a_54^2 * b_5 + - 60 * a_51^2 * a_52^3 * b_5 + - 180 * a_51^2 * a_52^2 * a_53 * b_5 + - 180 * a_51^2 * a_52^2 * a_54 * b_5 + - 180 * a_51^2 * a_52 * a_53^2 * b_5 + - 360 * a_51^2 * a_52 * a_53 * a_54 * b_5 + - 180 * a_51^2 * a_52 * a_54^2 * b_5 + - 60 * a_51^2 * a_53^3 * b_5 + - 180 * a_51^2 * a_53^2 * a_54 * b_5 + - 180 * a_51^2 * a_53 * a_54^2 * b_5 + - 60 * a_51^2 * a_54^3 * b_5 + - 30 * a_51 * a_52^4 * b_5 + - 120 * a_51 * a_52^3 * a_53 * b_5 + - 120 * a_51 * a_52^3 * a_54 * b_5 + - 180 * a_51 * a_52^2 * a_53^2 * b_5 + - 360 * a_51 * a_52^2 * a_53 * a_54 * b_5 + - 180 * a_51 * a_52^2 * a_54^2 * b_5 + - 120 * a_51 * a_52 * a_53^3 * b_5 + - 360 * a_51 * a_52 * a_53^2 * a_54 * b_5 + - 360 * a_51 * a_52 * a_53 * a_54^2 * b_5 + - 120 * a_51 * a_52 * a_54^3 * b_5 + - 30 * a_51 * a_53^4 * b_5 + - 120 * a_51 * a_53^3 * a_54 * b_5 + - 180 * a_51 * a_53^2 * a_54^2 * b_5 + - 120 * a_51 * a_53 * a_54^3 * b_5 + - 30 * a_51 * a_54^4 * b_5 + - 6 * a_52^5 * b_5 + - 30 * a_52^4 * a_53 * b_5 + - 30 * a_52^4 * a_54 * b_5 + - 60 * a_52^3 * a_53^2 * b_5 + - 120 * a_52^3 * a_53 * a_54 * b_5 + - 60 * a_52^3 * a_54^2 * b_5 + - 60 * a_52^2 * a_53^3 * b_5 + - 180 * a_52^2 * a_53^2 * a_54 * b_5 + - 180 * a_52^2 * a_53 * a_54^2 * b_5 + - 60 * a_52^2 * a_54^3 * b_5 + - 30 * a_52 * a_53^4 * b_5 + - 120 * a_52 * a_53^3 * a_54 * b_5 + - 180 * a_52 * a_53^2 * a_54^2 * b_5 + - 120 * a_52 * a_53 * a_54^3 * b_5 + - 30 * a_52 * a_54^4 * b_5 + - 6 * a_53^5 * b_5 + - 30 * a_53^4 * a_54 * b_5 + - 60 * a_53^3 * a_54^2 * b_5 + - 60 * a_53^2 * a_54^3 * b_5 + - 30 * a_53 * a_54^4 * b_5 + - 6 * a_54^5 * b_5 + - 6 * a_61^5 * b_6 + - 30 * a_61^4 * a_62 * b_6 + - 30 * a_61^4 * a_63 * b_6 + - 30 * a_61^4 * a_64 * b_6 + - 30 * a_61^4 * a_65 * b_6 + - 60 * a_61^3 * a_62^2 * b_6 + - 120 * a_61^3 * a_62 * a_63 * b_6 + - 120 * a_61^3 * a_62 * a_64 * b_6 + - 120 * a_61^3 * a_62 * a_65 * b_6 + - 60 * a_61^3 * a_63^2 * b_6 + - 120 * a_61^3 * a_63 * a_64 * b_6 + - 120 * a_61^3 * a_63 * a_65 * b_6 + - 60 * a_61^3 * a_64^2 * b_6 + - 120 * a_61^3 * a_64 * a_65 * b_6 + - 60 * a_61^3 * a_65^2 * b_6 + - 60 * a_61^2 * a_62^3 * b_6 + - 180 * a_61^2 * a_62^2 * a_63 * b_6 + - 180 * a_61^2 * a_62^2 * a_64 * b_6 + - 180 * a_61^2 * a_62^2 * a_65 * b_6 + - 180 * a_61^2 * a_62 * a_63^2 * b_6 + - 360 * a_61^2 * a_62 * a_63 * a_64 * b_6 + - 360 * a_61^2 * a_62 * a_63 * a_65 * b_6 + - 180 * a_61^2 * a_62 * a_64^2 * b_6 + - 360 * a_61^2 * a_62 * a_64 * a_65 * b_6 + - 180 * a_61^2 * a_62 * a_65^2 * b_6 + - 60 * a_61^2 * a_63^3 * b_6 + - 180 * a_61^2 * a_63^2 * a_64 * b_6 + - 180 * a_61^2 * a_63^2 * a_65 * b_6 + - 180 * a_61^2 * a_63 * a_64^2 * b_6 + - 360 * a_61^2 * a_63 * a_64 * a_65 * b_6 + - 180 * a_61^2 * a_63 * a_65^2 * b_6 + - 60 * a_61^2 * a_64^3 * b_6 + - 180 * a_61^2 * a_64^2 * a_65 * b_6 + - 180 * a_61^2 * a_64 * a_65^2 * b_6 + - 60 * a_61^2 * a_65^3 * b_6 + - 30 * a_61 * a_62^4 * b_6 + - 120 * a_61 * a_62^3 * a_63 * b_6 + - 120 * a_61 * a_62^3 * a_64 * b_6 + - 120 * a_61 * a_62^3 * a_65 * b_6 + - 180 * a_61 * a_62^2 * a_63^2 * b_6 + - 360 * a_61 * a_62^2 * a_63 * a_64 * b_6 + - 360 * a_61 * a_62^2 * a_63 * a_65 * b_6 + - 180 * a_61 * a_62^2 * a_64^2 * b_6 + - 360 * a_61 * a_62^2 * a_64 * a_65 * b_6 + - 180 * a_61 * a_62^2 * a_65^2 * b_6 + - 120 * a_61 * a_62 * a_63^3 * b_6 + - 360 * a_61 * a_62 * a_63^2 * a_64 * b_6 + - 360 * a_61 * a_62 * a_63^2 * a_65 * b_6 + - 360 * a_61 * a_62 * a_63 * a_64^2 * b_6 + - 720 * a_61 * a_62 * a_63 * a_64 * a_65 * b_6 + - 360 * a_61 * a_62 * a_63 * a_65^2 * b_6 + - 120 * a_61 * a_62 * a_64^3 * b_6 + - 360 * a_61 * a_62 * a_64^2 * a_65 * b_6 + - 360 * a_61 * a_62 * a_64 * a_65^2 * b_6 + - 120 * a_61 * a_62 * a_65^3 * b_6 + - 30 * a_61 * a_63^4 * b_6 + - 120 * a_61 * a_63^3 * a_64 * b_6 + - 120 * a_61 * a_63^3 * a_65 * b_6 + - 180 * a_61 * a_63^2 * a_64^2 * b_6 + - 360 * a_61 * a_63^2 * a_64 * a_65 * b_6 + - 180 * a_61 * a_63^2 * a_65^2 * b_6 + - 120 * a_61 * a_63 * a_64^3 * b_6 + - 360 * a_61 * a_63 * a_64^2 * a_65 * b_6 + - 360 * a_61 * a_63 * a_64 * a_65^2 * b_6 + - 120 * a_61 * a_63 * a_65^3 * b_6 + - 30 * a_61 * a_64^4 * b_6 + - 120 * a_61 * a_64^3 * a_65 * b_6 + - 180 * a_61 * a_64^2 * a_65^2 * b_6 + - 120 * a_61 * a_64 * a_65^3 * b_6 + - 30 * a_61 * a_65^4 * b_6 + - 6 * a_62^5 * b_6 + - 30 * a_62^4 * a_63 * b_6 + - 30 * a_62^4 * a_64 * b_6 + - 30 * a_62^4 * a_65 * b_6 + - 60 * a_62^3 * a_63^2 * b_6 + - 120 * a_62^3 * a_63 * a_64 * b_6 + - 120 * a_62^3 * a_63 * a_65 * b_6 + - 60 * a_62^3 * a_64^2 * b_6 + - 120 * a_62^3 * a_64 * a_65 * b_6 + - 60 * a_62^3 * a_65^2 * b_6 + - 60 * a_62^2 * a_63^3 * b_6 + - 180 * a_62^2 * a_63^2 * a_64 * b_6 + - 180 * a_62^2 * a_63^2 * a_65 * b_6 + - 180 * a_62^2 * a_63 * a_64^2 * b_6 + - 360 * a_62^2 * a_63 * a_64 * a_65 * b_6 + - 180 * a_62^2 * a_63 * a_65^2 * b_6 + - 60 * a_62^2 * a_64^3 * b_6 + - 180 * a_62^2 * a_64^2 * a_65 * b_6 + - 180 * a_62^2 * a_64 * a_65^2 * b_6 + - 60 * a_62^2 * a_65^3 * b_6 + - 30 * a_62 * a_63^4 * b_6 + - 120 * a_62 * a_63^3 * a_64 * b_6 + - 120 * a_62 * a_63^3 * a_65 * b_6 + - 180 * a_62 * a_63^2 * a_64^2 * b_6 + - 360 * a_62 * a_63^2 * a_64 * a_65 * b_6 + - 180 * a_62 * a_63^2 * a_65^2 * b_6 + - 120 * a_62 * a_63 * a_64^3 * b_6 + - 360 * a_62 * a_63 * a_64^2 * a_65 * b_6 + - 360 * a_62 * a_63 * a_64 * a_65^2 * b_6 + - 120 * a_62 * a_63 * a_65^3 * b_6 + - 30 * a_62 * a_64^4 * b_6 + - 120 * a_62 * a_64^3 * a_65 * b_6 + - 180 * a_62 * a_64^2 * a_65^2 * b_6 + - 120 * a_62 * a_64 * a_65^3 * b_6 + - 30 * a_62 * a_65^4 * b_6 + - 6 * a_63^5 * b_6 + - 30 * a_63^4 * a_64 * b_6 + - 30 * a_63^4 * a_65 * b_6 + - 60 * a_63^3 * a_64^2 * b_6 + - 120 * a_63^3 * a_64 * a_65 * b_6 + - 60 * a_63^3 * a_65^2 * b_6 + - 60 * a_63^2 * a_64^3 * b_6 + - 180 * a_63^2 * a_64^2 * a_65 * b_6 + - 180 * a_63^2 * a_64 * a_65^2 * b_6 + - 60 * a_63^2 * a_65^3 * b_6 + - 30 * a_63 * a_64^4 * b_6 + - 120 * a_63 * a_64^3 * a_65 * b_6 + - 180 * a_63 * a_64^2 * a_65^2 * b_6 + - 120 * a_63 * a_64 * a_65^3 * b_6 + - 30 * a_63 * a_65^4 * b_6 + - 6 * a_64^5 * b_6 + - 30 * a_64^4 * a_65 * b_6 + - 60 * a_64^3 * a_65^2 * b_6 + - 60 * a_64^2 * a_65^3 * b_6 + - 30 * a_64 * a_65^4 * b_6 + - 6 * a_65^5 * b_6 - 1 -] diff --git a/benchmark/scripts/runge-kutta/runge-kutta-8-7.jl b/benchmark/scripts/runge-kutta/runge-kutta-8-7.jl deleted file mode 100644 index 71f51292..00000000 --- a/benchmark/scripts/runge-kutta/runge-kutta-8-7.jl +++ /dev/null @@ -1,3716 +0,0 @@ -@polyvar a_21 a_31 a_32 a_41 a_42 a_43 a_51 a_52 a_53 a_54 a_61 a_62 a_63 a_64 a_65 a_71 a_72 a_73 a_74 a_75 a_76 a_81 a_82 a_83 a_84 a_85 a_86 a_87 b_1 b_2 b_3 b_4 b_5 b_6 b_7 b_8 - -system = [ - b_1 + b_2 + b_3 + b_4 + b_5 + b_6 + b_7 + b_8 - 1, - 2 * a_21 * b_2 + - 2 * b_3 * (a_31 + a_32) + - 2 * b_4 * (a_41 + a_42 + a_43) + - 2 * b_5 * (a_51 + a_52 + a_53 + a_54) + - 2 * b_6 * (a_61 + a_62 + a_63 + a_64 + a_65) + - 2 * b_7 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) + - 2 * b_8 * (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87) - 1, - 6 * a_21 * a_32 * b_3 + - 6 * b_4 * (a_21 * a_42 + a_43 * (a_31 + a_32)) + - 6 * b_5 * (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) + - 6 * - b_6 * - ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - ) + - 6 * - b_7 * - ( - a_21 * a_72 + - a_73 * (a_31 + a_32) + - a_74 * (a_41 + a_42 + a_43) + - a_75 * (a_51 + a_52 + a_53 + a_54) + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65) - ) + - 6 * - b_8 * - ( - a_21 * a_82 + - a_83 * (a_31 + a_32) + - a_84 * (a_41 + a_42 + a_43) + - a_85 * (a_51 + a_52 + a_53 + a_54) + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65) + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) - ) - 1, - 3 * a_21^2 * b_2 + - 3 * b_3 * (a_31 + a_32)^2 + - 3 * b_4 * (a_41 + a_42 + a_43)^2 + - 3 * b_5 * (a_51 + a_52 + a_53 + a_54)^2 + - 3 * b_6 * (a_61 + a_62 + a_63 + a_64 + a_65)^2 + - 3 * b_7 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2 + - 3 * b_8 * (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^2 - 1, - 24 * a_21 * a_32 * a_43 * b_4 + - 24 * b_5 * (a_21 * a_32 * a_53 + a_54 * (a_21 * a_42 + a_43 * (a_31 + a_32))) + - 24 * - b_6 * - ( - a_21 * a_32 * a_63 + - a_64 * (a_21 * a_42 + a_43 * (a_31 + a_32)) + - a_65 * (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) - ) + - 24 * - b_7 * - ( - a_21 * a_32 * a_73 + - a_74 * (a_21 * a_42 + a_43 * (a_31 + a_32)) + - a_75 * (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) + - a_76 * ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - ) - ) + - 24 * - b_8 * - ( - a_21 * a_32 * a_83 + - a_84 * (a_21 * a_42 + a_43 * (a_31 + a_32)) + - a_85 * (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) + - a_86 * ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - ) + - a_87 * ( - a_21 * a_72 + - a_73 * (a_31 + a_32) + - a_74 * (a_41 + a_42 + a_43) + - a_75 * (a_51 + a_52 + a_53 + a_54) + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65) - ) - ) - 1, - 12 * a_21^2 * a_32 * b_3 + - 12 * b_4 * (a_21^2 * a_42 + a_43 * (a_31 + a_32)^2) + - 12 * b_5 * (a_21^2 * a_52 + a_53 * (a_31 + a_32)^2 + a_54 * (a_41 + a_42 + a_43)^2) + - 12 * - b_6 * - ( - a_21^2 * a_62 + - a_63 * (a_31 + a_32)^2 + - a_64 * (a_41 + a_42 + a_43)^2 + - a_65 * (a_51 + a_52 + a_53 + a_54)^2 - ) + - 12 * - b_7 * - ( - a_21^2 * a_72 + - a_73 * (a_31 + a_32)^2 + - a_74 * (a_41 + a_42 + a_43)^2 + - a_75 * (a_51 + a_52 + a_53 + a_54)^2 + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65)^2 - ) + - 12 * - b_8 * - ( - a_21^2 * a_82 + - a_83 * (a_31 + a_32)^2 + - a_84 * (a_41 + a_42 + a_43)^2 + - a_85 * (a_51 + a_52 + a_53 + a_54)^2 + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65)^2 + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2 - ) - 1, - 8 * a_21 * a_32 * b_3 * (a_31 + a_32) + - 8 * b_4 * (a_21 * a_42 + a_43 * (a_31 + a_32)) * (a_41 + a_42 + a_43) + - 8 * - b_5 * - (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) * - (a_51 + a_52 + a_53 + a_54) + - 8 * - b_6 * - ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - ) * - (a_61 + a_62 + a_63 + a_64 + a_65) + - 8 * - b_7 * - ( - a_21 * a_72 + - a_73 * (a_31 + a_32) + - a_74 * (a_41 + a_42 + a_43) + - a_75 * (a_51 + a_52 + a_53 + a_54) + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65) - ) * - (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) + - 8 * - b_8 * - ( - a_21 * a_82 + - a_83 * (a_31 + a_32) + - a_84 * (a_41 + a_42 + a_43) + - a_85 * (a_51 + a_52 + a_53 + a_54) + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65) + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) - ) * - (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87) - 1, - 4 * a_21^3 * b_2 + - 4 * b_3 * (a_31 + a_32)^3 + - 4 * b_4 * (a_41 + a_42 + a_43)^3 + - 4 * b_5 * (a_51 + a_52 + a_53 + a_54)^3 + - 4 * b_6 * (a_61 + a_62 + a_63 + a_64 + a_65)^3 + - 4 * b_7 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^3 + - 4 * b_8 * (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^3 - 1, - 120 * a_21 * a_32 * a_43 * a_54 * b_5 + - 120 * - b_6 * - ( - a_21 * a_32 * a_43 * a_64 + - a_65 * (a_21 * a_32 * a_53 + a_54 * (a_21 * a_42 + a_43 * (a_31 + a_32))) - ) + - 120 * - b_7 * - ( - a_21 * a_32 * a_43 * a_74 + - a_75 * (a_21 * a_32 * a_53 + a_54 * (a_21 * a_42 + a_43 * (a_31 + a_32))) + - a_76 * ( - a_21 * a_32 * a_63 + - a_64 * (a_21 * a_42 + a_43 * (a_31 + a_32)) + - a_65 * (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) - ) - ) + - 120 * - b_8 * - ( - a_21 * a_32 * a_43 * a_84 + - a_85 * (a_21 * a_32 * a_53 + a_54 * (a_21 * a_42 + a_43 * (a_31 + a_32))) + - a_86 * ( - a_21 * a_32 * a_63 + - a_64 * (a_21 * a_42 + a_43 * (a_31 + a_32)) + - a_65 * (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) - ) + - a_87 * ( - a_21 * a_32 * a_73 + - a_74 * (a_21 * a_42 + a_43 * (a_31 + a_32)) + - a_75 * (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) + - a_76 * ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - ) - ) - ) - 1, - 60 * a_21^2 * a_32 * a_43 * b_4 + - 60 * b_5 * (a_21^2 * a_32 * a_53 + a_54 * (a_21^2 * a_42 + a_43 * (a_31 + a_32)^2)) + - 60 * - b_6 * - ( - a_21^2 * a_32 * a_63 + - a_64 * (a_21^2 * a_42 + a_43 * (a_31 + a_32)^2) + - a_65 * (a_21^2 * a_52 + a_53 * (a_31 + a_32)^2 + a_54 * (a_41 + a_42 + a_43)^2) - ) + - 60 * - b_7 * - ( - a_21^2 * a_32 * a_73 + - a_74 * (a_21^2 * a_42 + a_43 * (a_31 + a_32)^2) + - a_75 * (a_21^2 * a_52 + a_53 * (a_31 + a_32)^2 + a_54 * (a_41 + a_42 + a_43)^2) + - a_76 * ( - a_21^2 * a_62 + - a_63 * (a_31 + a_32)^2 + - a_64 * (a_41 + a_42 + a_43)^2 + - a_65 * (a_51 + a_52 + a_53 + a_54)^2 - ) - ) + - 60 * - b_8 * - ( - a_21^2 * a_32 * a_83 + - a_84 * (a_21^2 * a_42 + a_43 * (a_31 + a_32)^2) + - a_85 * (a_21^2 * a_52 + a_53 * (a_31 + a_32)^2 + a_54 * (a_41 + a_42 + a_43)^2) + - a_86 * ( - a_21^2 * a_62 + - a_63 * (a_31 + a_32)^2 + - a_64 * (a_41 + a_42 + a_43)^2 + - a_65 * (a_51 + a_52 + a_53 + a_54)^2 - ) + - a_87 * ( - a_21^2 * a_72 + - a_73 * (a_31 + a_32)^2 + - a_74 * (a_41 + a_42 + a_43)^2 + - a_75 * (a_51 + a_52 + a_53 + a_54)^2 + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65)^2 - ) - ) - 1, - 40 * a_21 * a_32 * a_43 * b_4 * (a_31 + a_32) + - 40 * - b_5 * - ( - a_21 * a_32 * a_53 * (a_31 + a_32) + - a_54 * (a_21 * a_42 + a_43 * (a_31 + a_32)) * (a_41 + a_42 + a_43) - ) + - 40 * - b_6 * - ( - a_21 * a_32 * a_63 * (a_31 + a_32) + - a_64 * (a_21 * a_42 + a_43 * (a_31 + a_32)) * (a_41 + a_42 + a_43) + - a_65 * - (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) * - (a_51 + a_52 + a_53 + a_54) - ) + - 40 * - b_7 * - ( - a_21 * a_32 * a_73 * (a_31 + a_32) + - a_74 * (a_21 * a_42 + a_43 * (a_31 + a_32)) * (a_41 + a_42 + a_43) + - a_75 * - (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) * - (a_51 + a_52 + a_53 + a_54) + - a_76 * - ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - ) * - (a_61 + a_62 + a_63 + a_64 + a_65) - ) + - 40 * - b_8 * - ( - a_21 * a_32 * a_83 * (a_31 + a_32) + - a_84 * (a_21 * a_42 + a_43 * (a_31 + a_32)) * (a_41 + a_42 + a_43) + - a_85 * - (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) * - (a_51 + a_52 + a_53 + a_54) + - a_86 * - ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - ) * - (a_61 + a_62 + a_63 + a_64 + a_65) + - a_87 * - ( - a_21 * a_72 + - a_73 * (a_31 + a_32) + - a_74 * (a_41 + a_42 + a_43) + - a_75 * (a_51 + a_52 + a_53 + a_54) + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65) - ) * - (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) - ) - 1, - 30 * a_21 * a_32 * a_43 * b_4 * (a_41 + a_42 + a_43) + - 30 * - b_5 * - (a_21 * a_32 * a_53 + a_54 * (a_21 * a_42 + a_43 * (a_31 + a_32))) * - (a_51 + a_52 + a_53 + a_54) + - 30 * - b_6 * - ( - a_21 * a_32 * a_63 + - a_64 * (a_21 * a_42 + a_43 * (a_31 + a_32)) + - a_65 * (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) - ) * - (a_61 + a_62 + a_63 + a_64 + a_65) + - 30 * - b_7 * - ( - a_21 * a_32 * a_73 + - a_74 * (a_21 * a_42 + a_43 * (a_31 + a_32)) + - a_75 * (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) + - a_76 * ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - ) - ) * - (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) + - 30 * - b_8 * - ( - a_21 * a_32 * a_83 + - a_84 * (a_21 * a_42 + a_43 * (a_31 + a_32)) + - a_85 * (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) + - a_86 * ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - ) + - a_87 * ( - a_21 * a_72 + - a_73 * (a_31 + a_32) + - a_74 * (a_41 + a_42 + a_43) + - a_75 * (a_51 + a_52 + a_53 + a_54) + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65) - ) - ) * - (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87) - 1, - 20 * a_21^3 * a_32 * b_3 + - 20 * b_4 * (a_21^3 * a_42 + a_43 * (a_31 + a_32)^3) + - 20 * b_5 * (a_21^3 * a_52 + a_53 * (a_31 + a_32)^3 + a_54 * (a_41 + a_42 + a_43)^3) + - 20 * - b_6 * - ( - a_21^3 * a_62 + - a_63 * (a_31 + a_32)^3 + - a_64 * (a_41 + a_42 + a_43)^3 + - a_65 * (a_51 + a_52 + a_53 + a_54)^3 - ) + - 20 * - b_7 * - ( - a_21^3 * a_72 + - a_73 * (a_31 + a_32)^3 + - a_74 * (a_41 + a_42 + a_43)^3 + - a_75 * (a_51 + a_52 + a_53 + a_54)^3 + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65)^3 - ) + - 20 * - b_8 * - ( - a_21^3 * a_82 + - a_83 * (a_31 + a_32)^3 + - a_84 * (a_41 + a_42 + a_43)^3 + - a_85 * (a_51 + a_52 + a_53 + a_54)^3 + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65)^3 + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^3 - ) - 1, - 15 * a_21^2 * a_32 * b_3 * (a_31 + a_32) + - 15 * b_4 * (a_21^2 * a_42 + a_43 * (a_31 + a_32)^2) * (a_41 + a_42 + a_43) + - 15 * - b_5 * - (a_21^2 * a_52 + a_53 * (a_31 + a_32)^2 + a_54 * (a_41 + a_42 + a_43)^2) * - (a_51 + a_52 + a_53 + a_54) + - 15 * - b_6 * - ( - a_21^2 * a_62 + - a_63 * (a_31 + a_32)^2 + - a_64 * (a_41 + a_42 + a_43)^2 + - a_65 * (a_51 + a_52 + a_53 + a_54)^2 - ) * - (a_61 + a_62 + a_63 + a_64 + a_65) + - 15 * - b_7 * - ( - a_21^2 * a_72 + - a_73 * (a_31 + a_32)^2 + - a_74 * (a_41 + a_42 + a_43)^2 + - a_75 * (a_51 + a_52 + a_53 + a_54)^2 + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65)^2 - ) * - (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) + - 15 * - b_8 * - ( - a_21^2 * a_82 + - a_83 * (a_31 + a_32)^2 + - a_84 * (a_41 + a_42 + a_43)^2 + - a_85 * (a_51 + a_52 + a_53 + a_54)^2 + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65)^2 + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2 - ) * - (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87) - 1, - 20 * a_21^2 * a_32^2 * b_3 + - 20 * b_4 * (a_21 * a_42 + a_43 * (a_31 + a_32))^2 + - 20 * b_5 * (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43))^2 + - 20 * - b_6 * - ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - )^2 + - 20 * - b_7 * - ( - a_21 * a_72 + - a_73 * (a_31 + a_32) + - a_74 * (a_41 + a_42 + a_43) + - a_75 * (a_51 + a_52 + a_53 + a_54) + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65) - )^2 + - 20 * - b_8 * - ( - a_21 * a_82 + - a_83 * (a_31 + a_32) + - a_84 * (a_41 + a_42 + a_43) + - a_85 * (a_51 + a_52 + a_53 + a_54) + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65) + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) - )^2 - 1, - 10 * a_21 * a_32 * b_3 * (a_31 + a_32)^2 + - 10 * b_4 * (a_21 * a_42 + a_43 * (a_31 + a_32)) * (a_41 + a_42 + a_43)^2 + - 10 * - b_5 * - (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) * - (a_51 + a_52 + a_53 + a_54)^2 + - 10 * - b_6 * - ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - ) * - (a_61 + a_62 + a_63 + a_64 + a_65)^2 + - 10 * - b_7 * - ( - a_21 * a_72 + - a_73 * (a_31 + a_32) + - a_74 * (a_41 + a_42 + a_43) + - a_75 * (a_51 + a_52 + a_53 + a_54) + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65) - ) * - (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2 + - 10 * - b_8 * - ( - a_21 * a_82 + - a_83 * (a_31 + a_32) + - a_84 * (a_41 + a_42 + a_43) + - a_85 * (a_51 + a_52 + a_53 + a_54) + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65) + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) - ) * - (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^2 - 1, - 5 * a_21^4 * b_2 + - 5 * b_3 * (a_31 + a_32)^4 + - 5 * b_4 * (a_41 + a_42 + a_43)^4 + - 5 * b_5 * (a_51 + a_52 + a_53 + a_54)^4 + - 5 * b_6 * (a_61 + a_62 + a_63 + a_64 + a_65)^4 + - 5 * b_7 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^4 + - 5 * b_8 * (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^4 - 1, - 720 * a_21 * a_32 * a_43 * a_54 * a_65 * b_6 + - 720 * - b_7 * - ( - a_21 * a_32 * a_43 * a_54 * a_75 + - a_76 * ( - a_21 * a_32 * a_43 * a_64 + - a_65 * (a_21 * a_32 * a_53 + a_54 * (a_21 * a_42 + a_43 * (a_31 + a_32))) - ) - ) + - 720 * - b_8 * - ( - a_21 * a_32 * a_43 * a_54 * a_85 + - a_86 * ( - 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) * - (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) + - 35 * - b_8 * - ( - a_21^4 * a_82 + - a_83 * (a_31 + a_32)^4 + - a_84 * (a_41 + a_42 + a_43)^4 + - a_85 * (a_51 + a_52 + a_53 + a_54)^4 + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65)^4 + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^4 - ) * - (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87) - 1, - 56 * a_21^4 * a_32^2 * b_3 + - 56 * b_4 * (a_21 * a_42 + a_43 * (a_31 + a_32)) * (a_21^3 * a_42 + a_43 * (a_31 + a_32)^3) + - 56 * - b_5 * - (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) * - (a_21^3 * a_52 + a_53 * (a_31 + a_32)^3 + a_54 * (a_41 + a_42 + a_43)^3) + - 56 * - b_6 * - ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - ) * - ( - a_21^3 * a_62 + - a_63 * (a_31 + a_32)^3 + - a_64 * (a_41 + a_42 + a_43)^3 + - a_65 * (a_51 + a_52 + a_53 + a_54)^3 - ) + - 56 * - b_7 * - ( - a_21 * a_72 + - a_73 * (a_31 + a_32) + - a_74 * (a_41 + a_42 + a_43) + - a_75 * (a_51 + a_52 + a_53 + a_54) + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65) - ) * - ( - a_21^3 * a_72 + - a_73 * (a_31 + a_32)^3 + - a_74 * (a_41 + a_42 + a_43)^3 + - a_75 * (a_51 + a_52 + a_53 + a_54)^3 + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65)^3 - ) + - 56 * - b_8 * - ( - a_21 * a_82 + - a_83 * (a_31 + a_32) + - a_84 * (a_41 + a_42 + a_43) + - a_85 * (a_51 + a_52 + a_53 + a_54) + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65) + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) - ) * - ( - a_21^3 * a_82 + - a_83 * (a_31 + a_32)^3 + - a_84 * (a_41 + a_42 + a_43)^3 + - a_85 * (a_51 + a_52 + a_53 + a_54)^3 + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65)^3 + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^3 - ) - 1, - 28 * a_21^3 * a_32 * b_3 * (a_31 + a_32)^2 + - 28 * b_4 * (a_21^3 * a_42 + a_43 * (a_31 + a_32)^3) * (a_41 + a_42 + a_43)^2 + - 28 * - b_5 * - (a_21^3 * a_52 + a_53 * (a_31 + a_32)^3 + a_54 * (a_41 + a_42 + a_43)^3) * - (a_51 + a_52 + a_53 + a_54)^2 + - 28 * - b_6 * - ( - a_21^3 * a_62 + - a_63 * (a_31 + a_32)^3 + - a_64 * (a_41 + a_42 + a_43)^3 + - a_65 * (a_51 + a_52 + a_53 + a_54)^3 - ) * - (a_61 + a_62 + a_63 + a_64 + a_65)^2 + - 28 * - b_7 * - ( - a_21^3 * a_72 + - a_73 * (a_31 + a_32)^3 + - a_74 * (a_41 + a_42 + a_43)^3 + - a_75 * (a_51 + a_52 + a_53 + a_54)^3 + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65)^3 - ) * - (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2 + - 28 * - b_8 * - ( - a_21^3 * a_82 + - a_83 * (a_31 + a_32)^3 + - a_84 * (a_41 + a_42 + a_43)^3 + - a_85 * (a_51 + a_52 + a_53 + a_54)^3 + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65)^3 + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^3 - ) * - (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^2 - 1, - 63 * a_21^4 * a_32^2 * b_3 + - 63 * b_4 * (a_21^2 * a_42 + a_43 * (a_31 + a_32)^2)^2 + - 63 * b_5 * (a_21^2 * a_52 + a_53 * (a_31 + a_32)^2 + a_54 * (a_41 + a_42 + a_43)^2)^2 + - 63 * - b_6 * - ( - a_21^2 * a_62 + - a_63 * (a_31 + a_32)^2 + - a_64 * (a_41 + a_42 + a_43)^2 + - a_65 * (a_51 + a_52 + a_53 + a_54)^2 - )^2 + - 63 * - b_7 * - ( - a_21^2 * a_72 + - a_73 * (a_31 + a_32)^2 + - a_74 * (a_41 + a_42 + a_43)^2 + - a_75 * (a_51 + a_52 + a_53 + a_54)^2 + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65)^2 - )^2 + - 63 * - b_8 * - ( - a_21^2 * a_82 + - a_83 * (a_31 + a_32)^2 + - a_84 * (a_41 + a_42 + a_43)^2 + - a_85 * (a_51 + a_52 + a_53 + a_54)^2 + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65)^2 + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2 - )^2 - 1, - 42 * a_21^3 * a_32^2 * b_3 * (a_31 + a_32) + - 42 * - b_4 * - (a_21 * a_42 + a_43 * (a_31 + a_32)) * - (a_21^2 * a_42 + a_43 * (a_31 + a_32)^2) * - (a_41 + a_42 + a_43) + - 42 * - b_5 * - (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) * - (a_21^2 * a_52 + a_53 * (a_31 + a_32)^2 + a_54 * (a_41 + a_42 + a_43)^2) * - (a_51 + a_52 + a_53 + a_54) + - 42 * - b_6 * - ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - ) * - ( - a_21^2 * a_62 + - a_63 * (a_31 + a_32)^2 + - a_64 * (a_41 + a_42 + a_43)^2 + - a_65 * (a_51 + a_52 + a_53 + a_54)^2 - ) * - (a_61 + a_62 + a_63 + a_64 + a_65) + - 42 * - b_7 * - ( - a_21 * a_72 + - a_73 * (a_31 + a_32) + - a_74 * (a_41 + a_42 + a_43) + - a_75 * (a_51 + a_52 + a_53 + a_54) + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65) - ) * - ( - a_21^2 * a_72 + - a_73 * (a_31 + a_32)^2 + - a_74 * (a_41 + a_42 + a_43)^2 + - a_75 * (a_51 + a_52 + a_53 + a_54)^2 + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65)^2 - ) * - (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) + - 42 * - b_8 * - ( - a_21 * a_82 + - a_83 * (a_31 + a_32) + - a_84 * (a_41 + a_42 + a_43) + - a_85 * (a_51 + a_52 + a_53 + a_54) + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65) + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) - ) * - ( - a_21^2 * a_82 + - a_83 * (a_31 + a_32)^2 + - a_84 * (a_41 + a_42 + a_43)^2 + - a_85 * (a_51 + a_52 + a_53 + a_54)^2 + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65)^2 + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2 - ) * - (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87) - 1, - 21 * a_21^2 * a_32 * b_3 * (a_31 + a_32)^3 + - 21 * b_4 * (a_21^2 * a_42 + a_43 * (a_31 + a_32)^2) * (a_41 + a_42 + a_43)^3 + - 21 * - b_5 * - (a_21^2 * a_52 + a_53 * (a_31 + a_32)^2 + a_54 * (a_41 + a_42 + a_43)^2) * - (a_51 + a_52 + a_53 + a_54)^3 + - 21 * - b_6 * - ( - a_21^2 * a_62 + - a_63 * (a_31 + a_32)^2 + - a_64 * (a_41 + a_42 + a_43)^2 + - a_65 * (a_51 + a_52 + a_53 + a_54)^2 - ) * - (a_61 + a_62 + a_63 + a_64 + a_65)^3 + - 21 * - b_7 * - ( - a_21^2 * a_72 + - a_73 * (a_31 + a_32)^2 + - a_74 * (a_41 + a_42 + a_43)^2 + - a_75 * (a_51 + a_52 + a_53 + a_54)^2 + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65)^2 - ) * - (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^3 + - 21 * - b_8 * - ( - a_21^2 * a_82 + - a_83 * (a_31 + a_32)^2 + - a_84 * (a_41 + a_42 + a_43)^2 + - a_85 * (a_51 + a_52 + a_53 + a_54)^2 + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65)^2 + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2 - ) * - (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^3 - 1, - 56 * a_21^3 * a_32^3 * b_3 + - 56 * b_4 * (a_21 * a_42 + a_43 * (a_31 + a_32))^3 + - 56 * b_5 * (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43))^3 + - 56 * - b_6 * - ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - )^3 + - 56 * - b_7 * - ( - a_21 * a_72 + - a_73 * (a_31 + a_32) + - a_74 * (a_41 + a_42 + a_43) + - a_75 * (a_51 + a_52 + a_53 + a_54) + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65) - )^3 + - 56 * - b_8 * - ( - a_21 * a_82 + - a_83 * (a_31 + a_32) + - a_84 * (a_41 + a_42 + a_43) + - a_85 * (a_51 + a_52 + a_53 + a_54) + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65) + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) - )^3 - 1, - 28 * a_21^2 * a_32^2 * b_3 * (a_31 + a_32)^2 + - 28 * b_4 * (a_21 * a_42 + a_43 * (a_31 + a_32))^2 * (a_41 + a_42 + a_43)^2 + - 28 * - b_5 * - (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43))^2 * - (a_51 + a_52 + a_53 + a_54)^2 + - 28 * - b_6 * - ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - )^2 * - (a_61 + a_62 + a_63 + a_64 + a_65)^2 + - 28 * - b_7 * - ( - a_21 * a_72 + - a_73 * (a_31 + a_32) + - a_74 * (a_41 + a_42 + a_43) + - a_75 * (a_51 + a_52 + a_53 + a_54) + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65) - )^2 * - (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^2 + - 28 * - b_8 * - ( - a_21 * a_82 + - a_83 * (a_31 + a_32) + - a_84 * (a_41 + a_42 + a_43) + - a_85 * (a_51 + a_52 + a_53 + a_54) + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65) + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) - )^2 * - (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^2 - 1, - 14 * a_21 * a_32 * b_3 * (a_31 + a_32)^4 + - 14 * b_4 * (a_21 * a_42 + a_43 * (a_31 + a_32)) * (a_41 + a_42 + a_43)^4 + - 14 * - b_5 * - (a_21 * a_52 + a_53 * (a_31 + a_32) + a_54 * (a_41 + a_42 + a_43)) * - (a_51 + a_52 + a_53 + a_54)^4 + - 14 * - b_6 * - ( - a_21 * a_62 + - a_63 * (a_31 + a_32) + - a_64 * (a_41 + a_42 + a_43) + - a_65 * (a_51 + a_52 + a_53 + a_54) - ) * - (a_61 + a_62 + a_63 + a_64 + a_65)^4 + - 14 * - b_7 * - ( - a_21 * a_72 + - a_73 * (a_31 + a_32) + - a_74 * (a_41 + a_42 + a_43) + - a_75 * (a_51 + a_52 + a_53 + a_54) + - a_76 * (a_61 + a_62 + a_63 + a_64 + a_65) - ) * - (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^4 + - 14 * - b_8 * - ( - a_21 * a_82 + - a_83 * (a_31 + a_32) + - a_84 * (a_41 + a_42 + a_43) + - a_85 * (a_51 + a_52 + a_53 + a_54) + - a_86 * (a_61 + a_62 + a_63 + a_64 + a_65) + - a_87 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76) - ) * - (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^4 - 1, - 7 * a_21^6 * b_2 + - 7 * b_3 * (a_31 + a_32)^6 + - 7 * b_4 * (a_41 + a_42 + a_43)^6 + - 7 * b_5 * (a_51 + a_52 + a_53 + a_54)^6 + - 7 * b_6 * (a_61 + a_62 + a_63 + a_64 + a_65)^6 + - 7 * b_7 * (a_71 + a_72 + a_73 + a_74 + a_75 + a_76)^6 + - 7 * b_8 * (a_81 + a_82 + a_83 + a_84 + a_85 + a_86 + a_87)^6 - 1 -] diff --git a/benchmark/scripts/runmq.jl b/benchmark/scripts/runmq.jl deleted file mode 100644 index ae920dff..00000000 --- a/benchmark/scripts/runmq.jl +++ /dev/null @@ -1,5 +0,0 @@ -include((@__DIR__) * "../../benchmark/systems/MQ/parser.jl") - -system = read_MQ_GF("mq_n15_m30_p2_s0") - -VSCodeServer.@profview gb = Groebner.groebner(system, linalg=:prob); diff --git a/benchmark/scripts/stuff.jl b/benchmark/scripts/stuff.jl deleted file mode 100644 index 4f950eae..00000000 --- a/benchmark/scripts/stuff.jl +++ /dev/null @@ -1,691 +0,0 @@ -using Primes - -cfs = Rational{BigInt}[ - 1, - 952031636635873122466558540126443872837256727109634671825482542897109828474093604351 // 2100413247143035122491210582569212645540334745409046860629593590090256564387839911495, - 61156369769925838132952461673507934256669974801115466393288947077538966971606219877503 // 8401652988572140489964842330276850582161338981636187442518374360361026257551359645980, - 3579901348185219793970027355016961928641712964268714830339873241244288207332275142725 // 1680330597714428097992968466055370116432267796327237488503674872072205251510271929196, - 2333055997156616491541767834336383587547701416035612742721464361531599460095494642507 // 1680330597714428097992968466055370116432267796327237488503674872072205251510271929196, - 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-using Nemo - -function ratrec_vec_1(rems, m) - quo = Vector{Rational{BigInt}}(undef, length(rems)) - nemo_modulo = Nemo.ZZRingElem(m) - for i in 1:length(rems) - nemo_rem = Nemo.ZZRingElem(rems[i]) - _, (a, b) = Groebner.ratrec_nemo(nemo_rem, nemo_modulo) - quo[i] = Base.unsafe_rational(a, b) - end - quo -end - -@assert ratrec_vec_1(rems, m) == cfs -@benchmark ratrec_vec_1($rems, $m) - -function ratrec_vec_2(rems, m) - quo = Vector{Rational{BigInt}}(undef, length(rems)) - d = BigInt(1) - nemo_modulo = Nemo.ZZRingElem(m) - for i in 1:length(rems) - nemo_rem = Nemo.ZZRingElem(rems[i]) - nemo_rem = mod(d * nemo_rem, nemo_modulo) - _, (a, b) = Groebner.ratrec_nemo(nemo_rem, nemo_modulo) - if !isone(b) - d = d * b - end - quo[i] = Base.unsafe_rational(a, d) - end - quo -end - -@assert ratrec_vec_2(rems, m) == cfs -@benchmark ratrec_vec_2($rems, $m) diff --git a/benchmark/scripts/symbolic-data.jl b/benchmark/scripts/symbolic-data.jl deleted file mode 100644 index 22b975f4..00000000 --- a/benchmark/scripts/symbolic-data.jl +++ /dev/null @@ -1,22 +0,0 @@ - -using LightXML - -function load_system_symbolic_data(filename) - # parse ex1.xml: - # xdoc is an instance of XMLDocument, which maintains a tree structure - xdoc = parse_file(filename) - - # get the root element - xroot = root(xdoc) # an instance of XMLElement - # print its name - println(name(xroot)) # this should print: bookstore - - # traverse all its child nodes and print element names - for c in child_nodes(xroot) # c is an instance of XMLNode - println(nodetype(c)) - if is_elementnode(c) - e = XMLElement(c) # this makes an XMLElement instance - println(name(e)) - end - end -end diff --git a/benchmark/scripts/threaded-bench-qq.jl b/benchmark/scripts/threaded-bench-qq.jl deleted file mode 100644 index d2273339..00000000 --- a/benchmark/scripts/threaded-bench-qq.jl +++ /dev/null @@ -1,111 +0,0 @@ -using BenchmarkTools, AbstractAlgebra, PrettyTables -using Base.Threads - -if !isdefined(Main, :Groebner) - using Groebner -end - -@info "Using $(nthreads()) Julia threads" - -Groebner.logging_enabled() = false -Groebner.invariants_enabled() = false - -#! format: off -R,(t1,t2,t3,a,b,c) = polynomial_ring(QQ, ["t1","t2","t3","a", "b", "c"], internal_ordering=:degrevlex) -hexapod = [1000000*a^2*t1^2+1000000*a^2*t2^2+1000000*a^2*t3^2+1000000*b^2*t1^2+1000000*b^2*t2^2+1000000*b^2*t3^2+1000000*c^2*t1^2+1000000*c^2*t2^2+1000000*c^2*t3^2-1065102000*a^2*t1-1566200000*a^2*t2+359610000*a^2*t3-4000000*a*b*t2-1574352000*a*b*t3+4000000*a*c*t1+273640000*a*c*t3-1065102000*b^2*t1+8152000*b^2*t2+355610000*b^2*t3-1574352000*b*c*t1-273640000*b*c*t2-791462000*c^2*t1-1566200000*c^2*t2+355610000*c^2*t3+740236705137*a^2-279943961360*a*b+47071636200*a*c+1574352000*a*t1-273640000*a*t2+126292488913*b^2+837307375312*b*c+4000000*b*t1-273640000*b*t3+612513941897*c^2+4000000*c*t2-1574352000*c*t3+1000000*t1^2+1000000*t2^2+1000000*t3^2-624135247952*a-50784764200*b-283060057360*c-791462000*t1+8152000*t2+359610000*t3+165673, 1000000*a^2*t1^2+1000000*a^2*t2^2+1000000*a^2*t3^2+1000000*b^2*t1^2+1000000*b^2*t2^2+1000000*b^2*t3^2+1000000*c^2*t1^2+1000000*c^2*t2^2+1000000*c^2*t3^2-1889130000*a^2*t1-139016000*a^2*t2+357608000*a^2*t3+550492000*a*b*t3+1500376000*a*c*t3-1889130000*b^2*t1-689508000*b^2*t2+357608000*b^2*t3+550492000*b*c*t1-1500376000*b*c*t2-388754000*c^2*t1-139016000*c^2*t2+357608000*c^2*t3+740396599024*a^2+98430171568*a*b+268273230304*a*c-550492000*a*t1-1500376000*a*t2+854420557476*b^2-2714848476*b*c-1500376000*b*t3-114024022072*c^2+550492000*c*t3+1000000*t1^2+1000000*t2^2+1000000*t3^2+624263610988*a-268273230304*b+98430171568*c-388754000*t1-689508000*t2+357608000*t3-63620, 4000000*a^2*t1^2+4000000*a^2*t2^2+4000000*a^2*t3^2+4000000*b^2*t1^2+4000000*b^2*t2^2+4000000*b^2*t3^2+4000000*c^2*t1^2+4000000*c^2*t2^2+4000000*c^2*t3^2-3295636000*a^2*t1+6825304000*a^2*t2+1438448000*a^2*t3-16000000*a*b*t2+4096192000*a*b*t3+16000000*a*c*t1+4906624000*a*c*t3-3295636000*b^2*t1+2729112000*b^2*t2+1422448000*b^2*t3+4096192000*b*c*t1-4906624000*b*c*t2+1610988000*c^2*t1+6825304000*c^2*t2+1422448000*c^2*t3+2962666483625*a^2+722869290752*a*b+875649162944*a*c-4096192000*a*t1-4906624000*a*t2+513760438633*b^2-3361285532000*b*c+16000000*b*t1-4906624000*b*t3+2443184693353*c^2+16000000*c*t2+4096192000*c*t3+4000000*t1^2+4000000*t2^2+4000000*t3^2-2498705324448*a-879018458944*b+741978122752*c+1610988000*t1+2729112000*t2+1438448000*t3+440361,4000000*a^2*t1^2+4000000*a^2*t2^2+4000000*a^2*t3^2+4000000*b^2*t1^2+4000000*b^2*t2^2+4000000*b^2*t3^2+4000000*c^2*t1^2+4000000*c^2*t2^2+4000000*c^2*t3^2+3295636000*a^2*t1+6824896000*a^2*t2+1430432000*a^2*t3+4094592000*a*b*t3-4906624000*a*c*t3+3295636000*b^2*t1+2730304000*b^2*t2+1430432000*b^2*t3+4094592000*b*c*t1+4906624000*b*c*t2-1610988000*c^2*t1+6824896000*c^2*t2+1430432000*c^2*t3+2961910911797*a^2+732129427968*a*b-877323997696*a*c-4094592000*a*t1+4906624000*a*t2+516620569397*b^2+3361357491776*b*c+4906624000*b*t3+2445290017525*c^2+4094592000*c*t3+4000000*t1^2+4000000*t2^2+4000000*t3^2+2499114213824*a+877323997696*b+732129427968*c-1610988000*t1+2730304000*t2+1430432000*t3-324875, 1000000*a^2*t1^2+1000000*a^2*t2^2+1000000*a^2*t3^2+1000000*b^2*t1^2+1000000*b^2*t2^2+1000000*b^2*t3^2+1000000*c^2*t1^2+1000000*c^2*t2^2+1000000*c^2*t3^2+1889602000*a^2*t1-138926000*a^2*t2+359604000*a^2*t3-4000000*a*b*t2+550036000*a*b*t3+4000000*a*c*t1-1500228000*a*c*t3+1889602000*b^2*t1-688962000*b^2*t2+355604000*b^2*t3+550036000*b*c*t1+1500228000*b*c*t2+389374000*c^2*t1-138926000*c^2*t2+355604000*c^2*t3+740903906549*a^2+99175424872*a*b-265964790856*a*c-550036000*a*t1+1500228000*a*t2+854030749541*b^2+2874521168*b*c+4000000*b*t1+1500228000*b*t3-114557203083*c^2+4000000*c*t2+550036000*c*t3+1000000*t1^2+1000000*t2^2+1000000*t3^2-623884900400*a+270522742856*b+97519648872*c+389374000*t1-688962000*t2+359604000*t3+55909, 250000*a^2*t1^2+250000*a^2*t2^2+250000*a^2*t3^2+250000*b^2*t1^2+250000*b^2*t2^2+250000*b^2*t3^2+250000*c^2*t1^2+250000*c^2*t2^2+250000*c^2*t3^2+266341000*a^2*t1-391502000*a^2*t2+89402000*a^2*t3-393620000*a*b*t3-68228000*a*c*t3+266341000*b^2*t1+2118000*b^2*t2+89402000*b^2*t3-393620000*b*c*t1+68228000*b*c*t2+198113000*c^2*t1-391502000*c^2*t2+89402000*c^2*t3+184958257568*a^2-70380830480*a*b-12199439312*a*c+393620000*a*t1+68228000*a*t2+31688927488*b^2-209385275032*b*c+68228000*b*t3+153269490056*c^2-393620000*c*t3+250000*t1^2+250000*t2^2+250000*t3^2+156251491928*a+12199439312*b-70380830480*c+198113000*t1+2118000*t2+89402000*t3+159976] -#! format: on - -systems = [ - # ("kat5", Groebner.Examples.katsuran(5, internal_ordering=:degrevlex, k=AbstractAlgebra.QQ)), - # ("kat6", Groebner.Examples.katsuran(6, internal_ordering=:degrevlex, k=AbstractAlgebra.QQ)), - # ("kat7", Groebner.Examples.katsuran(7, internal_ordering=:degrevlex, k=AbstractAlgebra.QQ)), - ("kat8", Groebner.Examples.katsuran(8, internal_ordering=:degrevlex, k=AbstractAlgebra.QQ)), - ("kat9", Groebner.Examples.katsuran(9, internal_ordering=:degrevlex, k=AbstractAlgebra.QQ)), - ("kat10", Groebner.Examples.katsuran(10, internal_ordering=:degrevlex, k=AbstractAlgebra.QQ)), - # ("kat11", Groebner.Examples.katsuran(11, internal_ordering=:degrevlex, k=AbstractAlgebra.QQ)), - # ("kat12", Groebner.Examples.katsuran(12, internal_ordering=:degrevlex, k=AbstractAlgebra.QQ)), - # ("hen5", Groebner.Examples.henrion5(internal_ordering=:degrevlex, k=AbstractAlgebra.QQ)), - # ("reim4", Groebner.Examples.reimern(4, internal_ordering=:degrevlex, k=AbstractAlgebra.QQ)), - # ("reim5", Groebner.Examples.reimern(5, internal_ordering=:degrevlex, k=AbstractAlgebra.QQ)), - # ("cyc4", Groebner.Examples.cyclicn(4, internal_ordering=:degrevlex, k=AbstractAlgebra.QQ)), - # ("cyc5", Groebner.Examples.cyclicn(5, internal_ordering=:degrevlex, k=AbstractAlgebra.QQ)), - ("cyc6", Groebner.Examples.cyclicn(6, internal_ordering=:degrevlex, k=AbstractAlgebra.QQ)), - ("cyc7", Groebner.Examples.cyclicn(7, internal_ordering=:degrevlex, k=AbstractAlgebra.QQ)), - ("cyc8", Groebner.Examples.cyclicn(8, internal_ordering=:degrevlex, k=AbstractAlgebra.QQ)), - ("eco10", Groebner.Examples.eco10(internal_ordering=:degrevlex, k=AbstractAlgebra.QQ)), - ("eco11", Groebner.Examples.eco11(internal_ordering=:degrevlex, k=AbstractAlgebra.QQ)), - # ("eco12", Groebner.Examples.eco12(internal_ordering=:degrevlex, k=AbstractAlgebra.QQ)), - # ("eco13", Groebner.Examples.eco13(internal_ordering=:degrevlex, k=AbstractAlgebra.QQ)) - # ("noon4", Groebner.Examples.noonn(4, internal_ordering=:degrevlex, k=AbstractAlgebra.QQ)), - # ("noon5", Groebner.Examples.noonn(5, internal_ordering=:degrevlex, k=AbstractAlgebra.QQ)), - # ("noon6", Groebner.Examples.noonn(6, internal_ordering=:degrevlex, k=AbstractAlgebra.QQ)), - ("noon7", Groebner.Examples.noonn(7, internal_ordering=:degrevlex, k=AbstractAlgebra.QQ)), - ("noon8", Groebner.Examples.noonn(8, internal_ordering=:degrevlex, k=AbstractAlgebra.QQ)), - ("hexapod", hexapod) -] - -table = Matrix{Any}(undef, (length(systems), 2)) - -function benchmark_system(system, trials=3; kwargs...) - timings = [] - GC.gc() - gb = nothing - for _ in 1:trials - time = @elapsed gb = Groebner.groebner(system; kwargs...) - push!(timings, time) - end - gb, minimum(timings) -end - -for (i, (name, s)) in enumerate(systems) - @info """ - $name: - total (default) / total (threaded)""" - # gb1, ti1 = benchmark_system(s; linalg=:deterministic, threaded=:no) - # gb2, ti2 = benchmark_system(s; linalg=:deterministic, threaded=:yes) - gb3, ti3 = benchmark_system(s; linalg=:randomized, threaded=:no) - gb4, ti4 = benchmark_system(s; linalg=:randomized, threaded=:yes) - - (ti3, ti4) = map(t -> BenchmarkTools.prettytime(t * 1e9), (ti3, ti4)) - # table[i, :] .= (ti1, ti2, ti3, ti4) - table[i, :] .= (ti3, ti4) - println("$ti3 / $ti4") - - # @assert gb1 == gb2 == gb3 == gb4 - @assert gb3 == gb4 -end - -pretty_table( - table, - header=["total (default)", "total (threaded)"], - tf=tf_markdown, - row_labels=map(first, systems) -) - -#= -| | linalg #1 | linalg #1 threaded | linalg #2 (default) | linalg #2 threaded | -|---------|------------|--------------------|---------------------|--------------------| -| kat5 | 649.900 μs | 1.170 ms | 594.000 μs | 881.500 μs | -| kat6 | 2.537 ms | 3.185 ms | 1.711 ms | 2.243 ms | -| kat7 | 15.282 ms | 12.524 ms | 8.027 ms | 6.787 ms | -| kat8 | 78.290 ms | 44.962 ms | 26.484 ms | 21.662 ms | -| kat9 | 534.722 ms | 260.607 ms | 126.397 ms | 94.352 ms | -| kat10 | 4.623 s | 2.205 s | 756.419 ms | 472.633 ms | -| hen5 | 2.232 ms | 2.883 ms | 1.948 ms | 2.209 ms | -| reim4 | 15.097 ms | 18.618 ms | 12.829 ms | 15.887 ms | -| reim5 | 761.353 ms | 730.773 ms | 672.574 ms | 654.266 ms | -| cyc4 | 118.600 μs | 366.000 μs | 119.800 μs | 220.800 μs | -| cyc5 | 665.000 μs | 1.187 ms | 663.300 μs | 958.200 μs | -| cyc6 | 2.980 ms | 5.121 ms | 2.595 ms | 3.339 ms | -| cyc7 | 158.597 ms | 117.256 ms | 78.787 ms | 66.732 ms | -| cyc8 | 3.498 s | 2.074 s | 1.080 s | 794.454 ms | -| eco10 | 130.946 ms | 82.692 ms | 54.565 ms | 50.291 ms | -| eco11 | 917.577 ms | 506.479 ms | 281.912 ms | 233.156 ms | -| eco12 | 7.901 s | 3.888 s | 1.801 s | 1.360 s | -| noon4 | 572.000 μs | 1.193 ms | 609.300 μs | 955.800 μs | -| noon5 | 3.485 ms | 4.406 ms | 3.247 ms | 4.047 ms | -| noon6 | 19.640 ms | 20.017 ms | 19.235 ms | 19.568 ms | -| noon7 | 132.158 ms | 111.749 ms | 126.367 ms | 114.704 ms | -| noon8 | 1.069 s | 858.967 ms | 1.066 s | 894.792 ms | -| hexapod | 4.124 ms | 4.974 ms | 3.343 ms | 4.365 ms | -=# diff --git a/benchmark/scripts/threaded-bench.jl b/benchmark/scripts/threaded-bench.jl deleted file mode 100644 index 0cc87ed0..00000000 --- a/benchmark/scripts/threaded-bench.jl +++ /dev/null @@ -1,117 +0,0 @@ -using BenchmarkTools, AbstractAlgebra, PrettyTables -using Base.Threads - -if !isdefined(Main, :Groebner) - using Groebner -end - -p = 2^30 + 3 - -@info "Using $(nthreads()) Julia threads" -@info "Using prime number of order 2^$(floor(log(2,p)))" - -Groebner.logging_enabled() = false -Groebner.invariants_enabled() = false - -#! format: off -R,(t1,t2,t3,a,b,c) = polynomial_ring(GF(2^27+29), ["t1","t2","t3","a", "b", "c"], internal_ordering=:degrevlex) -hexapod = [1000000*a^2*t1^2+1000000*a^2*t2^2+1000000*a^2*t3^2+1000000*b^2*t1^2+1000000*b^2*t2^2+1000000*b^2*t3^2+1000000*c^2*t1^2+1000000*c^2*t2^2+1000000*c^2*t3^2-1065102000*a^2*t1-1566200000*a^2*t2+359610000*a^2*t3-4000000*a*b*t2-1574352000*a*b*t3+4000000*a*c*t1+273640000*a*c*t3-1065102000*b^2*t1+8152000*b^2*t2+355610000*b^2*t3-1574352000*b*c*t1-273640000*b*c*t2-791462000*c^2*t1-1566200000*c^2*t2+355610000*c^2*t3+740236705137*a^2-279943961360*a*b+47071636200*a*c+1574352000*a*t1-273640000*a*t2+126292488913*b^2+837307375312*b*c+4000000*b*t1-273640000*b*t3+612513941897*c^2+4000000*c*t2-1574352000*c*t3+1000000*t1^2+1000000*t2^2+1000000*t3^2-624135247952*a-50784764200*b-283060057360*c-791462000*t1+8152000*t2+359610000*t3+165673, 1000000*a^2*t1^2+1000000*a^2*t2^2+1000000*a^2*t3^2+1000000*b^2*t1^2+1000000*b^2*t2^2+1000000*b^2*t3^2+1000000*c^2*t1^2+1000000*c^2*t2^2+1000000*c^2*t3^2-1889130000*a^2*t1-139016000*a^2*t2+357608000*a^2*t3+550492000*a*b*t3+1500376000*a*c*t3-1889130000*b^2*t1-689508000*b^2*t2+357608000*b^2*t3+550492000*b*c*t1-1500376000*b*c*t2-388754000*c^2*t1-139016000*c^2*t2+357608000*c^2*t3+740396599024*a^2+98430171568*a*b+268273230304*a*c-550492000*a*t1-1500376000*a*t2+854420557476*b^2-2714848476*b*c-1500376000*b*t3-114024022072*c^2+550492000*c*t3+1000000*t1^2+1000000*t2^2+1000000*t3^2+624263610988*a-268273230304*b+98430171568*c-388754000*t1-689508000*t2+357608000*t3-63620, 4000000*a^2*t1^2+4000000*a^2*t2^2+4000000*a^2*t3^2+4000000*b^2*t1^2+4000000*b^2*t2^2+4000000*b^2*t3^2+4000000*c^2*t1^2+4000000*c^2*t2^2+4000000*c^2*t3^2-3295636000*a^2*t1+6825304000*a^2*t2+1438448000*a^2*t3-16000000*a*b*t2+4096192000*a*b*t3+16000000*a*c*t1+4906624000*a*c*t3-3295636000*b^2*t1+2729112000*b^2*t2+1422448000*b^2*t3+4096192000*b*c*t1-4906624000*b*c*t2+1610988000*c^2*t1+6825304000*c^2*t2+1422448000*c^2*t3+2962666483625*a^2+722869290752*a*b+875649162944*a*c-4096192000*a*t1-4906624000*a*t2+513760438633*b^2-3361285532000*b*c+16000000*b*t1-4906624000*b*t3+2443184693353*c^2+16000000*c*t2+4096192000*c*t3+4000000*t1^2+4000000*t2^2+4000000*t3^2-2498705324448*a-879018458944*b+741978122752*c+1610988000*t1+2729112000*t2+1438448000*t3+440361,4000000*a^2*t1^2+4000000*a^2*t2^2+4000000*a^2*t3^2+4000000*b^2*t1^2+4000000*b^2*t2^2+4000000*b^2*t3^2+4000000*c^2*t1^2+4000000*c^2*t2^2+4000000*c^2*t3^2+3295636000*a^2*t1+6824896000*a^2*t2+1430432000*a^2*t3+4094592000*a*b*t3-4906624000*a*c*t3+3295636000*b^2*t1+2730304000*b^2*t2+1430432000*b^2*t3+4094592000*b*c*t1+4906624000*b*c*t2-1610988000*c^2*t1+6824896000*c^2*t2+1430432000*c^2*t3+2961910911797*a^2+732129427968*a*b-877323997696*a*c-4094592000*a*t1+4906624000*a*t2+516620569397*b^2+3361357491776*b*c+4906624000*b*t3+2445290017525*c^2+4094592000*c*t3+4000000*t1^2+4000000*t2^2+4000000*t3^2+2499114213824*a+877323997696*b+732129427968*c-1610988000*t1+2730304000*t2+1430432000*t3-324875, 1000000*a^2*t1^2+1000000*a^2*t2^2+1000000*a^2*t3^2+1000000*b^2*t1^2+1000000*b^2*t2^2+1000000*b^2*t3^2+1000000*c^2*t1^2+1000000*c^2*t2^2+1000000*c^2*t3^2+1889602000*a^2*t1-138926000*a^2*t2+359604000*a^2*t3-4000000*a*b*t2+550036000*a*b*t3+4000000*a*c*t1-1500228000*a*c*t3+1889602000*b^2*t1-688962000*b^2*t2+355604000*b^2*t3+550036000*b*c*t1+1500228000*b*c*t2+389374000*c^2*t1-138926000*c^2*t2+355604000*c^2*t3+740903906549*a^2+99175424872*a*b-265964790856*a*c-550036000*a*t1+1500228000*a*t2+854030749541*b^2+2874521168*b*c+4000000*b*t1+1500228000*b*t3-114557203083*c^2+4000000*c*t2+550036000*c*t3+1000000*t1^2+1000000*t2^2+1000000*t3^2-623884900400*a+270522742856*b+97519648872*c+389374000*t1-688962000*t2+359604000*t3+55909, 250000*a^2*t1^2+250000*a^2*t2^2+250000*a^2*t3^2+250000*b^2*t1^2+250000*b^2*t2^2+250000*b^2*t3^2+250000*c^2*t1^2+250000*c^2*t2^2+250000*c^2*t3^2+266341000*a^2*t1-391502000*a^2*t2+89402000*a^2*t3-393620000*a*b*t3-68228000*a*c*t3+266341000*b^2*t1+2118000*b^2*t2+89402000*b^2*t3-393620000*b*c*t1+68228000*b*c*t2+198113000*c^2*t1-391502000*c^2*t2+89402000*c^2*t3+184958257568*a^2-70380830480*a*b-12199439312*a*c+393620000*a*t1+68228000*a*t2+31688927488*b^2-209385275032*b*c+68228000*b*t3+153269490056*c^2-393620000*c*t3+250000*t1^2+250000*t2^2+250000*t3^2+156251491928*a+12199439312*b-70380830480*c+198113000*t1+2118000*t2+89402000*t3+159976] -#! format: on - -systems = [ - # ("kat5", Groebner.Examples.katsuran(5, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - # ("kat6", Groebner.Examples.katsuran(6, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - # ("kat7", Groebner.Examples.katsuran(7, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - # ("kat8", Groebner.Examples.katsuran(8, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - # ("kat9", Groebner.Examples.katsuran(9, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - # ("kat10", Groebner.Examples.katsuran(10, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - # ("kat11", Groebner.Examples.katsuran(11, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - # ("kat12", Groebner.Examples.katsuran(12, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - # ("hen5", Groebner.Examples.henrion5(internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - # ("reim4", Groebner.Examples.reimern(4, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - # ("reim5", Groebner.Examples.reimern(5, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - # ("cyc4", Groebner.Examples.cyclicn(4, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - # ("cyc5", Groebner.Examples.cyclicn(5, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - # ("cyc6", Groebner.Examples.cyclicn(6, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - # ("cyc7", Groebner.Examples.cyclicn(7, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - # ("cyc8", Groebner.Examples.cyclicn(8, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - # ("cyc9", Groebner.Examples.cyclicn(8, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - # ("eco10", Groebner.Examples.eco10(internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - # ("eco11", Groebner.Examples.eco11(internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - # ("eco12", Groebner.Examples.eco12(internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - # ("eco13", Groebner.Examples.eco13(internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - # ("noon4", Groebner.Examples.noonn(4, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - ("noon5", Groebner.Examples.noonn(5, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - ("noon6", Groebner.Examples.noonn(6, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - ("noon7", Groebner.Examples.noonn(7, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - ("noon8", Groebner.Examples.noonn(8, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))), - ("noon9", Groebner.Examples.noonn(9, internal_ordering=:degrevlex, k=AbstractAlgebra.GF(p))) - # ("hexapod", hexapod) -] - -table = Matrix{Any}(undef, (length(systems), 3)) - -function benchmark_system(system, trials=5; kwargs...) - timings = [] - GC.gc() - gb = nothing - for _ in 1:trials - time = @elapsed gb = Groebner.groebner(system; kwargs...) - push!(timings, time) - end - gb, minimum(timings) -end - -for (i, (name, s)) in enumerate(systems) - @info """ - $name: - total (default) / total (threaded) / total (auto)""" - # gb1, ti1 = benchmark_system(s; linalg=:deterministic, threaded=:no) - # gb2, ti2 = benchmark_system(s; linalg=:deterministic, threaded=:yes) - gb3, ti3 = benchmark_system(s; linalg=:randomized, threaded=:no) - gb4, ti4 = benchmark_system(s; linalg=:randomized, threaded=:yes) - gb5, ti5 = benchmark_system(s; linalg=:randomized, threaded=:auto) - - (ti3, ti4, ti5) = map(t -> BenchmarkTools.prettytime(t * 1e9), (ti3, ti4, ti5)) - # table[i, :] .= (ti1, ti2, ti3, ti4) - table[i, :] .= (ti3, ti4, ti5) - println("$ti3 / $ti4 / $ti5") - - # @assert gb1 == gb2 == gb3 == gb4 - @assert gb3 == gb4 -end - -pretty_table( - table, - header=["total (default)", "total (threaded)", "total (auto)"], - tf=tf_markdown, - row_labels=map(first, systems) -) - -#= -| | linalg #1 | linalg #1 threaded | linalg #2 (default) | linalg #2 threaded | -|---------|------------|--------------------|---------------------|--------------------| -| kat5 | 649.900 μs | 1.170 ms | 594.000 μs | 881.500 μs | -| kat6 | 2.537 ms | 3.185 ms | 1.711 ms | 2.243 ms | -| kat7 | 15.282 ms | 12.524 ms | 8.027 ms | 6.787 ms | -| kat8 | 78.290 ms | 44.962 ms | 26.484 ms | 21.662 ms | -| kat9 | 534.722 ms | 260.607 ms | 126.397 ms | 94.352 ms | -| kat10 | 4.623 s | 2.205 s | 756.419 ms | 472.633 ms | -| hen5 | 2.232 ms | 2.883 ms | 1.948 ms | 2.209 ms | -| reim4 | 15.097 ms | 18.618 ms | 12.829 ms | 15.887 ms | -| reim5 | 761.353 ms | 730.773 ms | 672.574 ms | 654.266 ms | -| cyc4 | 118.600 μs | 366.000 μs | 119.800 μs | 220.800 μs | -| cyc5 | 665.000 μs | 1.187 ms | 663.300 μs | 958.200 μs | -| cyc6 | 2.980 ms | 5.121 ms | 2.595 ms | 3.339 ms | -| cyc7 | 158.597 ms | 117.256 ms | 78.787 ms | 66.732 ms | -| cyc8 | 3.498 s | 2.074 s | 1.080 s | 794.454 ms | -| eco10 | 130.946 ms | 82.692 ms | 54.565 ms | 50.291 ms | -| eco11 | 917.577 ms | 506.479 ms | 281.912 ms | 233.156 ms | -| eco12 | 7.901 s | 3.888 s | 1.801 s | 1.360 s | -| noon4 | 572.000 μs | 1.193 ms | 609.300 μs | 955.800 μs | -| noon5 | 3.485 ms | 4.406 ms | 3.247 ms | 4.047 ms | -| noon6 | 19.640 ms | 20.017 ms | 19.235 ms | 19.568 ms | -| noon7 | 132.158 ms | 111.749 ms | 126.367 ms | 114.704 ms | -| noon8 | 1.069 s | 858.967 ms | 1.066 s | 894.792 ms | -| hexapod | 4.124 ms | 4.974 ms | 3.343 ms | 4.365 ms | -=# diff --git a/src/Groebner.jl b/src/Groebner.jl index 177ec1c9..7e68bd47 100644 --- a/src/Groebner.jl +++ b/src/Groebner.jl @@ -46,9 +46,6 @@ import Base.MultiplicativeInverses: UnsignedMultiplicativeInverse import Combinatorics -import HostCPUFeatures: - cpu_name, register_count, register_size, has_feature, pick_vector_width, fma_fast - using Logging # At the moment, used only for rational reconstruction @@ -81,7 +78,6 @@ end # Includes include("utils/invariants.jl") -include("utils/simd.jl") include("utils/packed.jl") # Test systems, such as katsura, cyclic, etc diff --git a/src/f4/sort.jl b/src/f4/sort.jl index da2c67e2..92989352 100644 --- a/src/f4/sort.jl +++ b/src/f4/sort.jl @@ -5,6 +5,12 @@ # msolve is distributed under GNU GPL v2+: # https://github.com/algebraic-solving/msolve/blob/master/COPYING +# y, s.t. y >= x and n | y. +align_up(x::Integer, n::Integer) = (x + (n - 1)) & (~(n - 1)) + +# y, s.t y <= x and n | y. +align_down(x::Integer, n::Integer) = x ⊻ (n - 1) + ### # Sorting monomials, polynomials, and other things. @@ -27,6 +33,25 @@ function sort_part!( nothing end +# Permute a part of the array from the given index according to the permutation. +function permute_array!( + arr::AbstractVector{T}, + perm::Vector{I}, + buf::Vector{T}, + from::Int, + sz::Int +) where {T, I} + @invariant length(buf) >= sz && sz <= length(perm) + @invariant from + sz - 1 <= length(arr) + @inbounds for i in 1:sz + buf[i] = arr[perm[i]] + end + @inbounds for i in 1:sz + arr[from + i - 1] = buf[i] + end + nothing +end + function sort_polys_by_lead_increasing!( basis::Basis, hashtable::MonomialHashtable, diff --git a/src/monomials/exponent_vector.jl b/src/monomials/exponent_vector.jl index c33fd81f..3be42e20 100644 --- a/src/monomials/exponent_vector.jl +++ b/src/monomials/exponent_vector.jl @@ -110,7 +110,11 @@ function monom_isless(ea::ExponentVector, eb::ExponentVector, ::DegRevLex{true}) elseif monom_totaldeg(ea) != monom_totaldeg(eb) return false end - _vec_cmp_revlex(ea, eb) + i = length(ea) + @inbounds while i > 2 && ea[i] == eb[i] + i -= 1 + end + @inbounds return ea[i] > eb[i] end # DegRevLex monomial comparison (shuffled variables). @@ -145,7 +149,7 @@ function monom_isless(ea::ExponentVector, eb::ExponentVector, ::DegLex{true}) elseif monom_totaldeg(ea) != monom_totaldeg(eb) return false end - _vec_cmp_lex(ea, eb) + monom_isless(ea, eb, Lex()) end # DegLex monomial comparison (shuffled variables). @@ -175,7 +179,11 @@ end function monom_isless(ea::ExponentVector, eb::ExponentVector, ::Lex{true}) @invariant length(ea) == length(eb) @invariant length(ea) > 1 - _vec_cmp_lex(ea, eb) + i = 2 + @inbounds while i < length(ea) && ea[i] == eb[i] + i += 1 + end + @inbounds return ea[i] < eb[i] end # Lex monomial comparison (shuffled variables). @@ -263,7 +271,12 @@ end # Checks if the gcd of monomials is constant. function monom_is_gcd_const(ea::ExponentVector{T}, eb::ExponentVector{T}) where {T} @invariant length(ea) == length(eb) - _vec_check_orth(ea, eb) + @inbounds for j in 2:length(ea) + if !iszero(ea[j]) && !iszero(eb[j]) + return false + end + end + true end # Returns the product of two monomials. Writes the result to ec. @@ -297,7 +310,12 @@ end # Checks monomial divisibility. function monom_is_divisible(ea::ExponentVector{T}, eb::ExponentVector{T}) where {T} @invariant length(ea) == length(eb) - _vec_not_any_lt(ea, eb)::Bool + @inbounds for j in 2:length(ea) + if ea[j] < eb[j] + return false + end + end + return true end # Checks monomial divisibility and performs division diff --git a/src/utils/packed.jl b/src/utils/packed.jl index 711d4c65..5fff9c51 100644 --- a/src/utils/packed.jl +++ b/src/utils/packed.jl @@ -1,7 +1,8 @@ # This file is a part of Groebner.jl. License is GNU GPL v2. ### -# This file provides some fast operations on packed vectors of integers. +# This file provides some operations on packed integers. +# One 64-bit integer packs 8 integers 8-bit each. # checks that a[i] >= b[i] for all i. @inline @generated function _packed_vec_ge(a::UInt64, b::UInt64) diff --git a/src/utils/simd.jl b/src/utils/simd.jl deleted file mode 100644 index 376ce154..00000000 --- a/src/utils/simd.jl +++ /dev/null @@ -1,487 +0,0 @@ -# This file is a part of Groebner.jl. License is GNU GPL v2. - -### -# This file provides some fast operations on vectors of integers. - -# The use of these functions must be limited. -# -# Debugging LLVM IR is a headache. The LLVM IR textual format is not guaranteed -# to be stable. -# -# At this moment, we are grudgingly writing the LLVM IR, and we hope that the -# bright future where the compiler does this for us is well within our grasp. - -# Functions in this file take their inspiration from -# https://github.com/SciML/FindFirstFunctions.jl - -const BitInteger = Union{Int16, Int32, Int64, Int8, UInt16, UInt32, UInt64, UInt8} - -jl_to_llvm_t(::Type{T}) where {T <: BitInteger} = "i$(8*sizeof(T))" - -# y, s.t. y >= x and n | y. -align_up(x::Integer, n::Integer) = (x + (n - 1)) & (~(n - 1)) - -# y, s.t y <= x and n | y. -align_down(x::Integer, n::Integer) = x ⊻ (n - 1) - -function pick_vector_width_clamp_8(::Type{T}) where {T} - N = pick_vector_width(T) - if N in (8, 16, 32) - return Int(N) - end - if N == 64 - return 32 - end - 1 -end - -# Permute a part of the array from the given index according to the permutation. -function permute_array!( - arr::AbstractVector{T}, - perm::Vector{I}, - buf::Vector{T}, - from::Int, - sz::Int -) where {T, I} - @invariant length(buf) >= sz && sz <= length(perm) - @invariant from + sz - 1 <= length(arr) - @inbounds for i in 1:sz - buf[i] = arr[perm[i]] - end - @inbounds for i in 1:sz - arr[from + i - 1] = buf[i] - end - nothing -end - -# Vector functions in this file assume that -# - input vectors are non-negative. -# - input vectors have the same length. - -# Returns false if a[i] < b[i] for ANY index i, and true otherwise. -@inline @generated function _vec_not_any_lt( - a::Vector{T}, - b::Vector{T}, - offset::Int=1 -) where {T <: BitInteger} - N = pick_vector_width_clamp_8(T) - - # Unfortunate case. Default to scalar code. - if N == 1 - return quote - @inbounds for j in (1 + offset):length(a) - if a[j] < b[j] - return false - end - end - return true - end - end - - # The case when IntN exists. - @assert N in (8, 16, 32, 64) - B = sizeof(T) - llvm_t = jl_to_llvm_t(T) - mask = align_down(typemax(Int), N) - textir = """ - declare <$N x $llvm_t> @llvm.masked.load.v$(N)$(llvm_t)(<$N x $llvm_t>*, i32, <$N x i1>, <$N x $llvm_t>); - define i8 @entry(i64 %0, i64 %1, i64 %2) #0 { - top: - %a = inttoptr i64 %0 to $llvm_t* - %b = inttoptr i64 %1 to $llvm_t* - %lenm$(N-1) = add nsw i64 %2, -$(N-1) - %dosimditer = icmp ugt i64 %2, $(N-1) - br i1 %dosimditer, label %L9.lr.ph, label %L32 - - L9.lr.ph: - %len$N = and i64 %2, $mask ; divisible by N - br label %L9 - - L9: - %i = phi i64 [ 0, %L9.lr.ph ], [ %vinc, %L30 ] - %api = getelementptr inbounds $llvm_t, $llvm_t* %a, i64 %i - %bpi = getelementptr inbounds $llvm_t, $llvm_t* %b, i64 %i - %avi = bitcast $llvm_t* %api to <$N x $llvm_t>* - %bvi = bitcast $llvm_t* %bpi to <$N x $llvm_t>* - %ai = load <$N x $llvm_t>, <$N x $llvm_t>* %avi, align $B - %bi = load <$N x $llvm_t>, <$N x $llvm_t>* %bvi, align $B - %mask = icmp ult <$N x $llvm_t> %ai, %bi - %compressed = bitcast <$N x i1> %mask to i$N - %matchnotfound = icmp eq i$N %compressed, 0 - br i1 %matchnotfound, label %L30, label %common.ret - - common.ret: - %retval = phi i8 [ 0, %L9 ], [ 1, %L32 ], [ 0, %L51 ], [ 1, %L67 ] - ret i8 %retval - - L30: - %vinc = add nuw nsw i64 %i, $N - %continue = icmp slt i64 %vinc, %lenm$(N-1) - br i1 %continue, label %L9, label %L32 - - L32: - %cumi = phi i64 [ 0, %top ], [ %len$N, %L30 ] - %done = icmp eq i64 %cumi, %2 - br i1 %done, label %common.ret, label %L51 - - L51: - %si = phi i64 [ %inc, %L67 ], [ %cumi, %L32 ] - %sapi = getelementptr inbounds $llvm_t, $llvm_t* %a, i64 %si - %sbpi = getelementptr inbounds $llvm_t, $llvm_t* %b, i64 %si - %savi = load $llvm_t, $llvm_t* %sapi, align $B - %sbvi = load $llvm_t, $llvm_t* %sbpi, align $B - %match = icmp ult $llvm_t %savi, %sbvi - br i1 %match, label %common.ret, label %L67 - - L67: - %inc = add i64 %si, 1 - %dobreak = icmp eq i64 %inc, %2 - br i1 %dobreak, label %common.ret, label %L51 - } - attributes #0 = { alwaysinline } - """ - quote - GC.@preserve a b begin - Base.llvmcall( - ($textir, "entry"), - Bool, - Tuple{Ptr{T}, Ptr{T}, Int64}, - pointer(a) + sizeof(T) * offset, - pointer(b) + sizeof(T) * offset, - length(a) - offset - ) - end - end -end - -# Returns true if a and b are orthogonal, and false otherwise. -@inline @generated function _vec_check_orth( - a::Vector{T}, - b::Vector{T}, - offset::Int=1 -) where {T <: BitInteger} - N = pick_vector_width_clamp_8(T) - - # Unfortunate case. Default to scalar code. - if N == 1 - return quote - @inbounds for j in (1 + offset):length(a) - if !iszero(a[j]) && !iszero(b[j]) - return false - end - end - return true - end - end - - # The case when IntN exists. - @assert N in (8, 16, 32, 64) - B = sizeof(T) - llvm_t = jl_to_llvm_t(T) - mask = align_down(typemax(Int), N) - textir = """ - define i8 @entry(i64 %0, i64 %1, i64 %2) #0 { - top: - %a = inttoptr i64 %0 to $llvm_t* - %b = inttoptr i64 %1 to $llvm_t* - %lenm$(N-1) = add nsw i64 %2, -$(N-1) - %dosimditer = icmp ugt i64 %2, $(N-1) - br i1 %dosimditer, label %L9.lr.ph, label %L32 - - L9.lr.ph: - %len$N = and i64 %2, $mask ; divisible by N - br label %L9 - - L9: - %i = phi i64 [ 0, %L9.lr.ph ], [ %vinc, %L30 ] - %api = getelementptr inbounds $llvm_t, $llvm_t* %a, i64 %i - %bpi = getelementptr inbounds $llvm_t, $llvm_t* %b, i64 %i - %avi = bitcast $llvm_t* %api to <$N x $llvm_t>* - %bvi = bitcast $llvm_t* %bpi to <$N x $llvm_t>* - %ai = load <$N x $llvm_t>, <$N x $llvm_t>* %avi, align $B - %bi = load <$N x $llvm_t>, <$N x $llvm_t>* %bvi, align $B - %mask1 = icmp ne <$N x $llvm_t> %ai, zeroinitializer - %mask2 = icmp ne <$N x $llvm_t> %bi, zeroinitializer - %mask3 = and <$N x i1> %mask1, %mask2 - %compressed = bitcast <$N x i1> %mask3 to i$N - %matchnotfound1 = icmp eq i$N %compressed, 0 - br i1 %matchnotfound1, label %L30, label %common.ret - - common.ret: - %retval = phi i8 [ 0, %L9 ], [ 1, %L32 ], [ 0, %L51 ], [ 1, %L67 ] - ret i8 %retval - - L30: - %vinc = add nuw nsw i64 %i, $N - %continue = icmp slt i64 %vinc, %lenm$(N-1) - br i1 %continue, label %L9, label %L32 - - L32: - %cumi = phi i64 [ 0, %top ], [ %len$N, %L30 ] - %done = icmp eq i64 %cumi, %2 - br i1 %done, label %common.ret, label %L51 - - L51: - %si = phi i64 [ %inc, %L67 ], [ %cumi, %L32 ] - %sapi = getelementptr inbounds $llvm_t, $llvm_t* %a, i64 %si - %sbpi = getelementptr inbounds $llvm_t, $llvm_t* %b, i64 %si - %savi = load $llvm_t, $llvm_t* %sapi, align $B - %sbvi = load $llvm_t, $llvm_t* %sbpi, align $B - %mask11 = icmp ne $llvm_t %savi, 0 - %mask12 = icmp ne $llvm_t %sbvi, 0 - %mask13 = and i1 %mask11, %mask12 - %matchnotfound2 = icmp eq i1 %mask13, 0 - br i1 %matchnotfound2, label %L67, label %common.ret - - L67: - %inc = add i64 %si, 1 - %dobreak = icmp eq i64 %inc, %2 - br i1 %dobreak, label %common.ret, label %L51 - } - attributes #0 = { alwaysinline } - """ - quote - GC.@preserve a b begin - Base.llvmcall( - ($textir, "entry"), - Bool, - Tuple{Ptr{T}, Ptr{T}, Int64}, - pointer(a) + sizeof(T) * offset, - pointer(b) + sizeof(T) * offset, - length(a) - offset - ) - end - end -end - -# Returns true if a < b lexicographically, and false otherwise. -@inline @generated function _vec_cmp_lex( - a::Vector{T}, - b::Vector{T}, - offset::Int=1 -) where {T <: BitInteger} - N = pick_vector_width_clamp_8(T) - - # Unfortunate case. Default to scalar code. - if N == 1 - return quote - i = 1 + offset - @inbounds while i < length(a) && a[i] == b[i] - i += 1 - end - @inbounds return a[i] < b[i] - end - end - - # The case when IntN exists. - @assert N in (8, 16, 32, 64) - B = sizeof(T) - llvm_t = jl_to_llvm_t(T) - mask = align_down(typemax(Int), N) - typecast_iN_to_i64(varname) = - if N == 64 - "" - else - "$(varname)64 = zext i$(N) $(varname)$(N) to i64\n" - end - textir = """ - declare i$N @llvm.cttz.i$N(i$N, i1); - define i8 @entry(i64 %0, i64 %1, i64 %2) #0 { - top: - %a = inttoptr i64 %0 to $llvm_t* - %b = inttoptr i64 %1 to $llvm_t* - %lenm$(N-1) = add nsw i64 %2, -$(N-1) - %dosimditer = icmp ugt i64 %2, $(N-1) - br i1 %dosimditer, label %L9.lr.ph, label %L32 - - L9.lr.ph: - %len$N = and i64 %2, $mask ; divisible by N - br label %L9 - - L9: - %i = phi i64 [ 0, %L9.lr.ph ], [ %vinc, %L30 ] - %api = getelementptr inbounds $llvm_t, $llvm_t* %a, i64 %i - %bpi = getelementptr inbounds $llvm_t, $llvm_t* %b, i64 %i - %avi = bitcast $llvm_t* %api to <$N x $llvm_t>* - %bvi = bitcast $llvm_t* %bpi to <$N x $llvm_t>* - %ai = load <$N x $llvm_t>, <$N x $llvm_t>* %avi, align $B - %bi = load <$N x $llvm_t>, <$N x $llvm_t>* %bvi, align $B - %mask = icmp ne <$N x $llvm_t> %ai, %bi - %compressed = bitcast <$N x i1> %mask to i$N - %matchfnotound = icmp eq i$N %compressed, 0 - br i1 %matchfnotound, label %L30, label %L17 - - L17: - %tz$N = call i$N @llvm.cttz.i$N(i$N %compressed, i1 true) - $(typecast_iN_to_i64("%tz")) - %vis = add nuw i64 %i, %tz64 - %sapi2 = getelementptr inbounds $llvm_t, $llvm_t* %a, i64 %vis - %sbpi2 = getelementptr inbounds $llvm_t, $llvm_t* %b, i64 %vis - %savi2 = load $llvm_t, $llvm_t* %sapi2, align $B - %sbvi2 = load $llvm_t, $llvm_t* %sbpi2, align $B - %flag1 = icmp ult $llvm_t %savi2, %sbvi2 - br label %common.ret - - common.ret: - %retflag = phi i1 [ %flag1, %L17 ], [ 0, %L32 ], [ %flag2, %L51 ], [ 0, %L67 ] - %retval = zext i1 %retflag to i8 - ret i8 %retval - - L30: - %vinc = add nuw nsw i64 %i, $N - %continue = icmp slt i64 %vinc, %lenm$(N-1) - br i1 %continue, label %L9, label %L32 - - L32: - %cumi = phi i64 [ 0, %top ], [ %len$N, %L30 ] - %done = icmp eq i64 %cumi, %2 - br i1 %done, label %common.ret, label %L51 - - L51: - %si = phi i64 [ %inc, %L67 ], [ %cumi, %L32 ] - %sapi = getelementptr inbounds $llvm_t, $llvm_t* %a, i64 %si - %sbpi = getelementptr inbounds $llvm_t, $llvm_t* %b, i64 %si - %savi = load $llvm_t, $llvm_t* %sapi, align $B - %sbvi = load $llvm_t, $llvm_t* %sbpi, align $B - %match = icmp eq $llvm_t %savi, %sbvi - %flag2 = icmp ult $llvm_t %savi, %sbvi - br i1 %match, label %L67, label %common.ret - - L67: - %inc = add i64 %si, 1 - %dobreak = icmp eq i64 %inc, %2 - br i1 %dobreak, label %common.ret, label %L51 - } - attributes #0 = { alwaysinline } - """ - quote - GC.@preserve a b begin - Base.llvmcall( - ($textir, "entry"), - Bool, - Tuple{Ptr{T}, Ptr{T}, Int64}, - pointer(a) + sizeof(T) * offset, - pointer(b) + sizeof(T) * offset, - length(a) - offset - ) - end - end -end - -# Returns true if a < b reversed lexicographically, and false otherwise. -@inline @generated function _vec_cmp_revlex( - a::Vector{T}, - b::Vector{T}, - offset::Int=1 -) where {T <: BitInteger} - N = pick_vector_width_clamp_8(T) - - # Unfortunate case. Default to scalar code. - if N == 1 - return quote - i = length(a) - @inbounds while i > 1 + offset && a[i] == b[i] - i -= 1 - end - @inbounds return a[i] > b[i] - end - end - - # The case when IntN exists. - @assert N in (8, 16, 32, 64) - B = sizeof(T) - llvm_t = jl_to_llvm_t(T) - mask = align_down(typemax(Int), N) - typecast_iN_to_i64(varname) = - if N == 64 - "" - else - "$(varname)64 = zext i$(N) $(varname)$(N) to i64\n" - end - - textir = """ - declare i$N @llvm.ctlz.i$N(i$N, i1); - define i8 @entry(i64 %0, i64 %1, i64 %2) #0 { - top: - %a = inttoptr i64 %0 to $llvm_t* - %b = inttoptr i64 %1 to $llvm_t* - %lenm$N = add nsw i64 %2, -$N - %lenm1 = add nsw i64 %2, -1 - %dosimditer = icmp sge i64 %2, $N - br i1 %dosimditer, label %L9.lr.ph, label %L32 - - L9.lr.ph: - %len$N = and i64 %2, $mask ; divisible by N - %lenmlen$N = sub nsw i64 %lenm1, %len$N - br label %L9 - - L9: - %i = phi i64 [ %lenm$N, %L9.lr.ph ], [ %vdec, %L30 ] - %api = getelementptr inbounds $llvm_t, $llvm_t* %a, i64 %i - %bpi = getelementptr inbounds $llvm_t, $llvm_t* %b, i64 %i - %avi = bitcast $llvm_t* %api to <$N x $llvm_t>* - %bvi = bitcast $llvm_t* %bpi to <$N x $llvm_t>* - %ai = load <$N x $llvm_t>, <$N x $llvm_t>* %avi, align $B - %bi = load <$N x $llvm_t>, <$N x $llvm_t>* %bvi, align $B - %mask = icmp ne <$N x $llvm_t> %ai, %bi - %compressed = bitcast <$N x i1> %mask to i$N - %matchfnotound = icmp eq i$N %compressed, 0 - br i1 %matchfnotound, label %L30, label %L17 - - L17: - %tz$N.rev = call i$N @llvm.ctlz.i$N(i$N %compressed, i1 true) - %tz$N = sub i$N $(N-1), %tz$N.rev - $(typecast_iN_to_i64("%tz")) - %vis = add nsw i64 %i, %tz64 - %sapi2 = getelementptr inbounds $llvm_t, $llvm_t* %a, i64 %vis - %sbpi2 = getelementptr inbounds $llvm_t, $llvm_t* %b, i64 %vis - %savi2 = load $llvm_t, $llvm_t* %sapi2, align $B - %sbvi2 = load $llvm_t, $llvm_t* %sbpi2, align $B - %flag1 = icmp ugt $llvm_t %savi2, %sbvi2 - br label %common.ret - - common.ret: - %retflag = phi i1 [ %flag1, %L17 ], [ 0, %L32 ], [ %flag2, %L51 ], [ 0, %L67 ] - %retval = zext i1 %retflag to i8 - ret i8 %retval - - L30: - %vdec = sub nsw i64 %i, $N - %continuesimd = icmp sge i64 %vdec, 0 - br i1 %continuesimd, label %L9, label %L32 - - L32: - %cumi = phi i64 [ %lenm1, %top ], [ %lenmlen$N, %L30 ] - %done = icmp eq i64 %cumi, -1 - br i1 %done, label %common.ret, label %L51 - - L51: - %si = phi i64 [ %dec, %L67 ], [ %cumi, %L32 ] - %sapi = getelementptr inbounds $llvm_t, $llvm_t* %a, i64 %si - %sbpi = getelementptr inbounds $llvm_t, $llvm_t* %b, i64 %si - %savi = load $llvm_t, $llvm_t* %sapi, align $B - %sbvi = load $llvm_t, $llvm_t* %sbpi, align $B - %match = icmp eq $llvm_t %savi, %sbvi - %flag2 = icmp ugt $llvm_t %savi, %sbvi - br i1 %match, label %L67, label %common.ret - - L67: - %dec = sub nsw i64 %si, 1 - %dobreak = icmp eq i64 %dec, -1 - br i1 %dobreak, label %common.ret, label %L51 - } - attributes #0 = { alwaysinline } - """ - quote - GC.@preserve a b begin - Base.llvmcall( - ($textir, "entry"), - Bool, - Tuple{Ptr{T}, Ptr{T}, Int64}, - pointer(a) + sizeof(T) * offset, - pointer(b) + sizeof(T) * offset, - length(a) - offset - ) - end - end -end diff --git a/test/groebner.jl b/test/groebner.jl index a0cd3781..29f52e36 100644 --- a/test/groebner.jl +++ b/test/groebner.jl @@ -365,7 +365,7 @@ end @test G == [y + 2131232232097 // 222222221111123 * z, x] P = prod(BigInt, prevprimes(2^31, 100)) - @test groebner([x^2 + P*x + 1]) == [x^2 + P*x + 1] + @test groebner([x^2 + P * x + 1]) == [x^2 + P * x + 1] end @testset "groebner output sorted" begin