DOC: show AlgebraicPetri SciML integration

docs/src/AlgebraicPetri.md

@@ -1,6 +1,3 @@
-````@meta
-Draft=false
-````
 # AlgebraicPetri.jl Integration
 
 You can construct a [`ContinuousResourceSharer`](@ref) from an Open Petri Net for any kind of network supported by [AlgebraicPetri.jl](https://algebraicjulia.github.io/AlgebraicPetri.jl/dev/) including:
@@ -13,6 +10,40 @@ You can construct a [`ContinuousResourceSharer`](@ref) from an Open Petri Net fo
 using AlgebraicPetri
 using AlgebraicDynamics
 using Catlab.Graphics
+Brusselator = PetriNet(6,
+  (1 => (5, 1)),
+  ((5, 5, 6) => (5, 5, 5)),
+  ((2, 5) => (6, 3, 2)),
+  (5 => 4)
+)
+to_graphviz(Brusselator)
+````
+You just call the constructor for ContinuousResourceSharer on an Open Petri Net. 
+The constructor knows where to use labels or integers for the state variables.
+It also knows to get parameters from the ReactionNet and enclose them into the dynamics.
+
+
+````@example AlgPetri
+open_bruss = Open([1, 3], Brusselator, [1, 2])
+rs = ContinuousResourceSharer{Float64}(open_bruss)
+````
+
+For the PetriNet case, you supply the state and parameters with regular arrays.
+
+````@example AlgPetri
+using OrdinaryDiffEq
+using Plots
+tspan = (0.0,100.0)
+params = [1.0, 1., 1., 1.0]
+u0 = [1,3.7,0.0,0.0,1,1]
+prob = ODEProblem(rs, u0, tspan, params)
+soln = solve(prob, Tsit5())
+plot(soln, idxs=[5,6])
+````
+
+For the LabelledPetriNet case, you supply the state and parameters with `LArray`.
+
+````@example AlgPetri
 Brusselator = LabelledPetriNet([:A, :B, :D, :E, :X, :Y],
   :t1 => (:A => (:X, :A)),
   :t2 => ((:X, :X, :Y) => (:X, :X, :X)),
@@ -22,11 +53,21 @@ Brusselator = LabelledPetriNet([:A, :B, :D, :E, :X, :Y],
 to_graphviz(Brusselator)
 ````
 
-You just call the constructor for ContinuousResourceSharer on an Open Petri Net. 
-The constructor knows where to use labels or integers for the state variables.
-It also knows to get parameters from the ReactionNet and enclose them into the dynamics.
-
 ````@example AlgPetri
 open_bruss = Open([:A, :D], Brusselator, [:A, :B])
 rs = ContinuousResourceSharer{Float64}(open_bruss)
+````
+
+!!! note
+@example AlgPetri
+    SciML integration for LabelledArrays is broken due to this [issue](https://github.com/SciML/LabelledArrays.jl/issues/162) on LabelledArrays.jl. Once that issue is closed, you should be able to solve LabelledPetriNets with SciML Solvers.
+
+````julia
+using LabelledArrays
+tspan = (0.0,100.0)
+params = LVector(t1=1.0, t2=1.2, t3=3.14, t4=0.1)
+u0 = LVector(A=1.0, B=3.17, D=0.0, E=0.0, X=1.0, Y=1.9)
+prob = ODEProblem((u,p,t) -> eval_dynamics(rs, u, p, t), u0, tspan, params)
+sol = solve(prob, Tsit5())
+plot(sol, idxs=[:X, :Y])
 ````