feat: clean up for algebras

docs/src/.vitepress/config.mts

@@ -95,6 +95,7 @@ export default defineConfig({
                 { text: 'Introduction', link: 'manual/algebras/intro'},
                 { text: 'Basics', link: 'manual/algebras/basics'},
                 { text: 'Structure constant algebras', link: 'manual/algebras/structureconstant'},
+                { text: 'Ideals', link: 'manual/algebras/ideals'},
               ]
             },
             {

docs/src/manual/algebras/basics.md

@@ -9,7 +9,7 @@ end
 
 ## Creation of algebras
 
-See the corresponding sections in ?????
+See the corresponding sections on [structure constant algebras](@ref SCA).
 ```@docs
 zero_algebra(::Field)
 ```

docs/src/manual/algebras/structureconstant.md

@@ -1,4 +1,4 @@
-# Structure constant algebras
+# [Structure constant algebras](@id SCA)
 
 ```@meta
 CurrentModule = Hecke

src/AlgAss/AbsAlgAss.jl

@@ -727,7 +727,7 @@ of the basis elements of $A$ and a map from $B$ to $A$.
 function regular_matrix_algebra(A::Union{ StructureConstantAlgebra, GroupAlgebra })
   K = base_ring(A)
   B = matrix_algebra(K, [ representation_matrix(A[i], :right) for i = 1:dim(A) ], isbasis = true)
-  return B, hom(B, A, identity_matrix(K, dim(A)), identity_matrix(K, dim(A)))
+  return B, hom(B, A, identity_matrix(K, dim(A)), identity_matrix(K, dim(A)); check = false)
 end
 
 ###############################################################################
@@ -1117,7 +1117,7 @@ function product_of_components_with_projection(A::AbstractAssociativeAlgebra, a:
   for b in basis(A)
     push!(imgs, sum(injstoB[i](injs[i]\b) for i in eachindex(a); init = zero(B)))
   end
-  p = hom(A, B, basis_matrix(imgs))
+  p = hom(A, B, basis_matrix(imgs); check = false)
   _transport_refined_wedderburn_decomposition_forward(p)
   return B, p
 end

src/AlgAss/AlgGrp.jl

@@ -10,7 +10,7 @@ denominator_of_multiplication_table(A::GroupAlgebra{QQFieldElem}) = one(ZZ)
 
 base_ring(A::GroupAlgebra{T}) where {T} = A.base_ring::parent_type(T)
 
-base_ring_type(::Type{GroupAlgebra{T}}) where {T} = parent_type(T)
+base_ring_type(::Type{GroupAlgebra{T, S, R}}) where {T, S, R} = parent_type(T)
 
 Generic.dim(A::GroupAlgebra) = size(multiplication_table(A, copy = false), 1)
 

src/AlgAss/AlgMat.jl

@@ -14,7 +14,13 @@
 
 coefficient_ring(A::MatAlgebra{T, S}) where {T, S} = A.coefficient_ring::base_ring_type(S)
 
-basis(A::MatAlgebra) = A.basis::Vector{elem_type(A)}
+function basis(A::MatAlgebra; copy::Bool = true)
+  if copy
+    return Base.copy(A.basis::Vector{elem_type(A)})
+  else
+    return A.basis::Vector{elem_type(A)}
+  end
+end
 
 has_one(A::MatAlgebra) = true
 

src/AlgAss/Elem.jl

@@ -644,6 +644,11 @@ function (A::GroupAlgebra)(a::GroupAlgebraElem)
   return a
 end
 
+function (A::MatAlgebra)(a::MatAlgebraElem)
+  @assert parent(a) == A "Wrong parent"
+  return a
+end
+
 # For polynomial substitution
 for T in subtypes(AbstractAssociativeAlgebra)
   @eval begin