add general matrix groups

src/matrix_groups/MatrixGroups.jl

@@ -9,10 +9,11 @@ import GroupsCore.Random # GroupsCore rand
 using ..Groups
 using Groups.KnuthBendix
 
-export SpecialLinearGroup, SymplecticGroup
+export MatrixGroup, SpecialLinearGroup, SymplecticGroup
 
 include("abstract.jl")
 
+include("matrix_group.jl")
 include("SLn.jl")
 include("Spn.jl")
 

src/matrix_groups/matrix_generators.jl

@@ -0,0 +1,36 @@
+struct MatrixElt{N,T,N²} <: Groups.GSymbol
+    id::Symbol
+    inv::Bool
+    mat::StaticArrays.SMatrix{N,N,T,N²}
+
+    function MatrixElt{N,T}(
+        id::Symbol,
+        mat::AbstractMatrix,
+        inv::Bool = false,
+    ) where {N,T}
+        n = LinearAlgebra.checksquare(mat)
+        @assert N == n
+        @assert !iszero(LinearAlgebra.det(mat))
+        return new{N,T,N^2}(id, inv, mat)
+    end
+end
+
+function MatrixElt{N}(
+    id::Symbol,
+    mat::AbstractMatrix,
+    inv::Bool = false,
+) where {N}
+    return MatrixElt{N,eltype(mat)}(id, mat, inv)
+end
+
+Base.show(io::IO, m::MatrixElt) = print(io, m.id, m.inv ? "⁻¹" : "")
+
+Base.:(==)(m::MatrixElt, n::MatrixElt) = m.mat == n.mat
+
+Base.hash(m::MatrixElt, h::UInt) = hash(m.mat, hash(typeof(m), h))
+
+function Base.inv(m::MatrixElt{N,T}) where {N,T}
+    return MatrixElt{N,T}(m.id, round.(T, inv(m.mat)), !m.inv)
+end
+
+matrix(m::MatrixElt) = m.mat

src/matrix_groups/matrix_group.jl

@@ -0,0 +1,25 @@
+include("matrix_generators.jl")
+
+struct MatrixGroup{N,T,R,S} <: AbstractMatrixGroup{N,T}
+    base_ring::R
+    alphabet::Alphabet{S}
+    gens::Vector{S}
+end
+
+function MatrixGroup{N}(
+    gens::AbstractVector{<:AbstractMatrix{T}},
+    base_ring = T,
+) where {N,T}
+    S = map(enumerate(gens)) do (i, mat)
+        id = Symbol('m', Groups.subscriptify(i))
+        return MatrixElt{N}(id, mat)
+    end
+    alphabet = Alphabet(S)
+
+    R = typeof(base_ring)
+    St = eltype(S)
+
+    return MatrixGroup{N,T,R,St}(base_ring, alphabet, S)
+end
+
+GroupsCore.ngens(M::MatrixGroup) = length(M.gens)