simplify parametrisation of SLn and Spn

src/matrix_groups/SLn.jl

@@ -1,25 +1,26 @@
 include("eltary_matrices.jl")
 
-struct SpecialLinearGroup{N,T,R,A,S} <: AbstractMatrixGroup{N,T}
+struct SpecialLinearGroup{N,T,R,S} <: AbstractMatrixGroup{N,T}
     base_ring::R
-    alphabet::A
-    gens::S
+    alphabet::Alphabet{S}
+    gens::Vector{S}
 
     function SpecialLinearGroup{N}(base_ring) where {N}
-        S = [ElementaryMatrix{N}(i, j, one(base_ring)) for i in 1:N for j in 1:N if i ≠ j]
+        S = [
+            ElementaryMatrix{N}(i, j, one(base_ring)) for i in 1:N for
+            j in 1:N if i ≠ j
+        ]
         alphabet = Alphabet(S)
 
-        return new{
-            N,
-            eltype(base_ring),
-            typeof(base_ring),
-            typeof(alphabet),
-            typeof(S)
-        }(base_ring, alphabet, S)
+        T = eltype(base_ring)
+        R = typeof(base_ring)
+        St = eltype(S)
+
+        return new{N,T,R,St}(base_ring, alphabet, S)
     end
 end
 
-GroupsCore.ngens(SL::SpecialLinearGroup{N}) where {N} = N^2 - N
+GroupsCore.ngens(SL::SpecialLinearGroup) = length(SL.gens)
 
 function Base.show(io::IO, ::SpecialLinearGroup{N,T}) where {N,T}
     return print(io, "SL{$N,$T}")

src/matrix_groups/Spn.jl

@@ -1,21 +1,19 @@
 include("eltary_symplectic.jl")
 
-struct SymplecticGroup{N,T,R,A,S} <: AbstractMatrixGroup{N,T}
+struct SymplecticGroup{N,T,R,S} <: AbstractMatrixGroup{N,T}
     base_ring::R
-    alphabet::A
-    gens::S
+    alphabet::Alphabet{S}
+    gens::Vector{S}
 
     function SymplecticGroup{N}(base_ring) where {N}
         S = symplectic_gens(N, eltype(base_ring))
         alphabet = Alphabet(S)
 
-        return new{
-            N,
-            eltype(base_ring),
-            typeof(base_ring),
-            typeof(alphabet),
-            typeof(S)
-        }(base_ring, alphabet, S)
+        T = eltype(base_ring)
+        R = typeof(base_ring)
+        St = eltype(S)
+
+        return new{N,T,R,St}(base_ring, alphabet, S)
     end
 end