formatting

src/abelianize.jl

@@ -1,7 +1,7 @@
 function _abelianize(
     i::Integer,
     source::AutomorphismGroup{<:FreeGroup},
-    target::MatrixGroups.SpecialLinearGroup{N, T}) where {N, T}
+    target::MatrixGroups.SpecialLinearGroup{N,T}) where {N,T}
     n = ngens(object(source))
     @assert n == N
     aut = alphabet(source)[i]
@@ -10,10 +10,10 @@ function _abelianize(
         # Automorphisms act on the right which corresponds to action on
         # the columns in the matrix case
         eij = MatrixGroups.ElementaryMatrix{N}(
-                aut.j,
+            aut.j,
-                aut.i,
+            aut.i,
-                ifelse(aut.inv, -one(T), one(T))
+            ifelse(aut.inv, -one(T), one(T))
-            )
+        )
         k = alphabet(target)[eij]
         return word_type(target)([k])
     else
@@ -24,7 +24,7 @@ end
 function _abelianize(
     i::Integer,
     source::AutomorphismGroup{<:Groups.SurfaceGroup},
-    target::MatrixGroups.SpecialLinearGroup{N, T}) where {N, T}
+    target::MatrixGroups.SpecialLinearGroup{N,T}) where {N,T}
     n = ngens(Groups.object(source))
     @assert n == N
     g = alphabet(source)[i].autFn_word
@@ -39,8 +39,8 @@ end
 function Groups._abelianize(
     i::Integer,
     source::AutomorphismGroup{<:Groups.SurfaceGroup},
-    target::MatrixGroups.SymplecticGroup{N, T}
+    target::MatrixGroups.SymplecticGroup{N,T}
-) where {N, T}
+) where {N,T}
     @assert iseven(N)
     As = alphabet(source)
     At = alphabet(target)
@@ -53,7 +53,7 @@ function Groups._abelianize(
     ab = Groups.Homomorphism(Groups._abelianize, source, SlN, check=false)
 
     matrix_spn_map = let S = gens(target)
-        Dict(MatrixGroups.matrix_repr(g)=> word(g) for g in union(S, inv.(S)))
+        Dict(MatrixGroups.matrix_repr(g) => word(g) for g in union(S, inv.(S)))
     end
 
     # renumeration:
@@ -63,7 +63,7 @@ function Groups._abelianize(
     p = [reverse(2:2:N); reverse(1:2:N)]
 
     g = source([i])
-    Mg = MatrixGroups.matrix_repr(ab(g))[p,p]
+    Mg = MatrixGroups.matrix_repr(ab(g))[p, p]
 
     return matrix_spn_map[Mg]
 end

src/aut_groups/gersten_relations.jl

@@ -1,4 +1,4 @@
-function gersten_alphabet(n::Integer; commutative::Bool = true)
+function gersten_alphabet(n::Integer; commutative::Bool=true)
     indexing = [(i, j) for i in 1:n for j in 1:n if i ≠ j]
     S = [ϱ(i, j) for (i, j) in indexing]
 
@@ -6,7 +6,7 @@ function gersten_alphabet(n::Integer; commutative::Bool = true)
         append!(S, [λ(i, j) for (i, j) in indexing])
     end
 
-    return Alphabet(S)
+    return Alphabet(mapreduce(x -> [x, inv(x)], union, S))
 end
 
 function _commutation_rule(
@@ -41,12 +41,12 @@ function _hexagonal_rule(
 end
 
 gersten_relations(n::Integer; commutative) =
-    gersten_relations(Word{UInt8}, n, commutative = commutative)
+    gersten_relations(Word{UInt8}, n, commutative=commutative)
 
 function gersten_relations(::Type{W}, n::Integer; commutative) where {W<:AbstractWord}
     @assert n > 1 "Gersten relations are defined only for n>1, got n=$n"
-    A = gersten_alphabet(n, commutative = commutative)
+    A = gersten_alphabet(n, commutative=commutative)
-    @assert length(A) <= KnuthBendix._max_alphabet_length(W) "Type $W can not represent words over alphabet with $(length(A)) letters."
+    @assert length(A) <= typemax(eltype(W)) "Type $W can not represent words over alphabet with $(length(A)) letters."
 
     rels = Pair{W,W}[]
 

src/aut_groups/mcg.jl

@@ -17,7 +17,7 @@ function Base.show(io::IO, S::SurfaceGroup)
     end
 end
 
-function SurfaceGroup(genus::Integer, boundaries::Integer)
+function SurfaceGroup(genus::Integer, boundaries::Integer, W=Word{Int16})
     @assert genus > 1
 
     # The (confluent) rewriting systems comes from
@@ -30,15 +30,15 @@ function SurfaceGroup(genus::Integer, boundaries::Integer)
 
     ltrs = String[]
     for i in 1:genus
-        subscript = join('₀'+d for d in reverse(digits(i)))
+        subscript = join('₀' + d for d in reverse(digits(i)))
         append!(ltrs, ["A" * subscript, "a" * subscript, "B" * subscript, "b" * subscript])
     end
     Al = Alphabet(reverse!(ltrs))
 
     for i in 1:genus
-        subscript = join('₀'+d for d in reverse(digits(i)))
+        subscript = join('₀' + d for d in reverse(digits(i)))
-        KnuthBendix.set_inversion!(Al, "a" * subscript, "A" * subscript)
+        KnuthBendix.setinverse!(Al, "a" * subscript, "A" * subscript)
-        KnuthBendix.set_inversion!(Al, "b" * subscript, "B" * subscript)
+        KnuthBendix.setinverse!(Al, "b" * subscript, "B" * subscript)
     end
 
     if boundaries == 0
@@ -46,10 +46,10 @@ function SurfaceGroup(genus::Integer, boundaries::Integer)
 
         for i in reverse(1:genus)
             x = 4 * i
-            append!(word, [x, x-2, x-1, x-3])
+            append!(word, [x, x - 2, x - 1, x - 3])
         end
-        comms = Word(word)
+        comms = W(word)
-        word_rels = [ comms => one(comms) ]
+        word_rels = [comms => one(comms)]
 
         rws = let R = KnuthBendix.RewritingSystem(word_rels, KnuthBendix.Recursive(Al))
             KnuthBendix.IndexAutomaton(KnuthBendix.knuthbendix(R))
@@ -60,11 +60,11 @@ function SurfaceGroup(genus::Integer, boundaries::Integer)
             KnuthBendix.IndexAutomaton(KnuthBendix.knuthbendix(R))
         end
     else
-        throw("Not Implemented")
+        throw("Not Implemented for MCG with $boundaryies boundary components")
     end
 
-    F = FreeGroup(alphabet(rws))
+    F = FreeGroup(Al)
-    rels = [F(lhs)=>F(rhs) for (lhs,rhs) in word_rels]
+    rels = [F(lhs) => F(rhs) for (lhs, rhs) in word_rels]
 
     return SurfaceGroup(genus, boundaries, [Al[i] for i in 2:2:length(Al)], rels, rws)
 end
@@ -77,13 +77,13 @@ function symplectic_twists(π₁Σ::SurfaceGroup)
 
     saut = SpecialAutomorphismGroup(FreeGroup(2g), max_rules=1000)
 
-    Aij  = [SymplecticMappingClass(saut, :A, i, j) for i in 1:g for j in 1:g if i≠j]
+    Aij = [SymplecticMappingClass(saut, :A, i, j) for i in 1:g for j in 1:g if i ≠ j]
 
-    Bij  = [SymplecticMappingClass(saut, :B, i, j) for i in 1:g for j in 1:g if i≠j]
+    Bij = [SymplecticMappingClass(saut, :B, i, j) for i in 1:g for j in 1:g if i ≠ j]
 
-    mBij = [SymplecticMappingClass(saut, :B, i, j, minus=true) for i in 1:g for j in 1:g if i≠j]
+    mBij = [SymplecticMappingClass(saut, :B, i, j, minus=true) for i in 1:g for j in 1:g if i ≠ j]
 
-    Bii  = [SymplecticMappingClass(saut, :B, i, i) for i in 1:g]
+    Bii = [SymplecticMappingClass(saut, :B, i, i) for i in 1:g]
 
     mBii = [SymplecticMappingClass(saut, :B, i, i, minus=true) for i in 1:g]
 
@@ -99,6 +99,6 @@ function AutomorphismGroup(π₁Σ::SurfaceGroup; kwargs...)
     # this is to fix the definitions of symplectic twists:
     # with i->gens(π₁Σ, i) the corresponding automorphisms return
     # reversed words
-    domain = ntuple(i->inv(gens(π₁Σ, i)), 2genus(π₁Σ))
+    domain = ntuple(i -> inv(gens(π₁Σ, i)), 2genus(π₁Σ))
     return AutomorphismGroup(π₁Σ, S, A, domain)
 end

src/aut_groups/sautFn.jl

@@ -1,7 +1,7 @@
 include("transvections.jl")
 include("gersten_relations.jl")
 
-function SpecialAutomorphismGroup(F::FreeGroup; ordering = KnuthBendix.LenLex, kwargs...)
+function SpecialAutomorphismGroup(F::FreeGroup; ordering=KnuthBendix.LenLex, kwargs...)
 
     n = length(alphabet(F)) ÷ 2
     A, rels = gersten_relations(n, commutative=false)
@@ -21,5 +21,5 @@ end
 
 function relations(G::AutomorphismGroup{<:FreeGroup})
     n = length(alphabet(object(G))) ÷ 2
-    return last(gersten_relations(n, commutative = false))
+    return last(gersten_relations(n, commutative=false))
 end

src/aut_groups/symplectic_twists.jl

@@ -73,7 +73,7 @@ function Te(λ::ΡΛ, ϱ::ΡΛ, i, j)
     @assert λ.id == :λ && ϱ.id == :ϱ
 
     @assert iseven(λ.N)
-    genus = λ.N÷2
+    genus = λ.N ÷ 2
     i = mod1(i, genus)
     j = mod1(j, genus)
 
@@ -118,7 +118,7 @@ end
 
 function rotation_element(λ::ΡΛ, ϱ::ΡΛ)
     @assert iseven(λ.N)
-    genus = λ.N÷2
+    genus = λ.N ÷ 2
     A = λ.A
 
     halftwists = map(1:genus-1) do i
@@ -168,7 +168,7 @@ function mcg_twists(G::AutomorphismGroup{<:FreeGroup})
     return Tas, Tαs, Tes
 end
 
-struct SymplecticMappingClass{T, F} <: GSymbol
+struct SymplecticMappingClass{T,F} <: GSymbol
     id::Symbol # :A, :B
     i::UInt
     j::UInt
@@ -187,13 +187,13 @@ function SymplecticMappingClass(
     id::Symbol,
     i::Integer,
     j::Integer;
-    minus = false,
+    minus=false,
-    inverse = false,
+    inverse=false
 )
     @assert i > 0 && j > 0
     id === :A && @assert i ≠ j
     @assert iseven(ngens(object(sautFn)))
-    genus = ngens(object(sautFn))÷2
+    genus = ngens(object(sautFn)) ÷ 2
 
     A = alphabet(sautFn)
     λ = ΡΛ(:λ, A, 2genus)
@@ -241,7 +241,7 @@ end
 
 function Base.show(io::IO, smc::SymplecticMappingClass)
     smc.minus && print(io, 'm')
-    if  smc.i < 10 && smc.j < 10
+    if smc.i < 10 && smc.j < 10
         print(io, smc.id, subscriptify(smc.i), subscriptify(smc.j))
     else
         print(io, smc.id, subscriptify(smc.i), ".", subscriptify(smc.j))

src/aut_groups/transvections.jl

@@ -4,7 +4,7 @@ struct Transvection <: GSymbol
     j::UInt16
     inv::Bool
 
-    function Transvection(id::Symbol, i::Integer, j::Integer, inv = false)
+    function Transvection(id::Symbol, i::Integer, j::Integer, inv=false)
         @assert id in (:ϱ, :λ)
         return new(id, i, j, inv)
     end
@@ -33,7 +33,7 @@ Base.hash(t::Transvection, h::UInt) = hash(hash(t.id, hash(t.i)), hash(t.j, hash
 Base.@propagate_inbounds @inline function evaluate!(
     v::NTuple{T,N},
     t::Transvection,
-    tmp = one(first(v)),
+    tmp=one(first(v)),
 ) where {T,N}
     i, j = t.i, t.j
     @assert 1 ≤ i ≤ length(v) && 1 ≤ j ≤ length(v)
@@ -92,4 +92,4 @@ Base.inv(p::PermRightAut) = PermRightAut(invperm(p.perm))
 Base.:(==)(p::PermRightAut, q::PermRightAut) = p.perm == q.perm
 Base.hash(p::PermRightAut, h::UInt) = hash(p.perm, hash(PermRightAut, h))
 
-evaluate!(v::NTuple{T,N}, p::PermRightAut, tmp = nothing) where {T,N} = v[p.perm]
+evaluate!(v::NTuple{T,N}, p::PermRightAut, tmp=nothing) where {T,N} = v[p.perm]

src/autgroups.jl

@@ -104,8 +104,8 @@ evaluate(f::AbstractFPGroupElement{<:AutomorphismGroup}) = evaluate!(domain(f),
 function evaluate!(
     t::NTuple{N,T},
     f::AbstractFPGroupElement{<:AutomorphismGroup{<:Group}},
-    tmp = one(first(t)),
+    tmp=one(first(t)),
-) where {N, T<:FPGroupElement}
+) where {N,T<:FPGroupElement}
     A = alphabet(f)
     for idx in word(f)
         t = @inbounds evaluate!(t, A[idx], tmp)::NTuple{N,T}
@@ -113,12 +113,12 @@ function evaluate!(
     return t
 end
 
-evaluate!(t::NTuple{N, T}, s::GSymbol, tmp=nothing) where {N, T} = throw("you need to implement `evaluate!(::$(typeof(t)), ::$(typeof(s)), ::Alphabet, tmp=one(first(t)))`")
+evaluate!(t::NTuple{N,T}, s::GSymbol, tmp=nothing) where {N,T} = throw("you need to implement `evaluate!(::$(typeof(t)), ::$(typeof(s)), ::Alphabet, tmp=one(first(t)))`")
 
 # forward evaluate by substitution
 
-struct LettersMap{T, A}
+struct LettersMap{T,A}
-    indices_map::Dict{Int, T}
+    indices_map::Dict{Int,T}
     A::A
 end
 
@@ -201,13 +201,14 @@ function generated_evaluate(a::FPGroupElement{<:AutomorphismGroup})
             throw("Letter $l doesn't seem to be mapped anywhere!")
         end
     end
-    locals = Dict{Expr, Symbol}()
+    locals = Dict{Expr,Symbol}()
     locals_counter = 0
-    for (i,v) in enumerate(args)
+    for (i, v) in enumerate(args)
         @assert length(v.args) >= 2
         if length(v.args) > 2
             for (j, a) in pairs(v.args)
-                if a isa Expr &&  a.head == :call "$a"
+                if a isa Expr && a.head == :call
+                    "$a"
                     @assert a.args[1] == :inv
                     if !(a in keys(locals))
                         locals[a] = Symbol("var_#$locals_counter")
@@ -222,7 +223,7 @@ function generated_evaluate(a::FPGroupElement{<:AutomorphismGroup})
     end
 
     q = quote
-        $([:(local $v = $k) for (k,v) in locals]...)
+        $([:(local $v = $k) for (k, v) in locals]...)
     end
 
     # return args, locals

src/constructions/direct_power.jl

@@ -30,7 +30,7 @@ function Base.iterate(G::DirectPower)
     res = iterate(itr)
     @assert res !== nothing
     elt = DirectPowerElement(first(res), G)
-    return elt, (iterator = itr, state = last(res))
+    return elt, (iterator=itr, state=last(res))
 end
 
 function Base.iterate(G::DirectPower, state)
@@ -38,7 +38,7 @@ function Base.iterate(G::DirectPower, state)
     res = iterate(itr, st)
     res === nothing && return nothing
     elt = DirectPowerElement(first(res), G)
-    return elt, (iterator = itr, state = last(res))
+    return elt, (iterator=itr, state=last(res))
 end
 
 function Base.IteratorSize(::Type{<:DirectPower{Gr,N}}) where {Gr,N}
@@ -52,7 +52,7 @@ Base.size(G::DirectPower) = ntuple(_ -> length(G.group), _nfold(G))
 GroupsCore.order(::Type{I}, G::DirectPower) where {I<:Integer} =
     convert(I, order(I, G.group)^_nfold(G))
 
-GroupsCore.ngens(G::DirectPower) = _nfold(G)*ngens(G.group)
+GroupsCore.ngens(G::DirectPower) = _nfold(G) * ngens(G.group)
 
 function GroupsCore.gens(G::DirectPower, i::Integer)
     k = ngens(G.group)
@@ -66,7 +66,7 @@ end
 function GroupsCore.gens(G::DirectPower)
     N = _nfold(G)
     S = gens(G.group)
-    tups = [ntuple(j->(i == j ? s : one(s)), N) for i in 1:N for s in S]
+    tups = [ntuple(j -> (i == j ? s : one(s)), N) for i in 1:N for s in S]
 
     return [DirectPowerElement(elts, G) for elts in tups]
 end
@@ -99,7 +99,7 @@ function Base.:(*)(g::DirectPowerElement, h::DirectPowerElement)
 end
 
 GroupsCore.order(::Type{I}, g::DirectPowerElement) where {I<:Integer} =
-    convert(I, reduce(lcm, (order(I, h) for h in g.elts), init = one(I)))
+    convert(I, reduce(lcm, (order(I, h) for h in g.elts), init=one(I)))
 
 Base.isone(g::DirectPowerElement) = all(isone, g.elts)
 

src/constructions/direct_product.jl

@@ -25,7 +25,7 @@ function Base.iterate(G::DirectProduct)
     res = iterate(itr)
     @assert res !== nothing
     elt = DirectProductElement(first(res), G)
-    return elt, (iterator = itr, state = last(res))
+    return elt, (iterator=itr, state=last(res))
 end
 
 function Base.iterate(G::DirectProduct, state)
@@ -33,7 +33,7 @@ function Base.iterate(G::DirectProduct, state)
     res = iterate(itr, st)
     res === nothing && return nothing
     elt = DirectProductElement(first(res), G)
-    return elt, (iterator = itr, state = last(res))
+    return elt, (iterator=itr, state=last(res))
 end
 
 function Base.IteratorSize(::Type{<:DirectProduct{Gt,Ht}}) where {Gt,Ht}

src/constructions/wreath_product.jl

@@ -52,7 +52,7 @@ function Base.iterate(G::WreathProduct)
     res = iterate(itr)
     @assert res !== nothing
     elt = WreathProductElement(first(res)..., G)
-    return elt, (iterator = itr, state = last(res))
+    return elt, (iterator=itr, state=last(res))
 end
 
 function Base.iterate(G::WreathProduct, state)
@@ -60,7 +60,7 @@ function Base.iterate(G::WreathProduct, state)
     res = iterate(itr, st)
     res === nothing && return nothing
     elt = WreathProductElement(first(res)..., G)
-    return elt, (iterator = itr, state = last(res))
+    return elt, (iterator=itr, state=last(res))
 end
 
 function Base.IteratorSize(::Type{<:WreathProduct{DP,PGr}}) where {DP,PGr}

src/homomorphisms.jl

@@ -58,8 +58,8 @@ true
 ```
 
 """
-struct Homomorphism{Gr1, Gr2, I, W}
+struct Homomorphism{Gr1,Gr2,I,W}
-    gens_images::Dict{I, W}
+    gens_images::Dict{I,W}
     source::Gr1
     target::Gr2
 
@@ -70,11 +70,11 @@ struct Homomorphism{Gr1, Gr2, I, W}
         check=true
     )
         A = alphabet(source)
-        dct = Dict(i=>convert(word_type(target), f(i, source, target))
+        dct = Dict(i => convert(word_type(target), f(i, source, target))
-            for i in 1:length(A))
+                   for i in 1:length(A))
         I = eltype(word_type(source))
         W = word_type(target)
-        hom = new{typeof(source), typeof(target), I, W}(dct, source, target)
+        hom = new{typeof(source),typeof(target),I,W}(dct, source, target)
 
         if check
             @assert hom(one(source)) == one(target)
@@ -83,8 +83,8 @@ struct Homomorphism{Gr1, Gr2, I, W}
                 @assert hom(x^-1) == hom(x)^-1
 
                 for y in gens(source)
-                    @assert hom(x*y) == hom(x)*hom(y)
+                    @assert hom(x * y) == hom(x) * hom(y)
-                    @assert hom(x*y)^-1 == hom(y^-1)*hom(x^-1)
+                    @assert hom(x * y)^-1 == hom(y^-1) * hom(x^-1)
                 end
             end
             for (lhs, rhs) in relations(source)

src/iteration.jl

@@ -1,4 +1,4 @@
-mutable struct FPGroupIter{S, T, GEl}
+mutable struct FPGroupIter{S,T,GEl}
     seen::S
     seen_iter_state::T
     current::GEl

src/matrix_groups/SLn.jl

@@ -1,12 +1,12 @@
 include("eltary_matrices.jl")
 
-struct SpecialLinearGroup{N, T, R, A, S} <: MatrixGroup{N,T}
+struct SpecialLinearGroup{N,T,R,A,S} <: MatrixGroup{N,T}
     base_ring::R
     alphabet::A
     gens::S
 
-    function SpecialLinearGroup{N}(base_ring) where N
+    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{
@@ -19,16 +19,16 @@ struct SpecialLinearGroup{N, T, R, A, S} <: MatrixGroup{N,T}
     end
 end
 
-GroupsCore.ngens(SL::SpecialLinearGroup{N}) where N = N^2 - N
+GroupsCore.ngens(SL::SpecialLinearGroup{N}) where {N} = N^2 - N
 
-Base.show(io::IO, SL::SpecialLinearGroup{N, T}) where {N, T} =
+Base.show(io::IO, SL::SpecialLinearGroup{N,T}) where {N,T} =
     print(io, "special linear group of $N×$N matrices over $T")
 
 function Base.show(
     io::IO,
     ::MIME"text/plain",
     sl::Groups.AbstractFPGroupElement{<:SpecialLinearGroup{N}}
-) where N
+) where {N}
 
     Groups.normalform!(sl)
 

src/matrix_groups/Spn.jl

@@ -1,11 +1,11 @@
 include("eltary_symplectic.jl")
 
-struct SymplecticGroup{N, T, R, A, S} <: MatrixGroup{N,T}
+struct SymplecticGroup{N,T,R,A,S} <: MatrixGroup{N,T}
     base_ring::R
     alphabet::A
     gens::S
 
-    function SymplecticGroup{N}(base_ring) where N
+    function SymplecticGroup{N}(base_ring) where {N}
         S = symplectic_gens(N, eltype(base_ring))
         alphabet = Alphabet(S)
 
@@ -21,7 +21,7 @@ end
 
 GroupsCore.ngens(Sp::SymplecticGroup) = length(Sp.gens)
 
-Base.show(io::IO, ::SymplecticGroup{N}) where N = print(io, "group of $N×$N symplectic matrices")
+Base.show(io::IO, ::SymplecticGroup{N}) where {N} = print(io, "group of $N×$N symplectic matrices")
 
 function Base.show(
     io::IO,
@@ -35,15 +35,15 @@ function Base.show(
     Base.print_array(io, matrix_repr(sp))
 end
 
-_offdiag_idcs(n) = ((i,j) for i in 1:n for j in 1:n if i ≠ j)
+_offdiag_idcs(n) = ((i, j) for i in 1:n for j in 1:n if i ≠ j)
 
 function symplectic_gens(N, T=Int8)
     iseven(N) || throw(ArgumentError("N needs to be even!"))
-    n = N÷2
+    n = N ÷ 2
 
-    a_ijs = [ElementarySymplectic{N}(:A, i,j, one(T)) for (i,j) in _offdiag_idcs(n)]
+    a_ijs = [ElementarySymplectic{N}(:A, i, j, one(T)) for (i, j) in _offdiag_idcs(n)]
-    b_is =  [ElementarySymplectic{N}(:B, n+i,i, one(T)) for i in 1:n]
+    b_is = [ElementarySymplectic{N}(:B, n + i, i, one(T)) for i in 1:n]
-    c_ijs = [ElementarySymplectic{N}(:B, n+i,j, one(T)) for (i,j) in _offdiag_idcs(n)]
+    c_ijs = [ElementarySymplectic{N}(:B, n + i, j, one(T)) for (i, j) in _offdiag_idcs(n)]
 
     S = [a_ijs; b_is; c_ijs]
 
@@ -53,18 +53,18 @@ function symplectic_gens(N, T=Int8)
 end
 
 function _std_symplectic_form(m::AbstractMatrix)
-    r,c = size(m)
+    r, c = size(m)
     r == c || return false
     iseven(r) || return false
 
-    n = r÷2
+    n = r ÷ 2
     𝕆 = zeros(eltype(m), n, n)
-    𝕀 = one(eltype(m))*LinearAlgebra.I
+    𝕀 = one(eltype(m)) * LinearAlgebra.I
     Ω = [𝕆 -𝕀
-         𝕀  𝕆]
+        𝕀 𝕆]
     return Ω
 end
 
-function issymplectic(mat::M, Ω = _std_symplectic_form(mat)) where M <: AbstractMatrix
+function issymplectic(mat::M, Ω=_std_symplectic_form(mat)) where {M<:AbstractMatrix}
     return Ω == transpose(mat) * Ω * mat
 end

src/matrix_groups/abstract.jl

@@ -1,17 +1,17 @@
-abstract type MatrixGroup{N, T} <: Groups.AbstractFPGroup end
+abstract type MatrixGroup{N,T} <: Groups.AbstractFPGroup end
-const MatrixGroupElement{N, T} = Groups.AbstractFPGroupElement{<:MatrixGroup{N, T}}
+const MatrixGroupElement{N,T} = Groups.AbstractFPGroupElement{<:MatrixGroup{N,T}}
 
-Base.isone(g::MatrixGroupElement{N, T}) where {N, T} =
+Base.isone(g::MatrixGroupElement{N,T}) where {N,T} =
     isone(word(g)) || matrix_repr(g) == LinearAlgebra.I
 
-function Base.:(==)(m1::M1, m2::M2) where {M1<:MatrixGroupElement, M2<:MatrixGroupElement}
+function Base.:(==)(m1::M1, m2::M2) where {M1<:MatrixGroupElement,M2<:MatrixGroupElement}
     parent(m1) === parent(m2) || return false
     word(m1) == word(m2) && return true
     return matrix_repr(m1) == matrix_repr(m2)
 end
 
-Base.size(m::MatrixGroupElement{N}) where N = (N, N)
+Base.size(m::MatrixGroupElement{N}) where {N} = (N, N)
-Base.eltype(m::MatrixGroupElement{N, T}) where {N, T} = T
+Base.eltype(m::MatrixGroupElement{N,T}) where {N,T} = T
 
 # three structural assumptions about matrix groups
 Groups.word(sl::MatrixGroupElement) = sl.word
@@ -22,9 +22,9 @@ Groups.rewriting(M::MatrixGroup) = alphabet(M)
 Base.hash(sl::MatrixGroupElement, h::UInt) =
     hash(matrix_repr(sl), hash(parent(sl), h))
 
-function matrix_repr(m::MatrixGroupElement{N, T}) where {N, T}
+function matrix_repr(m::MatrixGroupElement{N,T}) where {N,T}
     if isone(word(m))
-        return StaticArrays.SMatrix{N, N, T}(LinearAlgebra.I)
+        return StaticArrays.SMatrix{N,N,T}(LinearAlgebra.I)
     end
     A = alphabet(parent(m))
     return prod(matrix_repr(A[l]) for l in word(m))
@@ -33,7 +33,7 @@ end
 function Base.rand(
     rng::Random.AbstractRNG,
     rs::Random.SamplerTrivial{<:MatrixGroup},
-    )
+)
     Mgroup = rs[]
     S = gens(Mgroup)
     return prod(g -> rand(Bool) ? g : inv(g), rand(S, rand(1:30)))

src/matrix_groups/eltary_matrices.jl

@@ -1,9 +1,9 @@
-struct ElementaryMatrix{N, T} <: Groups.GSymbol
+struct ElementaryMatrix{N,T} <: Groups.GSymbol
     i::Int
     j::Int
     val::T
-    ElementaryMatrix{N}(i, j, val=1) where N =
+    ElementaryMatrix{N}(i, j, val=1) where {N} =
-        (@assert i≠j; new{N, typeof(val)}(i, j, val))
+        (@assert i ≠ j; new{N,typeof(val)}(i, j, val))
 end
 
 function Base.show(io::IO, e::ElementaryMatrix)
@@ -11,18 +11,18 @@ function Base.show(io::IO, e::ElementaryMatrix)
     !isone(e.val) && print(io, "^$(e.val)")
 end
 
-Base.:(==)(e::ElementaryMatrix{N}, f::ElementaryMatrix{N}) where N =
+Base.:(==)(e::ElementaryMatrix{N}, f::ElementaryMatrix{N}) where {N} =
     e.i == f.i && e.j == f.j && e.val == f.val
 
 Base.hash(e::ElementaryMatrix, h::UInt) =
     hash(typeof(e), hash((e.i, e.j, e.val), h))
 
-Base.inv(e::ElementaryMatrix{N}) where N =
+Base.inv(e::ElementaryMatrix{N}) where {N} =
     ElementaryMatrix{N}(e.i, e.j, -e.val)
 
-function matrix_repr(e::ElementaryMatrix{N, T}) where {N, T}
+function matrix_repr(e::ElementaryMatrix{N,T}) where {N,T}
-    m = StaticArrays.MMatrix{N, N, T}(LinearAlgebra.I)
+    m = StaticArrays.MMatrix{N,N,T}(LinearAlgebra.I)
     m[e.i, e.j] = e.val
-    x = StaticArrays.SMatrix{N, N}(m)
+    x = StaticArrays.SMatrix{N,N}(m)
     return x
 end

src/matrix_groups/eltary_symplectic.jl

@@ -1,18 +1,18 @@
-struct ElementarySymplectic{N, T} <: Groups.GSymbol
+struct ElementarySymplectic{N,T} <: Groups.GSymbol
     symbol::Symbol
     i::Int
     j::Int
     val::T
-    function ElementarySymplectic{N}(s::Symbol, i::Integer, j::Integer, val=1) where N
+    function ElementarySymplectic{N}(s::Symbol, i::Integer, j::Integer, val=1) where {N}
         @assert s ∈ (:A, :B)
         @assert iseven(N)
-        n = N÷2
+        n = N ÷ 2
         if s === :A
             @assert 1 ≤ i ≤ n && 1 ≤ j ≤ n && i ≠ j
         elseif s === :B
             @assert xor(1 ≤ i ≤ n, 1 ≤ j ≤ n) && xor(n < i ≤ N, n < j ≤ N)
         end
-        return new{N, typeof(val)}(s, i, j, val)
+        return new{N,typeof(val)}(s, i, j, val)
     end
 end
 
@@ -22,12 +22,12 @@ function Base.show(io::IO, s::ElementarySymplectic)
     !isone(s.val) && print(io, "^$(s.val)")
 end
 
-_ind(s::ElementarySymplectic{N}) where N = (s.i, s.j)
+_ind(s::ElementarySymplectic{N}) where {N} = (s.i, s.j)
-_local_ind(N_half::Integer, i::Integer) = ifelse(i<=N_half, i, i-N_half)
+_local_ind(N_half::Integer, i::Integer) = ifelse(i <= N_half, i, i - N_half)
-function _dual_ind(s::ElementarySymplectic{N}) where N
+function _dual_ind(s::ElementarySymplectic{N}) where {N}
     if s.symbol === :A && return _ind(s)
     else#if s.symbol === :B
-        return _dual_ind(N÷2, s.i, s.j)
+        return _dual_ind(N ÷ 2, s.i, s.j)
     end
 end
 
@@ -41,7 +41,7 @@ function _dual_ind(N_half, i, j)
     return i, j
 end
 
-function Base.:(==)(s::ElementarySymplectic{N}, t::ElementarySymplectic{M}) where {N, M}
+function Base.:(==)(s::ElementarySymplectic{N}, t::ElementarySymplectic{M}) where {N,M}
     N == M || return false
     s.symbol == t.symbol || return false
     s.val == t.val || return false
@@ -51,18 +51,18 @@ end
 Base.hash(s::ElementarySymplectic, h::UInt) =
     hash(Set([_ind(s); _dual_ind(s)]), hash(s.symbol, hash(s.val, h)))
 
-LinearAlgebra.transpose(s::ElementarySymplectic{N}) where N =
+LinearAlgebra.transpose(s::ElementarySymplectic{N}) where {N} =
     ElementarySymplectic{N}(s.symbol, s.j, s.i, s.val)
 
-Base.inv(s::ElementarySymplectic{N}) where N =
+Base.inv(s::ElementarySymplectic{N}) where {N} =
     ElementarySymplectic{N}(s.symbol, s.i, s.j, -s.val)
 
-function matrix_repr(s::ElementarySymplectic{N, T}) where {N, T}
+function matrix_repr(s::ElementarySymplectic{N,T}) where {N,T}
     @assert iseven(N)
     n = div(N, 2)
-    m = StaticArrays.MMatrix{N, N, T}(LinearAlgebra.I)
+    m = StaticArrays.MMatrix{N,N,T}(LinearAlgebra.I)
-    i,j = _ind(s)
+    i, j = _ind(s)
-    m[i,j] = s.val
+    m[i, j] = s.val
     if s.symbol === :A
         m[n+j, n+i] = -s.val
     else#if s.symbol === :B
@@ -72,5 +72,5 @@ function matrix_repr(s::ElementarySymplectic{N, T}) where {N, T}
             m[j-n, i+n] = s.val
         end
     end
-    return StaticArrays.SMatrix{N, N}(m)
+    return StaticArrays.SMatrix{N,N}(m)
 end

src/types.jl

@@ -96,7 +96,7 @@ mutable struct FPGroupElement{Gr<:AbstractFPGroup,W<:AbstractWord} <:
     FPGroupElement(
         word::W,
         G::AbstractFPGroup,
-        hash::UInt = UInt(0),
+        hash::UInt=UInt(0),
     ) where {W<:AbstractWord} = new{typeof(G),W}(word, hash, G)
 
     FPGroupElement{Gr,W}(word::AbstractWord, G::Gr) where {Gr,W} =
@@ -222,8 +222,8 @@ rewriting(G::FPGroup) = G.rw
 function FPGroup(
     G::AbstractFPGroup,
     rels::AbstractVector{<:Pair{GEl,GEl}};
-    ordering = KnuthBendix.ordering(G),
+    ordering=KnuthBendix.ordering(G),
-    kwargs...,
+    kwargs...
 ) where {GEl<:FPGroupElement}
     for (lhs, rhs) in rels
         @assert parent(lhs) === parent(rhs) === G

src/wl_ball.jl

@@ -1,20 +1,31 @@
 """
     wlmetric_ball(S::AbstractVector{<:GroupElem}
-        [, center=one(first(S)); radius=2, op=*])
+        [, center=one(first(S)); radius=2, op=*, threading=true])
 Compute metric ball as a list of elements of non-decreasing length, given the
 word-length metric on the group generated by `S`. The ball is centered at `center`
 (by default: the identity element). `radius` and `op` keywords specify the
 radius and multiplication operation to be used.
 """
-function wlmetric_ball_serial(S::AbstractVector{T}, center::T=one(first(S)); radius = 2, op = *) where {T}
+function wlmetric_ball(
+    S::AbstractVector{T},
+    center::T=one(first(S));
+    radius=2,
+    op=*,
+    threading=true
+) where {T}
+    threading && return wlmetric_ball_thr(S, center, radius=radius, op=op)
+    return wlmetric_ball_serial(S, center, radius=radius, op=op)
+end
+
+function wlmetric_ball_serial(S::AbstractVector{T}, center::T=one(first(S)); radius=2, op=*) where {T}
     @assert radius >= 1
-    old = union!([center], [center*s for s in S])
+    old = union!([center], [center * s for s in S])
     return _wlmetric_ball(S, old, radius, op, collect, unique!)
 end
 
-function wlmetric_ball_thr(S::AbstractVector{T}, center::T=one(first(S)); radius = 2, op = *) where {T}
+function wlmetric_ball_thr(S::AbstractVector{T}, center::T=one(first(S)); radius=2, op=*) where {T}
     @assert radius >= 1
-    old = union!([center], [center*s for s in S])
+    old = union!([center], [center * s for s in S])
     return _wlmetric_ball(S, old, radius, op, Folds.collect, Folds.unique)
 end
 
@@ -26,6 +37,7 @@ function _wlmetric_ball(S, old, radius, op, collect, unique)
                 (g = op(o, s); hash(g); g)
                 for o in @view(old[sizes[end-1]:end]) for s in S
             )
+
             append!(old, new)
             unique(old)
         end
@@ -34,13 +46,3 @@ function _wlmetric_ball(S, old, radius, op, collect, unique)
     return old, sizes[2:end]
 end
 
-function wlmetric_ball(
-    S::AbstractVector{T},
-    center::T = one(first(S));
-    radius = 2,
-    op = *,
-    threading = true,
-) where {T}
-    threading && return wlmetric_ball_thr(S, center, radius = radius, op = op)
-    return wlmetric_ball_serial(S, center, radius = radius, op = op)
-end

test/AutFn.jl

@@ -29,54 +29,54 @@
     end
 
     A4 = Alphabet(
-    [:a,:A,:b,:B,:c,:C,:d,:D],
+        [:a, :A, :b, :B, :c, :C, :d, :D],
-    [ 2, 1, 4, 3, 6, 5, 8, 7]
+        [2, 1, 4, 3, 6, 5, 8, 7]
     )
 
     A5 = Alphabet(
-    [:a,:A,:b,:B,:c,:C,:d,:D,:e,:E],
+        [:a, :A, :b, :B, :c, :C, :d, :D, :e, :E],
-    [ 2, 1, 4, 3, 6, 5, 8, 7,10, 9]
+        [2, 1, 4, 3, 6, 5, 8, 7, 10, 9]
     )
 
     F4 = FreeGroup([:a, :b, :c, :d], A4)
-    a,b,c,d = gens(F4)
+    a, b, c, d = gens(F4)
-    D = ntuple(i->gens(F4, i), 4)
+    D = ntuple(i -> gens(F4, i), 4)
 
     @testset "Transvection action correctness" begin
-        i,j = 1,2
+        i, j = 1, 2
-        r = Groups.Transvection(:ϱ,i,j)
+        r = Groups.Transvection(:ϱ, i, j)
-        l = Groups.Transvection(:λ,i,j)
+        l = Groups.Transvection(:λ, i, j)
 
         (t::Groups.Transvection)(v::Tuple) = Groups.evaluate!(v, t)
 
-        @test      r(deepcopy(D)) == (a*b,   b, c, d)
+        @test r(deepcopy(D)) == (a * b, b, c, d)
-        @test inv(r)(deepcopy(D)) == (a*b^-1,b, c, d)
+        @test inv(r)(deepcopy(D)) == (a * b^-1, b, c, d)
-        @test      l(deepcopy(D)) == (b*a,   b, c, d)
+        @test l(deepcopy(D)) == (b * a, b, c, d)
-        @test inv(l)(deepcopy(D)) == (b^-1*a,b, c, d)
+        @test inv(l)(deepcopy(D)) == (b^-1 * a, b, c, d)
 
-        i,j = 3,1
+        i, j = 3, 1
-        r = Groups.Transvection(:ϱ,i,j)
+        r = Groups.Transvection(:ϱ, i, j)
-        l = Groups.Transvection(:λ,i,j)
+        l = Groups.Transvection(:λ, i, j)
-        @test      r(deepcopy(D)) == (a, b, c*a,   d)
+        @test r(deepcopy(D)) == (a, b, c * a, d)
-        @test inv(r)(deepcopy(D)) == (a, b, c*a^-1,d)
+        @test inv(r)(deepcopy(D)) == (a, b, c * a^-1, d)
-        @test      l(deepcopy(D)) == (a, b, a*c,   d)
+        @test l(deepcopy(D)) == (a, b, a * c, d)
-        @test inv(l)(deepcopy(D)) == (a, b, a^-1*c,d)
+        @test inv(l)(deepcopy(D)) == (a, b, a^-1 * c, d)
 
-        i,j = 4,3
+        i, j = 4, 3
-        r = Groups.Transvection(:ϱ,i,j)
+        r = Groups.Transvection(:ϱ, i, j)
-        l = Groups.Transvection(:λ,i,j)
+        l = Groups.Transvection(:λ, i, j)
-        @test      r(deepcopy(D)) == (a, b, c, d*c)
+        @test r(deepcopy(D)) == (a, b, c, d * c)
-        @test inv(r)(deepcopy(D)) == (a, b, c, d*c^-1)
+        @test inv(r)(deepcopy(D)) == (a, b, c, d * c^-1)
-        @test      l(deepcopy(D)) == (a, b, c, c*d)
+        @test l(deepcopy(D)) == (a, b, c, c * d)
-        @test inv(l)(deepcopy(D)) == (a, b, c, c^-1*d)
+        @test inv(l)(deepcopy(D)) == (a, b, c, c^-1 * d)
 
-        i,j = 2,4
+        i, j = 2, 4
-        r = Groups.Transvection(:ϱ,i,j)
+        r = Groups.Transvection(:ϱ, i, j)
-        l = Groups.Transvection(:λ,i,j)
+        l = Groups.Transvection(:λ, i, j)
-        @test      r(deepcopy(D)) == (a, b*d,   c, d)
+        @test r(deepcopy(D)) == (a, b * d, c, d)
-        @test inv(r)(deepcopy(D)) == (a, b*d^-1,c, d)
+        @test inv(r)(deepcopy(D)) == (a, b * d^-1, c, d)
-        @test      l(deepcopy(D)) == (a, d*b,   c, d)
+        @test l(deepcopy(D)) == (a, d * b, c, d)
-        @test inv(l)(deepcopy(D)) == (a, d^-1*b,c, d)
+        @test inv(l)(deepcopy(D)) == (a, d^-1 * b, c, d)
     end
 
     A = SpecialAutomorphismGroup(F4, max_rules=1000)
@@ -91,33 +91,33 @@
 
     @testset "Automorphisms: hash and evaluate" begin
         @test Groups.domain(gens(A, 1)) == D
-        g, h = gens(A, 1), gens(A, 8)
+        g, h = gens(A, 1), gens(A, 8) # (ϱ₁.₂, ϱ₃.₂)
 
-        @test evaluate(g*h) == evaluate(h*g)
+        @test evaluate(g * h) == evaluate(h * g)
-        @test (g*h).savedhash == zero(UInt)
+        @test (g * h).savedhash == zero(UInt)
 
-        @test sprint(show, typeof(g)) == "Automorphism{FreeGroup{Symbol, KnuthBendix.LenLex{Symbol}}, …}"
+        @test contains(sprint(show, typeof(g)), "Automorphism{FreeGroup{Symbol")
 
-        a = g*h
+        a = g * h
-        b = h*g
+        b = h * g
         @test hash(a) != zero(UInt)
         @test hash(a) == hash(b)
         @test a.savedhash == b.savedhash
 
-        @test length(unique([a,b])) == 1
+        @test length(unique([a, b])) == 1
-        @test length(unique([g*h, h*g])) == 1
+        @test length(unique([g * h, h * g])) == 1
 
         # Not so simple arithmetic: applying starting on the left:
         # ϱ₁₂*ϱ₂₁⁻¹*λ₁₂*ε₂ == σ₂₁₃₄
 
         g = gens(A, 1)
         x1, x2, x3, x4 = Groups.domain(g)
-        @test evaluate(g) == (x1*x2, x2, x3, x4)
+        @test evaluate(g) == (x1 * x2, x2, x3, x4)
 
-        g = g*inv(gens(A, 4)) # ϱ₂₁
+        g = g * inv(gens(A, 4)) # ϱ₂₁
-        @test evaluate(g) == (x1*x2, x1^-1, x3, x4)
+        @test evaluate(g) == (x1 * x2, x1^-1, x3, x4)
 
-        g = g*gens(A, 13)
+        g = g * gens(A, 13)
         @test evaluate(g) == (x2, x1^-1, x3, x4)
     end
 
@@ -128,7 +128,7 @@
         S = gens(G)
         @test S isa Vector{<:FPGroupElement{<:AutomorphismGroup{<:FreeGroup}}}
 
-        @test length(S) == 2*N*(N-1)
+        @test length(S) == 2 * N * (N - 1)
         @test length(unique(S)) == length(S)
 
         S_sym = [S; inv.(S)]
@@ -136,12 +136,12 @@
 
         pushfirst!(S_sym, one(G))
 
-        B_2 = [i*j for (i,j) in Base.product(S_sym, S_sym)]
+        B_2 = [i * j for (i, j) in Base.product(S_sym, S_sym)]
         @test length(B_2) == 2401
         @test length(unique(B_2)) == 1777
 
-        @test all(g->isone(inv(g)*g), B_2)
+        @test all(g -> isone(inv(g) * g), B_2)
-        @test all(g->isone(g*inv(g)), B_2)
+        @test all(g -> isone(g * inv(g)), B_2)
     end
 
     @testset "Forward evaluate" begin
@@ -153,7 +153,7 @@
 
         f = gens(F)
 
-        @test a(f[1]) == f[1]*f[2]
+        @test a(f[1]) == f[1] * f[2]
         @test all(a(f[i]) == f[i] for i in 2:length(f))
 
         S = let s = gens(G)

test/AutSigma3.jl

@@ -3,6 +3,8 @@
 
     π₁Σ = Groups.SurfaceGroup(genus, 0)
 
+    @test contains(sprint(print, π₁Σ), "surface")
+
     Groups.PermRightAut(p::Perm) = Groups.PermRightAut(p.d)
     # Groups.PermLeftAut(p::Perm) = Groups.PermLeftAut(p.d)
     autπ₁Σ = let autπ₁Σ = AutomorphismGroup(π₁Σ)
@@ -18,7 +20,7 @@
             π₁Σ,
             autπ₁Σ.gens,
             A,
-            ntuple(i->inv(gens(π₁Σ, i)), 2Groups.genus(π₁Σ))
+            ntuple(i -> inv(gens(π₁Σ, i)), 2Groups.genus(π₁Σ))
         )
 
         autG
@@ -36,7 +38,7 @@
         λ = Groups.ΡΛ(:λ, A, 2genus)
         ϱ = Groups.ΡΛ(:ϱ, A, 2genus)
         @test sautFn(Groups.Te_diagonal(λ, ϱ, 1)) ==
-            conj(sautFn(Groups.Te_diagonal(λ, ϱ, 2)), τ)
+              conj(sautFn(Groups.Te_diagonal(λ, ϱ, 2)), τ)
 
         @test sautFn(Groups.Te_diagonal(λ, ϱ, 3)) == sautFn(Groups.Te(λ, ϱ, 3, 1))
     end

test/fp_groups.jl

@@ -1,5 +1,5 @@
 @testset "FPGroups" begin
-    A = Alphabet([:a, :A, :b, :B, :c, :C], [2,1,4,3,6,5])
+    A = Alphabet([:a, :A, :b, :B, :c, :C], [2, 1, 4, 3, 6, 5])
 
     @test FreeGroup(A) isa FreeGroup
     @test sprint(show, FreeGroup(A)) == "free group on 3 generators"
@@ -7,26 +7,26 @@
     F = FreeGroup([:a, :b, :c], A)
     @test sprint(show, F) == "free group on 3 generators"
 
-    a,b,c = gens(F)
+    a, b, c = gens(F)
-    @test c*b*a isa FPGroupElement
+    @test c * b * a isa FPGroupElement
 
     # quotient of F:
-    G = FPGroup(F, [a*b=>b*a, a*c=>c*a, b*c=>c*b])
+    G = FPGroup(F, [a * b => b * a, a * c => c * a, b * c => c * b])
 
     @test G isa FPGroup
     @test sprint(show, G) == "⟨ a  b  c | \n\t  a*b => b*a  a*c => c*a  b*c => c*b ⟩"
     @test rand(G) isa FPGroupElement
 
-    f = a*c*b
+    f = a * c * b
     @test word(f) isa Word{UInt8}
 
-    aG,bG,cG = gens(G)
+    aG, bG, cG = gens(G)
 
     @test aG isa FPGroupElement
     @test_throws AssertionError aG == a
     @test word(aG) == word(a)
 
-    g = aG*cG*bG
+    g = aG * cG * bG
 
     @test_throws AssertionError f == g
     @test word(f) == word(g)
@@ -34,7 +34,7 @@
     Groups.normalform!(g)
     @test word(g) == [1, 3, 5]
 
-    let g = aG*cG*bG
+    let g = aG * cG * bG
         # test that we normalize g before printing
         @test sprint(show, g) == "a*b*c"
     end
@@ -46,7 +46,7 @@
 
     @test h isa FPGroupElement
     @test_throws AssertionError h == g
-    @test_throws MethodError h*g
+    @test_throws MethodError h * g
 
     H′ = FPGroup(G, [aG^2 => cG, bG * cG => aG], max_rules=200)
     @test_throws AssertionError one(H) == one(H′)

test/matrix_groups.jl

@@ -4,23 +4,25 @@ using Groups.MatrixGroups
     @testset "SL(n, ℤ)" begin
         SL3Z = SpecialLinearGroup{3}(Int8)
 
-        S = gens(SL3Z); union!(S, inv.(S))
+        S = gens(SL3Z)
+        union!(S, inv.(S))
 
-        E, sizes = Groups.wlmetric_ball(S, radius=4)
+        _, sizes = Groups.wlmetric_ball(S, radius=4)
 
         @test sizes == [13, 121, 883, 5455]
 
-        E(i,j) = SL3Z([A[MatrixGroups.ElementaryMatrix{3}(i,j, Int8(1))]])
+        E(i, j) = SL3Z([A[MatrixGroups.ElementaryMatrix{3}(i, j, Int8(1))]])
 
         A = alphabet(SL3Z)
-        w = E(1,2)
+        w = E(1, 2)
-        r = E(2,3)^-3
+        r = E(2, 3)^-3
-        s = E(1,3)^2*E(3,2)^-1
+        s = E(1, 3)^2 * E(3, 2)^-1
 
-        S = [w,r,s]; S = unique([S; inv.(S)]);
+        S = [w, r, s]
-        _, sizes = Groups.wlmetric_ball(S, radius=4);
+        S = unique([S; inv.(S)])
+        _, sizes = Groups.wlmetric_ball(S, radius=4)
         @test sizes == [7, 33, 141, 561]
-        _, sizes = Groups.wlmetric_ball_serial(S, radius=4);
+        _, sizes = Groups.wlmetric_ball_serial(S, radius=4)
         @test sizes == [7, 33, 141, 561]
 
         Logging.with_logger(Logging.NullLogger()) do
@@ -34,10 +36,10 @@ using Groups.MatrixGroups
         end
 
 
-        x = w*inv(w)*r
+        x = w * inv(w) * r
 
         @test length(word(x)) == 5
-        @test size(x) == (3,3)
+        @test size(x) == (3, 3)
         @test eltype(x) == Int8
 
         @test contains(sprint(print, SL3Z), "special linear group of 3×3")
@@ -50,12 +52,14 @@ using Groups.MatrixGroups
     @testset "Sp(6, ℤ)" begin
         Sp6 = MatrixGroups.SymplecticGroup{6}(Int8)
 
-        @testset "GroupsCore conformance" begin
+        Logging.with_logger(Logging.NullLogger()) do
-            test_Group_interface(Sp6)
+            @testset "GroupsCore conformance" begin
-            g = Sp6(rand(1:length(alphabet(Sp6)), 10))
+                test_Group_interface(Sp6)
-            h = Sp6(rand(1:length(alphabet(Sp6)), 10))
+                g = Sp6(rand(1:length(alphabet(Sp6)), 10))
+                h = Sp6(rand(1:length(alphabet(Sp6)), 10))
 
-            test_GroupElement_interface(g, h)
+                test_GroupElement_interface(g, h)
+            end
         end
 
         @test contains(sprint(print, Sp6), "group of 6×6 symplectic matrices")
@@ -64,7 +68,7 @@ using Groups.MatrixGroups
         x *= inv(x) * gens(Sp6, 2)
 
         @test length(word(x)) == 3
-        @test size(x) == (6,6)
+        @test size(x) == (6, 6)
         @test eltype(x) == Int8
 
         @test contains(sprint(show, MIME"text/plain"(), x), "6×6 symplectic matrix:")