use perms{Int8} in AutGroup and in tests

src/AutGroup.jl

@@ -19,7 +19,7 @@ immutable FlipAut
 end
 
 immutable PermAut
-    p::Nemo.Generic.perm
+    p::Nemo.Generic.perm{Int8}
 end
 
 immutable Identity end
@@ -86,7 +86,7 @@ end
 
 # taken from ValidatedNumerics, under under the MIT "Expat" License:
 # https://github.com/JuliaIntervals/ValidatedNumerics.jl/blob/master/LICENSE.md
-function subscriptify(n::Int)
+function subscriptify(n::Integer)
     subscript_0 = Int(0x2080) # Char(0x2080) -> subscript 0
     return join([Char(subscript_0 + i) for i in reverse(digits(n))])
 end
@@ -115,7 +115,7 @@ function flip_autsymbol(i; pow::Int=1)
     end
 end
 
-function perm_autsymbol(p::Generic.perm; pow::Int=1)
+function perm_autsymbol(p::Generic.perm{Int8}; pow::Int=1)
     p = p^pow
     if p == parent(p)()
        return id_autsymbol()
@@ -125,9 +125,9 @@ function perm_autsymbol(p::Generic.perm; pow::Int=1)
     end
 end
 
-function perm_autsymbol(a::Vector{Int})
-   G = PermutationGroup(length(a))
-   return perm_autsymbol(G(a))
+function perm_autsymbol(a::Vector{T}) where T<:Integer
+   G = PermutationGroup(Int8(length(a)))
+   return perm_autsymbol(G(Vector{Int8}(a)))
 end
 
 domain(G::AutGroup) = deepcopy(G.domain)
@@ -152,7 +152,7 @@ function AutGroup(G::FreeGroup; special=false)
 
    if !special
       flips = [flip_autsymbol(i) for i in 1:n]
-      syms = [perm_autsymbol(p) for p in elements(PermutationGroup(n))][2:end]
+      syms = [perm_autsymbol(p) for p in elements(PermutationGroup(Int8(n)))][2:end]
 
       append!(S, [flips; syms])
 

test/AutGroup-tests.jl

@@ -1,6 +1,6 @@
 @testset "Automorphisms" begin
    using Nemo
-   G = PermutationGroup(4)
+   G = PermutationGroup(Int8(4))
 
    @testset "AutSymbol" begin
       @test_throws MethodError Groups.AutSymbol("a")
@@ -8,7 +8,7 @@
       f = Groups.AutSymbol("a", 1, Groups.FlipAut(2))
       @test isa(f, Groups.GSymbol)
       @test isa(f, Groups.AutSymbol)
-      @test isa(Groups.perm_autsymbol(G([1,2,3,4])), Groups.AutSymbol)
+      @test isa(Groups.perm_autsymbol([1,2,3,4]), Groups.AutSymbol)
       @test isa(Groups.rmul_autsymbol(1,2), Groups.AutSymbol)
       @test isa(Groups.lmul_autsymbol(3,4), Groups.AutSymbol)
       @test isa(Groups.flip_autsymbol(3), Groups.AutSymbol)
@@ -29,21 +29,21 @@
    end
 
    @testset "perm_autsymbol correctness" begin
-      σ = Groups.perm_autsymbol(G([1,2,3,4]))
       @test σ(domain) == domain
       @test inv(σ)(domain) == domain
+      σ = Groups.perm_autsymbol([1,2,3,4])
 
-      σ = Groups.perm_autsymbol(G([2,3,4,1]))
       @test σ(domain) == [b, c, d, a]
       @test inv(σ)(domain) == [d, a, b, c]
+      σ = Groups.perm_autsymbol([2,3,4,1])
 
-      σ = Groups.perm_autsymbol(G([2,1,4,3]))
       @test σ(domain) == [b, a, d, c]
       @test inv(σ)(domain) == [b, a, d, c]
+      σ = Groups.perm_autsymbol([2,1,4,3])
 
-      σ = Groups.perm_autsymbol(G([2,3,1,4]))
       @test σ(domain) == [b,c,a,d]
       @test inv(σ)(domain) == [c,a,b,d]
+      σ = Groups.perm_autsymbol([2,3,1,4])
    end
 
    @testset "rmul/lmul_autsymbol correctness" begin
@@ -115,21 +115,20 @@
       @test isa(A(Groups.flip_autsymbol(2)), AutGroupElem)
       @test A(Groups.flip_autsymbol(2)) in gens
 
-      @test isa(A(Groups.perm_autsymbol(PermutationGroup(2)([2,1]))),
-         AutGroupElem)
-      @test A(Groups.perm_autsymbol(PermutationGroup(2)([2,1]))) in gens
+      @test isa(A(Groups.perm_autsymbol([2,1])), AutGroupElem)
+      @test A(Groups.perm_autsymbol([2,1])) in gens
    end
 
    A = AutGroup(FreeGroup(4))
 
    @testset "eltary functions" begin
 
-      f = Groups.perm_autsymbol(G([2,3,4,1]))
+      f = Groups.perm_autsymbol([2,3,4,1])
       @test (Groups.change_pow(f, 2)).pow == 1
       @test (Groups.change_pow(f, -2)).pow == 1
       @test (inv(f)).pow == 1
 
-      f = Groups.perm_autsymbol(G([2,1,4,3]))
+      f = Groups.perm_autsymbol([2,1,4,3])
       @test isa(inv(f), Groups.AutSymbol)
 
       @test_throws DomainError f^-1
@@ -139,7 +138,7 @@
    end
 
    @testset "reductions/arithmetic" begin
-      f = Groups.perm_autsymbol(G([2,3,4,1]))
+      f = Groups.perm_autsymbol([2,3,4,1])
 
       f² = Groups.r_multiply(A(f), [f], reduced=false)
       @test Groups.simplify_perms!(f²) == false

test/DirectProd-tests.jl

@@ -8,7 +8,7 @@
    @testset "Constructors" begin
       @test isa(Groups.DirectProductGroup(G,2), Nemo.Group)
       @test isa(G×G, Nemo.Group)
-      @test isa(Groups.DirectProductGroup(G,2), Groups.DirectProductGroup{Generic.PermGroup})
+      @test isa(Groups.DirectProductGroup(G,2), Groups.DirectProductGroup{Generic.PermGroup{Int64}})
 
       GG = Groups.DirectProductGroup(G,2)
 
@@ -18,7 +18,7 @@
       @test GG(G(), G()) == GG()
 
       @test isa(GG([g, g^2]), GroupElem)
-      @test isa(GG([g, g^2]), Groups.DirectProductGroupElem{Generic.perm})
+      @test isa(GG([g, g^2]), Groups.DirectProductGroupElem{Generic.perm{Int64}})
 
       h = GG([g,g^2])
 

test/WreathProd-tests.jl

@@ -73,7 +73,7 @@
 
       Wr = WreathProduct(PermutationGroup(2),S_3)
 
-      @test isa([elements(Wr)...], Vector{Groups.WreathProductElem{Generic.perm}})
+      @test isa([elements(Wr)...], Vector{Groups.WreathProductElem{Generic.perm{Int64}}})
 
       elts = [elements(Wr)...]