From cdbd483e9e58351d2879d10432abe445cc4c7dfa Mon Sep 17 00:00:00 2001
From: kalmarek <kalmar@amu.edu.pl>
Date: Mon, 20 Apr 2020 02:41:24 +0200
Subject: [PATCH] more tests for AutGroup

---
 src/AutGroup.jl        |  2 +-
 src/DirectPower.jl     |  7 +-----
 test/AutGroup-tests.jl | 49 ++++++++++++++++++++++++++----------------
 3 files changed, 33 insertions(+), 25 deletions(-)

diff --git a/src/AutGroup.jl b/src/AutGroup.jl
index 232d98d..dcbb1e1 100644
--- a/src/AutGroup.jl
+++ b/src/AutGroup.jl
@@ -262,7 +262,7 @@ end
 
 function show(io::IO, G::AutGroup)
    print(io, "Automorphism Group of $(G.objectGroup)\n")
-   print(io, "Generated by $(join(G.gens, ","))")
+   print(io, "Generated by $(gens(G))")
 end
 
 ###############################################################################
diff --git a/src/DirectPower.jl b/src/DirectPower.jl
index fe87840..567444e 100644
--- a/src/DirectPower.jl
+++ b/src/DirectPower.jl
@@ -31,11 +31,6 @@ function DirectPower(G::DirectPowerGroup{N}, H::Group) where N
    return DirectPowerGroup(G.group, N+1)
 end
 
-function DirectPower(R::AbstractAlgebra.Ring, n::Int)
-   @warn "Creating DirectPower of the multilplicative group!"
-   return DirectPowerGroup(MultiplicativeGroup(R), n)
-end
-
 struct DirectPowerGroupElem{N, T<:GroupElem} <: GroupElem
    elts::NTuple{N,T}
 end
@@ -188,7 +183,6 @@ end
 ###############################################################################
 
 order(G::DirectPowerGroup{N}) where N = order(G.group)^N
-Base.length(G::DirectPowerGroup) = order(G)
 
 function iterate(G::DirectPowerGroup{N}) where N
    elts = collect(G.group)
@@ -212,3 +206,4 @@ function iterate(G::DirectPowerGroup{N}, state) where N
 end
 
 eltype(::Type{DirectPowerGroup{N, G}}) where {N, G} = DirectPowerGroupElem{N, elem_type(G)}
+Base.length(G::DirectPowerGroup) = order(G)
diff --git a/test/AutGroup-tests.jl b/test/AutGroup-tests.jl
index 17fefcf..54cc0f0 100644
--- a/test/AutGroup-tests.jl
+++ b/test/AutGroup-tests.jl
@@ -6,13 +6,17 @@
       @test_throws MethodError Groups.AutSymbol(:a)
       @test_throws MethodError Groups.AutSymbol(:a, 1)
       f = Groups.AutSymbol(:a, 1, Groups.FlipAut(2))
-      @test isa(f, Groups.GSymbol)
-      @test isa(f, Groups.AutSymbol)
-      @test isa(Groups.AutSymbol(perm"(4)"), Groups.AutSymbol)
-      @test isa(Groups.AutSymbol(perm"(1,2,3,4)"), Groups.AutSymbol)
-      @test isa(Groups.transvection_R(1,2), Groups.AutSymbol)
-      @test isa(Groups.transvection_R(3,4), Groups.AutSymbol)
-      @test isa(Groups.flip(3), Groups.AutSymbol)
+      @test f isa Groups.GSymbol
+      @test f isa Groups.AutSymbol
+      @test Groups.AutSymbol(perm"(4)") isa Groups.AutSymbol
+      @test Groups.AutSymbol(perm"(1,2,3,4)") isa Groups.AutSymbol
+      @test Groups.transvection_R(1,2) isa Groups.AutSymbol
+      @test Groups.transvection_R(3,4) isa Groups.AutSymbol
+      @test Groups.flip(3) isa Groups.AutSymbol
+
+      @test Groups.id_autsymbol() isa Groups.AutSymbol
+      @test inv(Groups.id_autsymbol()) isa Groups.AutSymbol
+      @test inv(Groups.id_autsymbol()) == Groups.id_autsymbol()
    end
 
    a,b,c,d = gens(FreeGroup(4))
@@ -88,35 +92,44 @@
       @test isa(Automorphism{3}(f), Automorphism)
       @test isa(AutGroup(FreeGroup(3)), AbstractAlgebra.Group)
       @test isa(AutGroup(FreeGroup(1)), Groups.AbstractFPGroup)
+
       A = AutGroup(FreeGroup(1))
-      @test isa(Groups.gens(A), Vector{Automorphism{1}})
+      @test Groups.gens(A) isa Vector{Automorphism{1}}
       @test length(Groups.gens(A)) == 1
+      @test length(Groups.gens(Aut(FreeGroup(1)))) == 1
+      @test Groups.gens(A) == [A(Groups.flip(1))]
+
       A = AutGroup(FreeGroup(1), special=true)
-      @test length(Groups.gens(A)) == 0
+      @test isempty(Groups.gens(A))
+      @test Groups.gens(SAut(FreeGroup(1))) == Automorphism{1}[]
+
       A = AutGroup(FreeGroup(2))
       @test length(Groups.gens(A)) == 7
       Agens = Groups.gens(A)
+      @test A(first(Agens)) isa Automorphism
 
-      @test isa(A(Groups.transvection_R(1,2)), Automorphism)
+      @test A(Groups.transvection_R(1,2)) isa Automorphism
       @test A(Groups.transvection_R(1,2)) in Agens
 
-      @test isa(A(Groups.transvection_R(2,1)), Automorphism)
+      @test A(Groups.transvection_R(2,1)) isa Automorphism
       @test A(Groups.transvection_R(2,1)) in Agens
 
-      @test isa(A(Groups.transvection_R(1,2)), Automorphism)
+      @test A(Groups.transvection_R(1,2)) isa Automorphism
       @test A(Groups.transvection_R(1,2)) in Agens
 
-      @test isa(A(Groups.transvection_R(2,1)), Automorphism)
+      @test A(Groups.transvection_R(2,1)) isa Automorphism
       @test A(Groups.transvection_R(2,1)) in Agens
 
-      @test isa(A(Groups.flip(1)), Automorphism)
+      @test A(Groups.flip(1)) isa Automorphism
       @test A(Groups.flip(1)) in Agens
 
-      @test isa(A(Groups.flip(2)), Automorphism)
+      @test A(Groups.flip(2)) isa Automorphism
       @test A(Groups.flip(2)) in Agens
 
-      @test isa(A(Groups.AutSymbol(perm"(1,2)")), Automorphism)
+      @test A(Groups.AutSymbol(perm"(1,2)")) isa Automorphism
       @test A(Groups.AutSymbol(perm"(1,2)")) in Agens
+
+      @test A(Groups.id_autsymbol()) isa Automorphism
    end
 
    A = AutGroup(FreeGroup(4))
@@ -144,8 +157,8 @@
       @test f²^2 == one(A)
       @test !isone(f²)
 
-      a = A(Groups.transvection_L(1,2))*Groups.flip(2)
-      b = Groups.flip(2)*A(inv(Groups.transvection_L(1,2)))
+      a = A(Groups.λ(1,2))*Groups.ε(2)
+      b = Groups.ε(2)*A(inv(Groups.λ(1,2)))
       @test a*b == b*a
       @test a^3 * b^3 == one(A)
       g,h = Groups.gens(A)[[1,8]] # (g, h) = (ϱ₁₂, ϱ₃₂)