more tests

test/runtests.jl

@@ -3,8 +3,8 @@ using Base.Test
 
 using Nemo
 
-# write your own tests here
-@testset "GroupRing constructors: PermutationGroup" begin
+@testset "GroupRings" begin
+   @testset "Constructors: PermutationGroup" begin
       G = PermutationGroup(3)
 
       @test isa(GroupRing(G), Nemo.Ring)
@@ -32,9 +32,9 @@ using Nemo
 
       @test RG == A
       @test RG == B
-end
+   end
 
-@testset "GroupRing constructors FreeGroup" begin
+   @testset "GroupRing constructors FreeGroup" begin
       using Groups
       F = FreeGroup(3)
       S = generators(F)
@@ -53,14 +53,19 @@ end
       B = GroupRing(F, basis, d, pm)
       @test A == B
 
-end
+   end
 
-@testset "GroupRingElems constructors/basic manipulation" begin
+   @testset "GroupRingElems constructors/basic manipulation" begin
       G = PermutationGroup(3)
       RG = GroupRing(G, full=true)
       a = rand(6)
       @test isa(GroupRingElem(a, RG), GroupRingElem)
       @test isa(RG(a), GroupRingElem)
+
+      for g in elements(G)
+         @test isa(RG(g), GroupRingElem)
+      end
+
       @test_throws String GroupRingElem([1,2,3], RG)
       @test isa(RG(G([2,3,1])), GroupRingElem)
       p = G([2,3,1])
@@ -70,9 +75,71 @@ end
 
       @test a.coeffs[5] == 1
       @test a[5] == 1
-   @test RG([0,0,0,0,1,0]) == a
       @test a[p] == 1
       @test a[G([1,2,3])] == 0
 
       @test string(a) == "1*[2, 3, 1]"
+
+      @test RG([0,0,0,0,1,0]) == a
+   end
+
+   @testset "Arithmetic" begin
+      G = PermutationGroup(3)
+      RG = GroupRing(G, full=true)
+      a = RG(ones(Int, order(G)))
+
+      @testset "scalar operators" begin
+
+         @test isa(-a, GroupRingElem)
+         @test (-a).coeffs == -(a.coeffs)
+
+         @test isa(2*a, GroupRingElem)
+         @test eltype(2*a) == typeof(2)
+         @test (2*a).coeffs == 2.*(a.coeffs)
+
+         @test isa(2.0*a, GroupRingElem)
+         @test eltype(2.0*a) == typeof(2.0)
+         @test (2.0*a).coeffs == 2.0.*(a.coeffs)
+
+         @test isa(a/2, GroupRingElem)
+         @test eltype(a/2) == typeof(1/2)
+         @test (a/2).coeffs == 0.5*(a.coeffs)
+
+         @test isa(convert(Rational{Int}, a), GroupRingElem)
+         @test eltype(convert(Rational{Int}, a)) == Rational{Int}
+         @test convert(Rational{Int}, a).coeffs ==
+            convert(Vector{Rational{Int}}, a.coeffs)
+
+         b = convert(Rational{Int}, a)
+
+         @test isa(b//4, GroupRingElem)
+         @test eltype(b//4) == Rational{Int}
+
+         @test isa(b//big(4), GroupElem)
+         @test eltype(b//(big(4)//1)) == Rational{BigInt}
+
+         @test isa(a//1, GroupRingElem)
+         @test eltype(a//1) == Rational{Int}
+         @test_throws MethodError (1.0*a)//1
+
+      end
+
+      @testset "Additive structure" begin
+         @test RG(ones(Int, order(G))) == sum(RG(g) for g in elements(G))
+         a = RG(ones(Int, order(G)))
+         b = sum((-1)^parity(g)*RG(g) for g in elements(G))
+
+      end
+
+      @testset "Multiplicative structure" begin
+         for g in elements(G), h in elements(G)
+            a = RG(g)
+            b = RG(h)
+            @test a*b == RG(g*h)
+            @test (a+b)*(a+b) == a*a + a*b + b*a + b*b
+            @test 
+         end
+      end
+
+   end
 end