actually cache and use savedhash + tests

src/AutGroup.jl

@@ -201,8 +201,11 @@ end
 hash(s::AutSymbol, h::UInt) = hash(s.str, hash(s.pow, hash(:AutSymbol, h)))
 
 function hash(g::AutGroupElem, h::UInt)
-   gs = gens(parent(g).objectGroup)
-   return hash(g(gs), hash(typeof(g), hash(parent(g), h)))
+   if g.modified
+      g.savedhash = hash(g(gens(parent(g).objectGroup)), hash(typeof(g), hash(parent(g), h)))
+      g.modified = false
+   end
+   return g.savedhash
 end
 
 function change_pow(s::AutSymbol, n::Int)
@@ -316,7 +319,7 @@ function reduce!(W::AutGroupElem)
         end
     end
 
-    W.modified = false
-    W.savedhash = hash(W.symbols,hash(typeof(W)))
+    W.modified = true
+
     return W
 end

test/AutGroup-tests.jl

@@ -149,6 +149,16 @@
       b = Groups.flip_autsymbol(2)*A(inv(Groups.rmul_autsymbol(1,2)))
       @test a*b == b*a
       @test a^3 * b^3 == A()
+      g,h = Nemo.gens(A)[[1,8]]
+      domain = Nemo.gens(A.objectGroup)
+      @test (g*h)(domain) == (h*g)(domain)
+      @test (g*h).savedhash != (h*g).savedhash
+      a = g*h
+      b = h*g
+      @test hash(a) == hash(b)
+      @test a.savedhash == b.savedhash
+      @test length(unique([a,b])) == 1
+      @test length(unique([g*h, h*g])) == 1
    end
 
    @testset "specific Aut(F4) tests" begin