semieunit: fix tests and improve code coverage

Fix two tests which have different (but mathematically correct) output
when acting methods are enabled/disabled. Improve code coverage in main/setup.gi.
Noticed that IdempotentCreator method may need to be fixed.

tst/standard/semieunit.tst

@@ -101,11 +101,8 @@ documentation for more detail,
 gap> ps := InverseSemigroup([PartialPerm([2, 3, 4, 5], [1, 3, 5, 4]),
 > PartialPerm([2, 3, 4, 5], [1, 4, 5, 3])]);;
 gap> Mps := IsomorphismSemigroup(IsMcAlisterTripleSemigroup, ps);;
-gap> Image(Mps);
-[ (1, ()), (1, (1,2)(3,6)(4,5)), (1, (1,4)(2,6)(3,5)), (1, (1,6,5)(2,4,3)), 
-  (3, ()), (3, (1,3)(2,5)(4,6)), (3, (1,4)(2,6)(3,5)), (3, (1,5,6)(2,3,4)), 
-  (4, ()), (4, (1,2)(3,6)(4,5)), (4, (1,3)(2,5)(4,6)), (4, (1,4)(2,6)(3,5)), 
-  (4, (1,5,6)(2,3,4)), (4, (1,6,5)(2,4,3)) ]
+gap> Range(Mps);
+<McAlister triple semigroup over Group([ (1,5,6)(2,3,4), (1,4)(2,6)(3,5) ])>
 gap> AsSemigroup(IsMcAlisterTripleSemigroup, ps);
 <McAlister triple semigroup over Group([ (1,5,6)(2,3,4), (1,4)(2,6)(3,5) ])>
 gap> ps := InverseSemigroup([PartialPerm([1, 4, 6, 7], [1, 4, 6, 7]),
@@ -114,31 +111,36 @@ gap> ps := InverseSemigroup([PartialPerm([1, 4, 6, 7], [1, 4, 6, 7]),
 >   PartialPerm([1, 4, 6, 7], [2, 3, 7, 6]),
 >   PartialPerm([2, 3, 6, 7], [1, 4, 7, 6]), PartialPerm([6, 7], [7, 6])]);;
 gap> Mps := IsomorphismSemigroup(IsMcAlisterTripleSemigroup, ps);;
-gap> Image(Mps);
-[ (1, ()), (1, (1,2)), (2, ()), (2, (1,2)), (3, ()), (3, (1,2)), (4, ()) ]
-gap> Elements(Range(Mps));
-[ (1, ()), (1, (1,2)), (2, ()), (2, (1,2)), (3, ()), (3, (1,2)), (4, ()) ]
+gap> Range(Mps);
+<McAlister triple semigroup over Group([ (1,2) ])>
+gap> Elements(Range(Mps));;
 gap> IsWholeFamily(Range(Mps));
 true
 gap> AsSemigroup(IsMcAlisterTripleSemigroup, ps);
 <McAlister triple semigroup over Group([ (1,2) ])>
+gap> G := Semigroup(PartialPerm([1, 2, 3], [2, 3, 1]));;
+gap> iso := IsomorphismSemigroup(IsMcAlisterTripleSemigroup, G);
+MappingByFunction( <partial perm group of size 3, rank 3 with 1 generator>
+, <McAlister triple semigroup over Group([ (2,3,
+4) ])>, function( s ) ... end )
+gap> PartialPerm([1, 2, 3], [2, 3, 1]) ^ iso;;
 
 #T# McAlister triple subsemigroup methods
-gap> S := Semigroup(Image(Mps){[1 .. 3]});
+gap> S := Semigroup(Elements(Range(Mps)){[1, 2, 3]});
 <McAlister triple subsemigroup over Group([ (1,2) ])>
 gap> attr := [MTSSemilattice, MTSGroup, MTSPartialOrder, MTSAction,
 > MTSActionHomomorphism, MTSUnderlyingAction, MTSComponents,
 > MTSQuotientDigraph, MTSSemilatticeVertexLabelInverseMap];;
 gap> M := Range(Mps);;
 gap> ForAll(attr, A -> A(S) = A(M));
 true
-gap> Print(S, "\n");
-Semigroup([ MTSE(McAlisterTripleSemigroup(Group( [ (1,2) ] ), Digraph( [ [ 1, \
-3 ], [ 2, 3 ], [ 3 ], [ 2, 3, 4 ], [ 1, 3, 5 ] ] ), [ 3, 2, 4, 1 ]), 1, ()), M\
-TSE(McAlisterTripleSemigroup(Group( [ (1,2) ] ), Digraph( [ [ 1, 3 ], [ 2, 3 ]\
-, [ 3 ], [ 2, 3, 4 ], [ 1, 3, 5 ] ] ), [ 3, 2, 4, 1 ]), 1, (1,2)), MTSE(McAlis\
-terTripleSemigroup(Group( [ (1,2) ] ), Digraph( [ [ 1, 3 ], [ 2, 3 ], [ 3 ], [\
- 2, 3, 4 ], [ 1, 3, 5 ] ] ), [ 3, 2, 4, 1 ]), 2, ()) ]
+gap> Print(Semigroup(Elements(M1){[1, 2, 3]}), "\n");
+Semigroup([ MTSE(McAlisterTripleSemigroup(SymmetricGroup( [ 2 .. 5 ] ), Digrap\
+h( [ [ 1 ], [ 1, 2 ], [ 1, 3 ], [ 1, 4 ], [ 1, 5 ] ] ), [ 1 .. 4 ]), 1, ()), M\
+TSE(McAlisterTripleSemigroup(SymmetricGroup( [ 2 .. 5 ] ), Digraph( [ [ 1 ], [\
+ 1, 2 ], [ 1, 3 ], [ 1, 4 ], [ 1, 5 ] ] ), [ 1 .. 4 ]), 1, (4,5)), MTSE(McAlis\
+terTripleSemigroup(SymmetricGroup( [ 2 .. 5 ] ), Digraph( [ [ 1 ], [ 1, 2 ], [\
+ 1, 3 ], [ 1, 4 ], [ 1, 5 ] ] ), [ 1 .. 4 ]), 1, (3,4)) ]
 
 #T# AsSemigroup with bad input
 gap> T := Semigroup([PartialPerm([1], [3]),
@@ -235,7 +237,7 @@ gap> M7 := McAlisterTripleSemigroup(Group((5, 6)), x4, x4);;
 gap> IsomorphismSemigroups(M6, M7);
 fail
 
-#T# IsomorphicSemigroups with bad input
+#T# IsomorphismSemigroups with bad input
 gap> x1 := Digraph([[1], [1, 2], [1, 3]]);;
 gap> G := Group((2, 3));;
 gap> M1 := McAlisterTripleSemigroup(G, x1, x1);;
@@ -341,6 +343,24 @@ true
 gap> S = Range(cov);
 true
 
+#T# acting semgroups 
+#TODO: Are these functions necessary? They aren't used anywhere else in tests.
+gap> G := SymmetricGroup([2 .. 5]);;
+gap> x := Digraph([[1], [1, 2], [1, 3], [1, 4], [1, 5]]);;
+gap> y := Digraph([[1], [1, 2], [1, 3], [1, 4]]);;
+gap> M := McAlisterTripleSemigroup(G, x, y, OnPoints);;
+gap> x1 := Generators(M)[1];;
+gap> ActionDegree(Elements(M){[1, 2]});;
+gap> MinActionRank(M);;
+gap> LambdaRank(M)(0);
+0
+gap> RhoRank(M)(0);
+0
+gap> RhoInverse(M)(x1, x1);;
+gap> LambdaConjugator(M)(x1, x1);;
+gap> IdempotentTester(M)(x1, x1);;
+gap> IdempotentCreator(M);;  # TODO: needs more coverage, may be broken
+
 #T# SEMIGROUPS_UnbindVariables
 gap> Unbind(A);
 gap> Unbind(act);