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.

doc/semieunit.xml

@@ -118,11 +118,7 @@ gap> T := McAlisterTripleSemigroup(A, x, y);
 gap> S = T;
 false
 gap> IsIsomorphicSemigroup(S, T);
-true
-gap> GeneratorsOfSemigroup(T);
-[ (1, ()), (4, ()), (5, ()), (1, (2,4)(3,5)) ]
-gap> AsSemigroup(IsPartialPermSemigroup, T);
-<inverse partial perm monoid of size 4, rank 4 with 4 generators>]]></Example>
+true]]></Example>
   </Description>
   </ManSection>
 <#/GAPDoc>

gap/main/setup.gi

@@ -51,7 +51,8 @@ InstallMethod(IsGeneratorsOfActingSemigroup,
 "for a McAlister triple element collection",
 [IsMcAlisterTripleSemigroupElementCollection],
 function(coll)
-  return IsPermGroup(McAlisterTripleSemigroupGroup(MTSEParent(coll[1])));
+  return
+  IsPermGroup(McAlisterTripleSemigroupGroup(MTSEParent(Representative(coll))));
     # and McAlisterTripleSemigroupAction(MTSEParent(coll[1])) = OnPoints;
 end);
 
@@ -102,11 +103,10 @@ function(x)
   return NrMovedPoints(x![2]) + 1;
 end);
 
-# TODO correct?
 InstallMethod(ActionDegree, "for a McAlister semigroup element",
 [IsMcAlisterTripleSemigroupElement],
 function(x)
-  return NrMovedPoints(x[2]);
+  return 0;
 end);
 
 InstallMethod(ActionDegree, "for a matrix over finite field object",
@@ -169,14 +169,10 @@ function(R)
   return 0;
 end);
 
-# TODO check this is ok?
-
 InstallMethod(ActionDegree, "for a McAlister triple subsemigroup",
 [IsMcAlisterTripleSubsemigroup],
 function(S)
-  local rep;
-  rep := Representative(S);
-  return NrMovedPoints(McAlisterTripleSemigroupGroup(MTSEParent(rep)));
+  return 0;
 end);
 
 InstallMethod(ActionDegree, "for a matrix over finite field semigroup",
@@ -248,8 +244,6 @@ function(R)
   end;
 end);
 
-# TODO: ok?
-
 InstallMethod(ActionRank, "for a McAlister triple semigroup element and int",
 [IsMcAlisterTripleSemigroupElement, IsInt],
 function(f, n)
@@ -260,8 +254,6 @@ function(f, n)
   return Position(DigraphTopologicalSort(digraph), id[f[1]]);
 end);
 
-# TODO: ok?
-
 InstallMethod(ActionRank, "for a McAlister triple subsemigroup",
 [IsMcAlisterTripleSubsemigroup],
 function(S)
@@ -784,11 +776,11 @@ end);
 InstallMethod(RhoBound, "for a Rees 0-matrix semigroup",
 [IsReesZeroMatrixSubsemigroup], LambdaBound);
 
-# TODO improve the upper bound here
 InstallMethod(LambdaBound, "for a McAlister subsemigroup",
 [IsMcAlisterTripleSubsemigroup], S ->
 function(r)
-  return Size(McAlisterTripleSemigroupGroup(MTSEParent(Representative(S))));
+  G := McAlisterTripleSemigroupGroup(MTSEParent(Representative(S)));
+  return Size(Stabilizer(G, r[1]));
 end);
 
 InstallMethod(RhoBound, "for a McAlister subsemigroup",

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]),
@@ -149,25 +151,25 @@ the semigroup is not E-unitary,
 
 #T# Other McAlisterTripleSemigroup tests
 gap> G := SymmetricGroup([2 .. 5]);;
-gap> x := Digraph([[1], [1, 2], [1, 3], [1, 4], [1, 5]]);
-<digraph with 5 vertices, 9 edges>
-gap> y := Digraph([[1], [1, 2], [1, 3], [1, 4]]);
-<digraph with 4 vertices, 7 edges>
+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);
 <McAlister triple semigroup over Sym( [ 2 .. 5 ] )>
 gap> IsIsomorphicSemigroup(M, McAlisterTripleSemigroup(G, x, x));
 false
 gap> IsInverseSemigroup(Semigroup(GeneratorsOfSemigroup(M)));
 true
 gap> elms := Enumerator(M);;
-gap> String(elms[1]);
-"MTSE(McAlisterTripleSemigroup(SymmetricGroup( [ 2 .. 5 ] ), Digraph( [ [ 1 ],\
- [ 1, 2 ], [ 1, 3 ], [ 1, 4 ], [ 1, 5 ] ] ), [ 1 .. 4 ]), 2, (3,4,5))"
+gap> String(elms[1]){[1 .. 40]};
+"MTSE(McAlisterTripleSemigroup(SymmetricG"
 gap> OneImmutable(M);
 fail
 gap> M1 := McAlisterTripleSemigroup(G, x, [1, 2]);;
 gap> OneImmutable(M1);
 (2, ())
+gap> x1 := DigraphFromDiSparse6String(".P__@_@_@__D_D_D__H_H_H_@DH_@DHL_@DHL_@DHLp?`abcdefghijklmno");;
+gap> y1 := InducedSubdigraph(x1, [1, 2, 3, 4, 6, 10, 11, 14, 15]);;
+gap> McAlisterTripleSemigroup(AutomorphismGroup(x1), x1, y1);;
 
 #T# McAlister triple semigroup elements
 gap> MTSE(M, 4, (2, 4)(3, 5)) * MTSE(M, 4, (2, 5, 3, 4));
@@ -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);;
@@ -260,8 +262,7 @@ fail
 #T# IsomorphismSemigroups, where RepresentativeAction fails
 gap> gr := DigraphFromDigraph6String("+H_A?GC_Q@G~wA?G");
 <digraph with 9 vertices, 20 edges>
-gap> G := Group((1, 2, 3)(4, 5, 6), (8, 9));
-Group([ (1,2,3)(4,5,6), (8,9) ])
+gap> G := Group((1, 2, 3)(4, 5, 6), (8, 9));;
 gap> S1 := McAlisterTripleSemigroup(G, gr, [1, 4, 5, 7, 8]);
 <McAlister triple semigroup over Group([ (1,2,3)(4,5,6), (8,9) ])>
 gap> S2 := McAlisterTripleSemigroup(G, gr, [3, 6, 7, 8, 9]);