Changed tests in testinstall that did rely on immediate methods

Ditto for manual examples, including
some stability (do not test for values of `Random` etc.)

Includes slight modification for DerivedSubgroup of fp group
if subgroup of finite index is cyclic. (This might look overly specialized,
but is apparently of interest for some test examples, in any case it comes
at little cost to other calculations.)

also Further github remarks.

Fixed algmat.ytst in different way:

It seems this test file is run in different configurations, in which a
basis for a 0-dim space in one example is considered SemiEchelon (and thus
prints differently), in the other case not. Thus remove the display.
(Another example why the concept of testing for verbatim output is flawed.)

lib/ctbl.gd

@@ -3584,6 +3584,8 @@ DeclareGlobalVariable( "CharacterTableDisplayDefaults" );
 ##  tbl:=rec();
 ##  tbl.Irr:=
 ##  [ [ 1, 1 ], [ 1, -1 ] ];
+##  tbl.IsFinite:=
+##  true;
 ##  tbl.NrConjugacyClasses:=
 ##  2;
 ##  tbl.Size:=

lib/grp.gd

@@ -784,6 +784,8 @@ InstallFactorMaintenance( IsSolvableGroup,
 InstallTrueMethod( IsSolvableGroup, IsMonomialGroup );
 InstallTrueMethod( IsSolvableGroup, IsSupersolvableGroup );
 
+InstallTrueMethod( HasIsPerfectGroup, IsGroup and IsSolvableGroup and IsNonTrivial );
+
 
 #############################################################################
 ##

lib/grp.gi

@@ -31,7 +31,7 @@ InstallImmediateMethod( IsFinitelyGeneratedGroup,
 #M  IsCyclic( <G> ) . . . . . . . . . . . . . . . . test if a group is cyclic
 ##
 #  This used to be an immediate method. It was replaced by an ordinary
-#  method sine the flag is typically set when creating the group.
+#  method since the flag is typically set when creating the group.
 InstallMethod( IsCyclic, true, [IsGroup and HasGeneratorsOfGroup], 0,
     function( G )
     if Length( GeneratorsOfGroup( G ) ) = 1 then
@@ -439,13 +439,6 @@ InstallMethod( IsNilpotentGroup,
 ##
 #M  IsPerfectGroup( <G> ) . . . . . . . . . . . .  test if a group is perfect
 ##
-#  This used to be an immediate method. It was replaced by a TrueMethod (in
-#  the gd file)
-#InstallImmediateMethod( IsPerfectGroup,
-#    IsSolvableGroup and HasIsTrivial,
-#    0,
-#    IsTrivial );
-
 InstallImmediateMethod( IsPerfectGroup,
     IsGroup and HasIsAbelian and IsSimpleGroup,
     0,

lib/grpfp.gi

@@ -955,6 +955,11 @@ local iso,hom,u;
   if HasIsAbelian(G) and IsAbelian(G) then
     return TrivialSubgroup(G);
   elif Size(Image(hom))=infinity then
+    # test a special case -- one generator
+    if Length(GeneratorsOfGroup(G))=1 then
+      SetIsAbelian(G,true);
+      return TrivialSubgroup(G);
+    fi;
     Error("Derived subgroup has infinite index, cannot represent");
   elif Size(Range(hom))=1 then
     return G; # this is needed because the trivial quotient is represented

lib/object.gd

@@ -665,8 +665,7 @@ DeclareOperation( "ObjByExtRep", [ IsFamily, IsObject ] );
 ##  gap> KnownAttributesOfObject(g);
 ##  [ "Size", "OneImmutable", "NrMovedPoints", "MovedPoints", 
 ##    "GeneratorsOfMagmaWithInverses", "MultiplicativeNeutralElement", 
-##    "HomePcgs", "Pcgs", "GeneralizedPcgs", "StabChainMutable", 
-##    "StabChainOptions" ]
+##    "HomePcgs", "Pcgs", "StabChainMutable", "StabChainOptions" ]
 ##  ]]></Example>
 ##  </Description>
 ##  </ManSection>
@@ -707,28 +706,29 @@ DeclareOperation( "KnownPropertiesOfObject", [ IsObject ] );
 ##  <Example><![CDATA[
 ##  gap> g:=Group((1,2),(1,2,3));;
 ##  gap> KnownPropertiesOfObject(g);
-##  [ "IsFinite", "CanEasilyCompareElements", "CanEasilySortElements", 
-##    "IsDuplicateFree", "IsGeneratorsOfMagmaWithInverses", 
-##    "IsAssociative", "IsGeneratorsOfSemigroup", "IsSimpleSemigroup", 
-##    "IsRegularSemigroup", "IsInverseSemigroup", 
-##    "IsCompletelyRegularSemigroup", "IsCompletelySimpleSemigroup", 
-##    "IsGroupAsSemigroup", "IsMonoidAsSemigroup", "IsOrthodoxSemigroup", 
-##    "IsFinitelyGeneratedGroup", "IsSubsetLocallyFiniteGroup", 
-##    "KnowsHowToDecompose", "IsInfiniteAbelianizationGroup", 
-##    "IsNilpotentByFinite" ]
+##  [ "IsEmpty", "IsTrivial", "IsNonTrivial", "IsFinite",
+##    "CanEasilyCompareElements", "CanEasilySortElements",
+##    "IsDuplicateFree", "IsGeneratorsOfMagmaWithInverses",
+##    "IsAssociative", "IsGeneratorsOfSemigroup", "IsSimpleSemigroup",
+##    "IsRegularSemigroup", "IsInverseSemigroup",
+##    "IsCompletelyRegularSemigroup", "IsCompletelySimpleSemigroup",
+##    "IsGroupAsSemigroup", "IsMonoidAsSemigroup", "IsOrthodoxSemigroup",
+##    "IsFinitelyGeneratedGroup", "IsSubsetLocallyFiniteGroup",
+##    "KnowsHowToDecompose", "IsInfiniteAbelianizationGroup",
+##    "IsNilpotentByFinite", "IsTorsionFree", "IsFreeAbelian" ]
 ##  gap> Size(g);
 ##  6
 ##  gap> KnownPropertiesOfObject(g);
-##  [ "IsEmpty", "IsTrivial", "IsNonTrivial", "IsFinite", 
-##    "CanEasilyCompareElements", "CanEasilySortElements", 
-##    "IsDuplicateFree", "IsGeneratorsOfMagmaWithInverses", 
-##    "IsAssociative", "IsGeneratorsOfSemigroup", "IsSimpleSemigroup", 
-##    "IsRegularSemigroup", "IsInverseSemigroup", 
-##    "IsCompletelyRegularSemigroup", "IsCompletelySimpleSemigroup", 
-##    "IsGroupAsSemigroup", "IsMonoidAsSemigroup", "IsOrthodoxSemigroup", 
-##    "IsFinitelyGeneratedGroup", "IsSubsetLocallyFiniteGroup", 
-##    "KnowsHowToDecompose", "IsPerfectGroup", "IsSolvableGroup", 
-##    "IsPolycyclicGroup", "IsInfiniteAbelianizationGroup", 
+##  [ "IsEmpty", "IsTrivial", "IsNonTrivial", "IsFinite",
+##    "CanEasilyCompareElements", "CanEasilySortElements",
+##    "IsDuplicateFree", "IsGeneratorsOfMagmaWithInverses",
+##    "IsAssociative", "IsGeneratorsOfSemigroup", "IsSimpleSemigroup",
+##    "IsRegularSemigroup", "IsInverseSemigroup",
+##    "IsCompletelyRegularSemigroup", "IsCompletelySimpleSemigroup",
+##    "IsGroupAsSemigroup", "IsMonoidAsSemigroup", "IsOrthodoxSemigroup",
+##    "IsFinitelyGeneratedGroup", "IsSubsetLocallyFiniteGroup",
+##    "KnowsHowToDecompose", "IsPerfectGroup", "IsSolvableGroup",
+##    "IsPolycyclicGroup", "IsInfiniteAbelianizationGroup",
 ##    "IsNilpotentByFinite", "IsTorsionFree", "IsFreeAbelian" ]
 ##  gap> KnownTruePropertiesOfObject(g);
 ##  [ "IsNonTrivial", "IsFinite", "CanEasilyCompareElements", 

tst/testbugfix/00005.tst

@@ -15,4 +15,4 @@ gap> G:=GroupByGenerators( [ [ [ 0, -1, 0, 0 ], [ 1, 0, 0, 0 ],
 Group([ [ [ 0, -1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 0, -1 ], [ 0, 0, 1, 0 ] ] 
  ])
 gap> Centralizer(N,G);
-<matrix group of size infinity with 6 generators>
+<matrix group with 6 generators>

tst/testinstall/algmat.tst

@@ -256,8 +256,7 @@ gap> n:= NullAlgebra( GF(3) );
 <algebra over GF(3)>
 gap> Dimension( n );
 0
-gap> b:= Basis( n );
-SemiEchelonBasis( <algebra of dimension 0 over GF(3)>, [  ] )
+gap> b:= Basis( n );;
 gap> BasisVectors( b );
 [  ]
 gap> zero:= Zero( n );

tst/testinstall/coll.tst

@@ -97,13 +97,11 @@ Error, cannot test whether <C> contains the family of its elements
 # Size
 #
 
-# immediate method for collections knowing they are infinite
+## method for collections knowing they are infinite
 gap> c2:=ConjugacyClass(F, F.1);;
 gap> HasSize(c2);
 false
 gap> SetIsFinite(c2, false);
-gap> HasSize(c2);
-true
 gap> Size(c2);
 infinity
 

tst/testinstall/semigrp.tst

@@ -376,7 +376,7 @@ gap> GeneratorsOfInverseSemigroup(S);
 gap> GeneratorsOfInverseMonoid(S);
 [ <identity partial perm on [ 1 ]> ]
 gap> S := Group(IdentityTransformation);
-<transformation group of degree 0 with 1 generator>
+<trivial transformation group of degree 0 with 1 generator>
 gap> GeneratorsOfSemigroup(S);
 [ IdentityTransformation ]
 gap> GeneratorsOfMonoid(S);
@@ -474,12 +474,11 @@ true
 gap> Semigroup(Idempotents(S)) = S;
 true
 
-# test the methods for Random
+# test the methods for Random, but do not test for the values of random
+# elements
 gap> S := FreeSemigroup(3);;
-gap> Random(S);
-s1*s2
-gap> Random(GlobalRandomSource, S);
-s3*s2^2
+gap> Random(S);;
+gap> Random(GlobalRandomSource, S);;
 
 #T# Test DisplaySemigroup
 gap> DisplaySemigroup(FullTransformationSemigroup(1));

tst/testinstall/semitran.tst

@@ -141,7 +141,7 @@ gap> S := Group(Transformation([2,1,3]));
 gap> DegreeOfTransformationSemigroup(S);
 2
 gap> S := Group(IdentityTransformation);
-<transformation group of degree 0 with 1 generator>
+<trivial transformation group of degree 0 with 1 generator>
 gap> GeneratorsOfGroup(S);
 [ IdentityTransformation ]
 gap> S := Semigroup(IdentityTransformation);