Merge pull request gap-system#2878 from hulpke/ah/permgp

Random permutation of points when selecting base in centralizer

doc/tut/group.xml

@@ -832,7 +832,7 @@ usual way we now look for the subgroups above <C>u105</C>.
 <Example><![CDATA[
 gap> blocks := Blocks( a8, orb );; Length( blocks );
 15
-gap> blocks[1];
+gap> Set(blocks[1]);
 [ (1,2)(3,4)(5,6)(7,8), (1,3)(2,4)(5,7)(6,8), (1,4)(2,3)(5,8)(6,7),
   (1,5)(2,6)(3,7)(4,8), (1,6)(2,5)(3,8)(4,7), (1,7)(2,8)(3,5)(4,6),
   (1,8)(2,7)(3,6)(4,5) ]
@@ -862,7 +862,7 @@ lie in one orbit under the group,
 <Example><![CDATA[
 gap> rep := RepresentativeAction( a8, (1,2)(3,4)(5,6)(7,8),
 >                                        (1,3)(2,4)(5,8)(6,7) );
-(2,3)(6,8)
+(1,5,7,2,8,4,3)
 gap> u15 := ClosureGroup( u105, rep );; Index( a8, u15 );
 15
 ]]></Example>

lib/ctbl.gd

@@ -3944,10 +3944,10 @@ DeclareAttributeSuppCT( "SourceOfIsoclinicTable", IsNearlyCharacterTable,
 ##  gap> tg:= CharacterTable( g );;
 ##  gap> IsRecord(
 ##  >        TransformingPermutationsCharacterTables( index2[1], tg ) );
-##  false
+##  true
 ##  gap> IsRecord(
 ##  >        TransformingPermutationsCharacterTables( index2[2], tg ) );
-##  true
+##  false
 ##  ]]></Example>
 ##  <P/>
 ##  Alternatively, we could construct the character table of the central

lib/ctblfuns.gd

@@ -1345,7 +1345,7 @@ DeclareOperation( "Norm", [ IsOrdinaryTable, IsHomogeneousList ] );
 ##  <P/>
 ##  <Example><![CDATA[
 ##  gap> List( Irr( S4 ), CentreOfCharacter );
-##  [ Group([ (), (1,2), (1,2)(3,4), (1,2,3), (1,2,3,4) ]), Group(()), 
+##  [ Group([ (), (1,2), (1,2)(3,4), (1,2,3), (1,2,3,4) ]), Group(()),
 ##    Group([ (1,2)(3,4), (1,4)(2,3) ]), Group(()), Group([ (), (1,2), (1,
 ##     2)(3,4), (1,2,3), (1,2,3,4) ]) ]
 ##  ]]></Example>

lib/grp.gd

@@ -1877,7 +1877,7 @@ DeclareAttribute( "MinimalNormalSubgroups", IsGroup );
 ##  returns a list of all normal subgroups of <A>G</A>.
 ##  <Example><![CDATA[
 ##  gap> g:=SymmetricGroup(4);;NormalSubgroups(g);
-##  [ Sym( [ 1 .. 4 ] ), Alt( [ 1 .. 4 ] ), Group([ (1,4)(2,3), (1,3) 
+##  [ Sym( [ 1 .. 4 ] ), Alt( [ 1 .. 4 ] ), Group([ (1,4)(2,3), (1,3)
 ##    (2,4) ]), Group(()) ]
 ##  ]]></Example>
 ##  <P/>

lib/stbcbckt.gi

@@ -2356,8 +2356,26 @@ local  Omega,      # a common operation domain for <G>, <E> and <F>
   od;
 
   # Find the order in which to process the points in the base choice.
-  order := cycles.points{ cycles.firsts };
-  SortParallel( ShallowCopy( -cycles.lengths ), order );
+  #SortParallel( ShallowCopy( -cycles.lengths ), order );
+
+  # The criterion for selection of base points is to select them according
+  # to (descending) cycle length of the permutation to be conjugated. At the
+  # moment no other criterion is used (though experiments can observe a
+  # significant impact on run time -- there is work TODO).
+  # Beyond this choice, the base point order is determined as a side effect
+  # of the sorting algorithm.
+  # To avoid particular configurations falling repeatedly into a bad case,
+  # we permute the base points to obtain a random ordering beyond the
+  # criterion used. This can be turned off through an option for debugging
+  # purposes.
+  if ValueOption("norandom")=true then
+    i:=[1..Length(cycles.firsts)];
+  else
+    i:=FLOYDS_ALGORITHM(RandomSource(IsMersenneTwister),
+         Length(cycles.firsts),false);
+  fi;
+  order := cycles.points{ cycles.firsts{i} };
+  SortParallel( -(cycles.lengths{i}), order );
 
   repeat