tomlib: fusion problem for group 2.(A4xA4).2.2

[vdlee37]

 ┌───────┐   GAP 4.10.2 of 19-Jun-2019
 │  GAP  │   https://www.gap-system.org
 └───────┘   Architecture: i686-pc-cygwin-default32-kv3

gap> t:=TableOfMarks("2.(A4xA4).2.2");
TableOfMarks( "2.(A4xA4).2.2" )

gap> c:=CharacterTable("2.(A4xA4).2.2");
fail

gap> g:=UnderlyingGroup(t);
Group([ (1,11,9,5)(2,7,3,6)(4,12,10,8)(13,16,15,14)(17,23,22,18)(19,24)(20,21), (1,4,3,2)(5,14,12,6)(8,11)(9,15,13,10)
(17,19,20,23)(18,22,24,21), (1,15,13,9,10,3,2,4)(5,21,11,22,12,20,8,17)(6,19,7,23,14,24,16,18) ])

gap> c:=CharacterTable(g);
CharacterTable( Group([ (1,11,9,5)(2,7,3,6)(4,12,10,8)(13,16,15,14)(17,23,22,18)(19,24)(20,21), (1,4,3,2)(5,14,12,6)
(8,11)(9,15,13,10)(17,19,20,23)(18,22,24,21), (1,15,13,9,10,3,2,4)(5,21,11,22,12,20,8,17)(6,19,7,23,14,24,16,18) ]) )

gap> f:=FusionCharTableTom(c,t);
[ 1, 2, 4, 25, 9, 38, 11, 40, 108, 48, 10, 32, 18, 76, 3, 7, 8, 14, 44, 50, 5, 6, 13, 39, fail ]
                                                                                          ====

Notice that the final entry has value FAIL.

[ThomasBreuer]

@vdlee37 Thanks for this bug report.
The reason for the problem seems to be that RepresentativeTom does not return the correct representatives.

gap> t:= TableOfMarks( "2.(A4xA4).2.2" );;
gap> g:= UnderlyingGroup( t );;
gap> IsConjugate( g, RepresentativeTom( t, 39 ), RepresentativeTom( t, 43 ) );
true

I have opened an issue for that in the issue tracker of the TomLib package.

Concerning the original idea to use the table of marks and the character table from the GAP databases, the names of corresponding tables are not necessary equal, but you can do the following.

gap> t:= TableOfMarks( "2.(A4xA4).2.2" );
TableOfMarks( "2.(A4xA4).2.2" )
gap> c:= CharacterTable( t );
CharacterTable( "w(f4)" )
gap> f:=FusionCharTableTom(c,t);
[ 1, 2, 4, 25, 11, 40, 9, 38, 10, 48, 108, 3, 18, 32, 76, 5, 6, 8, 7, 13, 14, 
  43, 39, 44, 50 ]

[DominikBernhardt]

@ThomasBreuer As you have transfered this issue to the Issue tracker of the TomLib package,
can this Issue be closed?

[ThomasBreuer]

@DominikBernhardt I think it depends. If one regards a problem as solved as soon as it has been reported to some responsible person then yes. If one regards a problem as solved as soon as it disappears then no.

[DominikBernhardt]

@ThomasBreuer I thought our policy was to close Issues if they are moved to a package (and belong there). Maybe I was mistaken.

[fingolfin]

Fixed in gap-packages/tomlib#28, which needs to be merged and then tomlib needs a new release

[vdlee37]

Thanks everyone!

[fingolfin]

A fixed tomlib was released, and will be shipped with GAP 4.11