Strange bug connected to GAP as a backend

[Peter Mueller]

The following lines do what is to be expected:

sage: g = SymmetricGroup(3)
....: u = g.subgroup([])
....: x1 = u.trivial_character().induct(g)
....: dummy = g.conjugacy_classes_subgroups()
....: x2 = u.trivial_character().induct(g)
....: print(x1 == x2)
....: print(x1.scalar_product(x1))
....: print(x2.scalar_product(x2))
True
6
6

However

sage: print(x1.scalar_product(x2))

raises a traceback. It seems that calling "g.conjugacy_classes_subgroups()" before creating x2, even though completely unrelated, messes something up internally.

This is well reproducible, as it happens with versions 9.7,  9.8.beta3, and also on the SageCell.

-- Peter Müller

(Remark: I reported a variant of this behavior previously at https://groups.google.com/g/sage-support/c/N4mAcl_fGCE.)

[Dima Pasechnik]

These pexpect-based GAP classed in Sage are a mess.
The only reason they are still there is that few things are actually
implemented in Cython, avoiding GAP,
and they are somehow faster (while many things are much slower)...
(one needs to update https://trac.sagemath.org/ticket/26902 here)

Anyhow, GAP (and libgap) seem to be fine, and you can do essentially
the same using libgap:

sage: g = libgap.SymmetricGroup(3)
sage: u = g.TrivialSubgroup()
sage: x1 = libgap.InducedClassFunction(u.TrivialCharacter(),g); x1
Character( CharacterTable( Sym( [ 1 .. 3 ] ) ), [ 6, 0, 0 ] )
sage: _ = g.ConjugacyClassesSubgroups()
sage: x2 = libgap.InducedClassFunction(u.TrivialCharacter(),g)
sage: x1.ScalarProduct(x2)
6
sage: x1.ScalarProduct(x1)
6
sage: x2.ScalarProduct(x2)
6


By the way, you can instead write
x1 = u.TrivialCharacter().InducedClassFunction(g)
...
x2 = u.TrivialCharacter().InducedClassFunction(g)

Dima

(PS. That was computed with GAP 4.12.1, as in
https://trac.sagemath.org/ticket/34391
- where the bug you reported is still reproducible; so it's not a GAP bug)

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