#7454: Make comparison of character tables sensible
----------------------------+-----------------------------------------------
Reporter: kcrisman | Owner: joyner
Type: enhancement | Status: new
Priority: minor | Milestone: sage-4.3
Component: group_theory | Keywords:
Work_issues: | Author:
Reviewer: | Merged:
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This seems annoying:
{{{
sage: S = SymmetricGroup(3).direct_product(CyclicPermutationGroup(2))[0]
sage: S
Permutation Group with generators [(1,2,3), (1,2), (4,5)]
sage: S.character_table()
[ 1 1 1 1 1 1]
[ 1 -1 -1 1 1 -1]
[ 1 -1 1 -1 1 -1]
[ 1 1 -1 -1 1 1]
[ 2 -2 0 0 -1 1]
[ 2 2 0 0 -1 -1]
sage: D = DihedralGroup(6)
sage: D.character_table()
[ 1 1 1 1 1 1]
[ 1 -1 -1 1 1 1]
[ 1 -1 1 -1 1 -1]
[ 1 1 -1 -1 1 -1]
[ 2 0 0 1 -1 -2]
[ 2 0 0 -1 -1 2]
sage: S.character_table()==D.character_table()
False
}}}
This is despite the fact that these groups are isomorphic (a fun
exercise!). The reason is
{{{
sage: type(S.character_table())
<type 'sage.matrix.matrix_cyclo_dense.Matrix_cyclo_dense'>
}}}
and the matrices above are obviously not identical. Which shouldn't
necessarily be changed, but nonetheless this is annoying. Maybe at least
a .has_same_character_table_as() method? At least for pedagogical
purposes. Better might be to have a separate class for character tables,
with a .matrix() method, but that would be perhaps backwards-incompatible.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7454>
Sage <http://www.sagemath.org>
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