#15817: Bug in computation of moliens series
-------------------------+-------------------------------------------------
Reporter: | Owner:
nborie | Status: needs_review
Type: | Milestone: sage-6.4
defect | Resolution:
Priority: | Merged in:
critical | Reviewers:
Component: group | Work issues:
theory | Commit:
Keywords: | 6149bbdc55692816d9df2308d0c02d2028f3a37f
moliens series | Stopgaps:
Authors: |
Frédéric Chapoton |
Report Upstream: N/A |
Branch: |
u/chapoton/15817 |
Dependencies: |
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Comment (by nborie):
--> Maybe the current algo only work for groups with no fixed points ?
Yes, I think that is why the last code was restricted to transitive group.
Anyway, the Moliens series is WELL defined for a finite group of matrices.
So, for the trivial group, it depends how you see it as a group of
matrices.
Here, my PermutationGroup([[(5,)]]) forces to see it as a subgroup of the
symmetric group of order 5 and my result correspond exactly to the q
analogue of n! for n=5 (which give the dimension degree by degree of the
co-invariant of S_5)
{{{
sage: G = PermutationGroup ([[(5,)]])
sage: secondary_enumeration_polynomial(G)
q^10 + 4*q^9 + 9*q^8 + 15*q^7 + 20*q^6 + 22*q^5 + 20*q^4 + 15*q^3 + 9*q^2
+ 4*q + 1
sage: from sage.combinat.q_analogues import q_factorial
sage: q_factorial(5)
q^10 + 4*q^9 + 9*q^8 + 15*q^7 + 20*q^6 + 22*q^5 + 20*q^4 + 15*q^3 + 9*q^2
+ 4*q + 1
}}}
My last one example should be check with
{{{
sage: G = PermutationGroup([[(5,)]])
sage: G.degree()
5
sage: G.molien_series() / SymmetricGroup(5).molien_series()
.....
}}}
If I remember correctly, there are some other place in Sage in which fixed
point did produce problems.
--
Ticket URL: <http://trac.sagemath.org/ticket/15817#comment:11>
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