#15817: Bug in computation of moliens series
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Reporter: nborie | Owner:
Type: PLEASE CHANGE | Status: new
Priority: critical | Milestone: sage-6.2
Component: group theory | Keywords: moliens series
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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Using a new algorithm from the hells, I try to check my results with the
current implementation of Moliens series... And I fall on this
{{{
sage: G = PermutationGroup([[(1,2,3,4)]])
sage: S4 = SymmetricGroup(4)
sage: secondary_enumeration_polynomial(G)
q^5 + 2*q^4 + q^3 + q^2 + 1
sage: G.molien_series() / S4.molien_series()
x^5 + 2*x^4 + x^3 + x^2 + 1
sage: G = PermutationGroup([[(1,2)],[(3,4)]])
sage: secondary_enumeration_polynomial(G)
q^4 + q^3 + 2*q^2 + q + 1
sage: G.molien_series() / S4.molien_series()
-x^5 - x^3 + x^2 + 1
}}}
`secondary_enumeration_polynomial` is my new function (which I hope,
compute the degree of secondary invariants polynomial associated to the
symmetric polynomial as primary invariants)... The quotient of the two
series MUST BE a polynomial with positive coefficients since the theory
says that for any subgroup `G` of `S_n`, the ring of invariant under the
action of `G` is a free module over the ring of symmetric polynomials.
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Ticket URL: <http://trac.sagemath.org/ticket/15817>
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