#20145: Hilbert series bug
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Reporter: stumpc5 | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-7.1
Component: commutative algebra | Resolution:
Keywords: Hilbert series, polynomial | Merged in:
ring | Reviewers:
Authors: | Work issues:
Report Upstream: N/A | Commit:
Branch: | Stopgaps:
Dependencies: |
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Comment (by dimpase):
Replying to [comment:4 stumpc5]:
> Replying to [comment:3 dimpase]:
> > well, for m=10 you only get the output above due to the fact that
numerator has a factor (t-1)^27^ that gets cancelled.
>
> I am not sure I follow what you mean
You can read the code of `I.hilbert_series` to see that it takes
`I.hilbert_numerator()`, which is computed by Singular (again, read the
code), and divides it by (t-1)^P.ngens()^.
> -- in the m=10 case, the (afaik) correct Hilbert series is
> {{{
> ( 84*t^3 + 108*t^2 + 27*t + 1 ) / (1 - t)^13
> }}}
> which is what I get above. But in the m=11 case, the (afaik) correct
Hilbert series is
> {{{
> ( 120*t^3 + 135*t^2 + 30*t + 1 ) / (1 - t)^14
> }}}
> which is not what I get above. In particular, the numerator output of
singular should be divisible by {{{(1-t)^30}}}, but - as you write - it is
irreducible instead.
So it is a bug in Singular, indeed.
--
Ticket URL: <http://trac.sagemath.org/ticket/20145#comment:6>
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