#11855: Hilbert series, Hilbert functions of a given ideal
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Reporter: dangtuanhiep | Owner: malb
Type: defect | Status: new
Priority: trivial | Milestone: sage-4.7.2
Component: commutative algebra | Keywords: sd34
Work_issues: | Upstream: N/A
Reviewer: | Author: Hiep Dang
Merged: | Dependencies:
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Changes (by burcin):
* type: enhancement => defect
Comment:
Replying to [comment:1 malb]:
> Huh, it's already there.
>
{{{
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| Sage Version 4.7.1, Release Date: 2011-08-11 |
| Type notebook() for the GUI, and license() for information. |
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sage: K.<w> = GF(27)
sage: P.<x, y> = PolynomialRing(K, 2, order='lex')
sage: I = Ideal([ x^8 + y + 2, y^6 + x*y^5 + x^2 ])
sage: I.hi
I.hilbert_polynomial I.hilbert_series
}}}
The return value of the existing function is a fraction field element, not
a power series.
{{{
sage: I.hilbert_series()
(-t - 1)/(t - 1)
sage: type(I.hilbert_series())
<type 'sage.rings.fraction_field_element.FractionFieldElement'>
}}}
Singular cannot represent power series in its interpreter, but we can. :)
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11855#comment:2>
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