#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: Simon King | Author: Hiep Dang, Burcin Erocal
Merged: | Dependencies:
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Changes (by SimonKing):
* reviewer: => Simon King
Comment:
Replying to [comment:5 malb]:
> The patch adds a second hilbert_series function instead of the changing
the one that exists already
Yes. Clearly it is a bad idea to implement another hilbert_series method
from scratch. Obviously, if one wants hilber_series to return a power
series, then one should modify the existing hilbert_serie method.
Moreover, I think we don't want it to return a power series. Isn't a power
series in Sage an object with a finite precision? Hence, while a quotient
(i.e., fraction field element) of two polynomials generates ''all''
(infinitely many) terms of the Hilbert series, a power series can only
provide finitely many terms, isn't it?
So, I am against that change. I could only imagine that one has an
optional parameter "as_power_series" (default False). Then,
`I.hilber_series()` would return the ''full'' Hilbert series (namely as a
quotient of two polynomials), while
`I.hilbert_series(as_power_series=True)` would return a (truncated) power
series.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11855#comment:6>
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