#20145: Hilbert series bug
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Reporter: stumpc5 | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-7.1
Component: | Keywords: Hilbert series, polynomial
commutative algebra | ring
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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This works correctly:
{{{
sage: n=4;m=10;P = PolynomialRing(QQ,n*m,"x"); x = P.gens(); M =
Matrix(n,x)
sage: M
[ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9]
[x10 x11 x12 x13 x14 x15 x16 x17 x18 x19]
[x20 x21 x22 x23 x24 x25 x26 x27 x28 x29]
[x30 x31 x32 x33 x34 x35 x36 x37 x38 x39]
sage: I = P.ideal(M.minors(2))
sage: I.hilbert_series().numerator()
-84*t^3 - 108*t^2 - 27*t - 1
sage: factor(I.hilbert_series().denominator())
(t - 1)^13
}}}
but if I increase the number of columns by one, I get
{{{
sage: n=4;m=11;P = PolynomialRing(QQ,n*m,"x"); x = P.gens(); M =
Matrix(n,x)
sage: M
[ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10]
[x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21]
[x22 x23 x24 x25 x26 x27 x28 x29 x30 x31 x32]
[x33 x34 x35 x36 x37 x38 x39 x40 x41 x42 x43]
sage: I = P.ideal(M.minors(2))
sage: I.hilbert_series().numerator()
120*t^33 - 3465*t^32 + 48180*t^31 - 429374*t^30 + 2753520*t^29 -
13522410*t^28 + 52832780*t^27 - 168384150*t^26 + 445188744*t^25 -
987193350*t^24 + 1847488500*t^23 + 1372406746*t^22 - 403422496*t^21 -
8403314*t^20 - 471656596*t^19 + 1806623746*t^18 + 752776200*t^17 +
752776200*t^16 - 1580830020*t^15 + 1673936550*t^14 - 1294246800*t^13 +
786893250*t^12 - 382391100*t^11 + 146679390*t^10 - 42299400*t^9 +
7837830*t^8 - 172260*t^7 - 468930*t^6 + 183744*t^5 - 39270*t^4 + 5060*t^3
- 330*t^2 + 1
sage: factor(I.hilbert_series().denominator())
(t - 1)^44
}}}
which is clearly not correct, as it can be checked with
{{{
sage: from sage.libs.singular.function import singular_function
sage: hilb = singular_function("hilb")
sage: std = singular_function("std")
sage: hilb(std(I))
// ** _ is no standard basis
...
// 1 t^0
// 30 t^1
// 135 t^2
// 120 t^3
// dimension (proj.) = 13
// degree (proj.) = 286
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/20145>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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