Wrong computation of Hilbert polynomials

[loefflerd]

sage: R.<X, Y, Z> = QQ[]
sage: I = R.ideal([X^2*Y^3, X*Z])
sage: I.hilbert_polynomial()
-t - 5

The Hilbert polynomial, by definition, has to take non-negative integer values at all sufficiently large integers t, so this computation can't possibly be right. The correct answer is t + 5, which is what one gets with the algorithm='singular' option.

Inspecting the code, it looks like the denominator of the Hilbert series is getting normalised wrongly in some cases.

Component: commutative algebra

Author: Frédéric Chapoton, Kwankyu Lee

Branch/Commit: 98f118d

Reviewer: Kwankyu Lee, Frédéric Chapoton

Issue created by migration from https://trac.sagemath.org/ticket/33597

[fchapoton]

Branch: u/chapoton/33597

[fchapoton]

Author: Frédéric Chapoton

[fchapoton]

New commits:

51cb095

fixes in Hilbert polynomial

[fchapoton]

Commit: 51cb095

[fchapoton]

comment:6

bot is morally green, so please review

[kwankyu]

Changed branch from u/chapoton/33597 to u/klee/33597

[kwankyu]

Reviewer: Kwankyu Lee

[kwankyu]

comment:8

Sorry for hijacking this ticket. I made a few modifications to the patch so that

(1) we do not assume denom[0] can be only -1.

(2) the code is a bit more efficient.

Before your patch

sage: R.<X, Y, Z> = QQ[]
sage: I = R.ideal([X^2*Y^3, X*Z])
sage: I.hilbert_polynomial() 
sage: I.hilbert_polynomial()
-t - 5
sage: timeit('I.hilbert_polynomial()')
625 loops, best of 3: 409 μs per loop
sage: timeit('I.hilbert_polynomial()')
625 loops, best of 3: 416 μs per loop

After your patch

sage: R.<X, Y, Z> = QQ[]
sage: I = R.ideal([X^2*Y^3, X*Z])
sage: I.hilbert_polynomial()
t + 5
sage: timeit('I.hilbert_polynomial()')
625 loops, best of 3: 299 μs per loop
sage: timeit('I.hilbert_polynomial()')
625 loops, best of 3: 298 μs per loop

After my modifications

sage: R.<X, Y, Z> = QQ[]
sage: I = R.ideal([X^2*Y^3, X*Z])
sage: I.hilbert_polynomial()
t + 5
sage: timeit('I.hilbert_polynomial()')
625 loops, best of 3: 230 μs per loop
sage: timeit('I.hilbert_polynomial()')
625 loops, best of 3: 235 μs per loop

I am positive to the patch.

[kwankyu]

Changed commit from 51cb095 to b8630ac

[sagetrac-git]

Changed commit from b8630ac to 98f118d

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

98f118d

Minor edits

[fchapoton]

comment:10

ok, good to go, thanks

[fchapoton]

Changed reviewer from Kwankyu Lee to Kwankyu Lee, Frédéric Chapoton

[fchapoton]

Changed author from Frédéric Chapoton to Frédéric Chapoton, Kwankyu Lee

[kwankyu]

comment:11

Thank you!

[vbraun]

Changed branch from u/klee/33597 to 98f118d