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Move hilbert_numerator test to its proper place #35977

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Merged
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Jul 30, 2023
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Move hilbert_numerator test to its proper place #35977

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8 changes: 0 additions & 8 deletions src/sage/rings/polynomial/hilbert.pyx
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Original file line number Diff line number Diff line change
Expand Up @@ -576,14 +576,6 @@ def hilbert_poincare_series(I, grading=None):
120*t^3 + 135*t^2 + 30*t + 1
sage: hilbert_poincare_series(J).denominator().factor()
(t - 1)^14

This example exceeded the capabilities of Singular before version 4.2.1p2.
In Singular 4.3.1, it works correctly on 64-bit, but on 32-bit, it prints overflow warnings
and omits some terms::

sage: J.hilbert_numerator(algorithm='singular')
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 # 64-bit
...120*t^33 - 3465*t^32 + 48180*t^31 - ... # 32-bit
"""
cdef Polynomial_integer_dense_flint HP
HP, grading = first_hilbert_series(I, grading=grading, return_grading=True)
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8 changes: 8 additions & 0 deletions src/sage/rings/polynomial/multi_polynomial_ideal.py
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Expand Up @@ -3105,6 +3105,14 @@ def hilbert_numerator(self, grading=None, algorithm='sage'):
sage: I.hilbert_numerator() # optional - sage.rings.number_field
-t^5 + 1

This example returns a wrong answer due to an integer overflow in Singular::

sage: n=4; m=11; P = PolynomialRing(QQ, n*m, "x"); x = P.gens(); M = Matrix(n, x)
sage: I = P.ideal(M.minors(2))
sage: J = P * [m.lm() for m in I.groebner_basis()]
sage: J.hilbert_numerator(algorithm='singular')
...120*t^33 - 3465*t^32 + 48180*t^31 - ...

Our two algorithms should always agree; not tested until
:trac:`33178` is fixed::

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