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Fix tests with singular 4.3.2p4 #36018

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Aug 27, 2023
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Fix tests with singular 4.3.2p4 #36018

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23 changes: 3 additions & 20 deletions src/sage/interfaces/singular.py
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Original file line number Diff line number Diff line change
Expand Up @@ -604,24 +604,15 @@ def eval(self, x, allow_semicolon=True, strip=True, **kwds):
sage: i = singular.ideal(['x^2','y^2','z^2'])
sage: s = i.std()
sage: singular.eval('hilb(%s)'%(s.name()))
'// 1 t^0\n// -3 t^2\n// 3 t^4\n// -1 t^6\n\n// 1 t^0\n//
3 t^1\n// 3 t^2\n// 1 t^3\n// dimension (affine) = 0\n//
'...// dimension (affine) = 0\n//
degree (affine) = 8'

::

sage: from sage.misc.verbose import set_verbose
sage: set_verbose(1)
sage: o = singular.eval('hilb(%s)'%(s.name()))
// 1 t^0
// -3 t^2
// 3 t^4
// -1 t^6
// 1 t^0
// 3 t^1
// 3 t^2
// 1 t^3
// dimension (affine) = 0
...// dimension (affine) = 0
// degree (affine) = 8

This is mainly useful if this method is called implicitly. Because
Expand All @@ -631,15 +622,7 @@ def eval(self, x, allow_semicolon=True, strip=True, **kwds):
::

sage: o = s.hilb()
// 1 t^0
// -3 t^2
// 3 t^4
// -1 t^6
// 1 t^0
// 3 t^1
// 3 t^2
// 1 t^3
// dimension (affine) = 0
...// dimension (affine) = 0
// degree (affine) = 8
// ** right side is not a datum, assignment ignored
...
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36 changes: 13 additions & 23 deletions src/sage/libs/singular/function.pyx
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Expand Up @@ -1241,32 +1241,22 @@ cdef class SingularFunction(SageObject):
sage: I = Ideal([x^3*y^2 + 3*x^2*y^2*z + y^3*z^2 + z^5])
sage: I = Ideal(I.groebner_basis())
sage: hilb = sage.libs.singular.function_factory.ff.hilb
sage: hilb(I) # Singular will print // ** _ is no standard basis
// ** _ is no standard basis
// 1 t^0
// -1 t^5
<BLANKLINE>
// 1 t^0
// 1 t^1
// 1 t^2
// 1 t^3
// 1 t^4
// dimension (proj.) = 1
// degree (proj.) = 5
sage: from sage.misc.sage_ostools import redirection
sage: out = tmp_filename()
sage: with redirection(sys.stdout, open(out, 'w')):
....: hilb(I) # Singular will print // ** _ is no standard basis
sage: with open(out) as f:
....: 'is no standard basis' in f.read()
True
So we tell Singular that ``I`` is indeed a Groebner basis::
sage: hilb(I,attributes={I:{'isSB':1}}) # no complaint from Singular
// 1 t^0
// -1 t^5
<BLANKLINE>
// 1 t^0
// 1 t^1
// 1 t^2
// 1 t^3
// 1 t^4
// dimension (proj.) = 1
// degree (proj.) = 5
sage: out = tmp_filename()
sage: with redirection(sys.stdout, open(out, 'w')):
....: hilb(I,attributes={I:{'isSB':1}}) # no complaint from Singular
sage: with open(out) as f:
....: 'is no standard basis' in f.read()
False
TESTS:
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9 changes: 6 additions & 3 deletions src/sage/rings/polynomial/multi_polynomial_ideal.py
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Expand Up @@ -3123,13 +3123,16 @@ def hilbert_numerator(self, grading=None, algorithm='sage'):
sage: I.hilbert_numerator() # needs sage.rings.number_field
-t^5 + 1

This example returns a wrong answer due to an integer overflow in Singular::
This example returns a wrong answer in singular < 4.3.2p4 due to an integer overflow::

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 - ...
sage: J.hilbert_numerator(algorithm='singular') # known bug
Traceback (most recent call last):
....
RuntimeError: error in Singular function call 'hilb':
overflow at t^22

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