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convert two methods to libsingular in affine subscheme #38367

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convert two methods to libsingular in affine subscheme #38367

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32362ac
convert two methods to libsingular in affine subscheme
fchapoton Jul 14, 2024
5b9940e
Merge branch 'develop' into libsingular_affine_subscheme
fchapoton Sep 19, 2024
6d55740
mute the libsingular warnings
fchapoton Sep 19, 2024
375667a
Merge branch 'develop' into libsingular_affine_subscheme
kwankyu Oct 2, 2024
3950cb0
Merge branch 'develop' into libsingular_affine_subscheme
fchapoton Jun 5, 2025
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29 changes: 24 additions & 5 deletions src/sage/schemes/affine/affine_subscheme.py
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Original file line number Diff line number Diff line change
Expand Up @@ -20,6 +20,10 @@
# ****************************************************************************

from sage.categories.fields import Fields
from sage.libs.singular.function import (singular_function,
lib as singular_lib,
get_printlevel, set_printlevel)
from sage.libs.singular.option import opt_verb
from sage.schemes.generic.algebraic_scheme import AlgebraicScheme_subscheme

from .affine_morphism import SchemeMorphism_polynomial_affine_subscheme_field
Expand Down Expand Up @@ -415,15 +419,22 @@ def intersection_multiplicity(self, X, P):
Iloc = R.ideal([f(chng_coords) for f in I.gens()])
Jloc = R.ideal([f(chng_coords) for f in J.gens()])
# compute the intersection multiplicity with Serre's Tor formula using Singular
from sage.interfaces.singular import singular
singular.lib("homolog.lib")
singular_lib("homolog.lib")
Tor = singular_function("Tor")
std = singular_function("std")
hilb = singular_function("hilb")
saved_printlevel = get_printlevel()
set_printlevel(-1)
opt_verb['not_warn_sb'] = True
i = 0
s = 0
t = sum(singular.Tor(i, Iloc, Jloc).std().hilb(2).sage())
t = sum(hilb(std(Tor(i, Iloc, Jloc)), 2))
while t != 0:
s += (-1)**i * t
i += 1
t = sum(singular.Tor(i, Iloc, Jloc).std().hilb(2).sage())
t = sum(hilb(std(Tor(i, Iloc, Jloc)), 2))
opt_verb.reset_default()
set_printlevel(saved_printlevel)
return s

def multiplicity(self, P):
Expand Down Expand Up @@ -497,7 +508,15 @@ def multiplicity(self, P):
chng_coords = [AA.gens()[i] + P[i] for i in range(AA.dimension_relative())]
R = AA.coordinate_ring().change_ring(order='negdegrevlex')
I = R.ideal([f(chng_coords) for f in self.defining_polynomials()])
return singular.mult(singular.std(I)).sage()
std = singular_function("std")
mult = singular_function("mult")
saved_printlevel = get_printlevel()
set_printlevel(-1)
opt_verb['not_warn_sb'] = True
result = mult(std(I))
opt_verb.reset_default()
set_printlevel(saved_printlevel)
return result


class AlgebraicScheme_subscheme_affine_field(AlgebraicScheme_subscheme_affine):
Expand Down
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