Why does elimination_ideal not work here?

asked 2022-10-22 15:50:06 +0100

Siggi
11 ●1

updated 2022-10-23 09:33:39 +0100

5311 ●4 ●44 ●118

from sage.all import *
p = 1125899906842679
R = PolynomialRing(GF(p), 'x,y')
R.inject_variables()
I = Ideal(3*x**4 + 740736*x**2 + 4854540*x + 1125884665458743, -x**3 + y**2 + 1125899906719223*x + 1125899906438134)
J = I.elimination_ideal(y)

Here, elimination_ideal leads to an error. I have no clue why. For other examples, like other finite fields, it works. Has someone an idea, why?

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For other examples, like other finite fields, it works.

Can you give such an example ?

Emmanuel Charpentier ( 2022-10-23 00:45:08 +0100 )edit

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answered 2022-10-24 16:07:50 +0100

Max Alekseyev

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.elimination_ideal() is computed by Singular, which has a restriction for the field characteristic to be below $2^{31}$. Check this out:

P.<x,y> = GF(previous_prime(2^31))[]
print(P.parent())
P.<x,y> = GF(next_prime(2^31))[]
print(P.parent())

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Asked: 2022-10-22 15:50:06 +0100

Seen: 196 times

Last updated: Oct 24 '22

Why does elimination_ideal not work here? edit