Hi,
one of my colleagues discovered a limitation of SAGE: apparently one cannot
compute over multivariate ideals over GF(p) for p >= 2^31:
sage: R.<x,y> = PolynomialRing(GF(2147483659))
sage: ideal([x^3-2*y^2,3*x+y^4]).groebner_basis()
...
<type 'exceptions.TypeError'>: Singular error:
? `2147483659` greater than 2147483647(max. integer representation)
? error occurred in STDIN line 10: `ring sage4=2147483659,(x, y),dp;`
? expected ring-expression. type 'help ring;'
An alternative to SAGE is to use Magma:
> R<x,y> := PolynomialRing(GF(2147483659),2);
> GroebnerBasis(Ideal([x^3-2*y^2,3*x+y^4]));
[
x + 1431655773*y^4,
y^12 + 54*y^2
]
or even Maple:
> Groebner[Basis]([x^3-2*y^2,3*x+y^4], plex(x,y), characteristic=2147483659);
12 2 4
[y + 54 y , x + 1431655773 y ]
Is there a workaround? If no, are there plans to remove that limitation?
Regards,
Paul
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