#6472: ideal.groebner_basis gives incorrect answers
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Reporter: broune | Owner: tbd
Type: defect | Status: new
Priority: major | Milestone: sage-4.1
Component: algebra | Keywords:
Reviewer: | Author:
Merged: |
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This is wrong:
{{{
sage: R.<a,b,c,d>=PolynomialRing(QQ,order="lex")
sage: ideal(a-b^16,b-c^16,c-d^1024).groebner_basis()
[a - d^4096, b - d^16384, c - d^1024]
}}}
The correct answer as given by Macaulay 2:
{{{
i30 : R=QQ[a,b,c,d, MonomialOrder=>Lex];
i31 : I=ideal(a-b^16,b-c^16,c-d^1024);
i32 : gens gb I
o32 = | c-d1024 b-d16384 a-d262144 |
}}}
In particular the binomial involving a should raise d to the power
262144=2^18^, not 4096=2^12^ as Sage reports.
I suspect that the reason is that by default Sage uses Singular to
implement groebner_basis, and Singular has limitations on the size of
exponents. See http://www.singular.uni-
kl.de/Manual/latest/sing_343.htm#SEC384 which in particular says
{{{
the maximal allowed exponent of a ring variable depends on the ordering of
the ring and is at least 32767.
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6472>
Sage <http://sagemath.org/>
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