#17676: bug in Singulars groebner basis computation over integers
-------------------------+-------------------------------------------------
Reporter: | Owner:
jakobkroeker | Status: new
Type: defect | Milestone: sage-6.5
Priority: major | Keywords: Singular
Component: packages: | Authors:
standard | Report Upstream: Reported upstream. Developers
Merged in: | acknowledge bug.
Reviewers: | Branch:
Work issues: | Dependencies:
Commit: |
Stopgaps: |
-------------------------+-------------------------------------------------
The following groebner basis computation over integers is
not correct (compare with M2 or Magma):
{{{
sage: R.<x,y,z> = PolynomialRing(ZZ, 3, order='lex')
sage: I = Ideal(13*x*y*z+6*x*y+78*x*z+36*x-11*y^2*z-66*y*z,
168*x*y*z+84*x*y+1008*x*z+504*x+12*y^3-154*y^2*z+72*y^2-924*y*z,
-168*x^2*y*z^2-84*x^2*y*z-1008*x^2*z^2-504*x^2*z+x*y^3*z+6*x*y^3+154*x*y^2*z^2+6*x*y^2*z+36*x*y^2+924*x*y*z^2-11*y^4*z-66*y^3*z
);
sage: gI = R*( I.groebner_basis() )
sage: len(gens(gI)) # expected 3
4
sage: gI
Ideal (x*y*z + 78*x*y + 6*x*z + 468*x + 144*y^3 - 143*y^2*z + 864*y^2 -
858*y*z, 84*x*y + 504*x + 156*y^3 - 154*y^2*z + 936*y^2 - 924*y*z,
156*y^5*z + 72*y^5 + 1562*y^4*z^2 + 1728*y^4*z + 432*y^4 - 1694*y^3*z^3 +
9372*y^3*z^2 + 4752*y^3*z - 10164*y^2*z^3, 312*y^3*z + 144*y^3 -
308*y^2*z^2 + 1872*y^2*z + 864*y^2 - 1848*y*z^2) of Multivariate
Polynomial Ring in x, y, z over Integer Ring
}}}
M2 code:
{{{
R = ZZ[x,y,z,MonomialOrder=>Lex]
I = ideal{13*x*y*z+6*x*y+78*x*z+36*x-11*y^2*z-66*y*z,
168*x*y*z+84*x*y+1008*x*z+504*x+12*y^3-154*y^2*z+72*y^2-924*y*z,
-168*x^2*y*z^2-84*x^2*y*z-1008*x^2*z^2-504*x^2*z+x*y^3*z+6*x*y^3+154*x*y^2*z^2+6*x*y^2*z+36*x*y^2+924*x*y*z^2-11*y^4*z-66*y^3*z}
gens gb I
}}}
The corresponding upstream bug report is:
http://www.singular.uni-kl.de:8002/trac/ticket/629
--
Ticket URL: <http://trac.sagemath.org/ticket/17676>
Sage <http://www.sagemath.org>
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