#6581: Groebner basis not working over symbolic ring
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Reporter: rhinton | Owner: tbd
Type: defect | Status: new
Priority: major | Milestone: sage-5.0
Component: commutative algebra | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Comment(by malb):
Here's a smaller example:
{{{
sage: P.<a> = QQ[]
sage: K = Frac(P)
sage: P.<x,y,z> = PolynomialRing(K)
sage: I = Ideal([P.random_element(), P.random_element(),
P.random_element()])
sage: I
Ideal (((a^2 - 3/4*a - 1)/(a^2 + a))*y*z + ((2/3*a^2 - 5/3*a - 1)/(-9*a^2
+ 5/6*a - 9/2))*z^2 + ((3/2*a^2 - a - 5/2)/(-1/20*a - 5/57))*x + ((2/3*a^2
- a - 1)/(-1/2*a^2 + 5*a + 7/4))*y + (7/3*a^2 - 5*a - 1)/(1/3*a^2 - 1/3*a
+ 3), ((1/2*a^2 - a - 1/2)/(-a^2 + 7))*x*y + ((-5/6*a^2 + 3*a - 1)/(-a^2 +
2/3*a - 1/4))*x*z + ((a^2 + 3/5*a + 1)/(-6*a^2 - a + 95))*y*z + ((-3*a^2 +
21/2)/(-a^2 - 1/5*a - 1))*z^2 + ((-1/3*a - 1/2)/(-1/3*a^2 - 1/8*a - 3))*z,
((a^2 + a)/(-3/2*a^2 - 1/3*a - 1))*x*y + 1/2*a*y^2 + ((1/31*a^2 -
1/8)/(-4*a^2 + 1/5*a - 2/3))*x*z + ((a^2 - a)/(a^2 - 1/20*a - 1/2))*z^2 +
(-1/15*a^2 + 1/315*a + 7/15)*y) of Multivariate Polynomial Ring in x, y, z
over Fraction Field of Univariate Polynomial Ring in a over Rational Field
sage: %time gb = I.groebner_basis()
CPU times: user 0.08 s, sys: 0.02 s, total: 0.09 s
Wall time: 0.33 s
sage: gb[-1]
y*z + ((-5472*a^4 + 8208*a^3 + 21888*a^2 + 8208*a)/(73872*a^4 - 62244*a^3
- 31806*a^2 - 20862*a - 36936))*z^2 + ((-2216160*a^4 - 738720*a^3 +
5171040*a^2 + 3693600*a)/(73872*a^3 + 74196*a^2 - 171072*a - 129600))*x +
((-98496*a^4 + 49248*a^3 + 295488*a^2 + 147744*a)/(73872*a^4 - 794124*a^3
+ 221616*a^2 + 932634*a + 258552))*y + (517104*a^4 - 590976*a^3 -
1329696*a^2 - 221616*a)/(73872*a^4 - 129276*a^3 + 646380*a^2 - 424764*a -
664848)
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6581#comment:6>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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