Problem computing Grobner basis

asked 2014-09-28 01:35:09 +0100

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I'm have the following code:

R0.<c4,e2,e3,e4> = QQ[]
F0 = Frac(R0)
R1.<a,b,m1,m2,m3,m4,r1,r2,r3,r4,s1,s2,s3,s4> = PolynomialRing(F0,14,order='degrevlex')
R2.<r,s,v,w> = R1[]

m = a + b*w
Mst = m1*m + m2*r + m3*s + m4
Rst = r1*m + r2*r + r3*s + r4
Sst = s1*m + s2*r + s3*s + s4

P1l = s + c4*v
P1r = m
P2l = m + e2*r + e3*s + e4*v 
P2r = r

Q1l = Sst + c4*v
Q1r = Mst
Q2l = Mst + e2*Rst + e3*Sst + e4*v 
Q2r = Rst

P = P1l*P1r - P2l*P2r
Q = Q1l*Q1r - Q2l*Q2r
H = P-Q
I = ideal(H.coefficients())
J = I.groebner_basis()

I get back an error from Singular:

SingularError: Singular error:
   ? unknown option `set`
   ? unknown option `sage7`
   ? error occurred in or before STDIN line 11: `option(set,sage7);`

Any idea what is going on? It won't crash with the "lex" ordering, but I'm running the computation in parallel on different cores with different orderings hoping one of them will eventually find something.

answered 2014-09-28 18:15:37 +0100

nbruin
4143 ●3 ●45 ●90

updated 2014-09-30 19:44:23 +0100

On sage 6.4beta2 with singular version 3-1-6 (Dec. 2012) I see no such error. The answer returned is:

[r2*s3^2 + ((-c4^2*e2*e3 + 2*c4*e2*e4 + e4^2)/(c4^2*e3^2 - 2*c4*e3*e4 + e4^2))*r3*s3^2 + ((-e4)/(-c4*e3 + e4))*s3^2 + ((-c4^2*e2*e3 - c4*e3*e4)/(c4^2*e3^2 - 2*c4*e3*e4 + e4^2))*r3 + (c4*e3/(-c4*e3 + e4))*s3,
 a*m1 + ((-e4)/(-c4*e3))*a*r2 + ((-2*c4*e2*e4 - c4*e3*e4 - e4^2)/(c4^2*e3^2 - c4*e3*e4))*a*r3 + ((c4*e3 + e4)/(-c4*e3))*a + m4,
 b*m1 + ((-e4)/(-c4*e3))*b*r2 + ((-2*c4*e2*e4 - c4*e3*e4 - e4^2)/(c4^2*e3^2 - c4*e3*e4))*b*r3 + ((c4*e3 + e4)/(-c4*e3))*b,
 b*m4,
 a*r1 + ((-1)/(-e3))*a*r2 + ((-2*c4*e2 - c4*e3 - e4)/(c4*e3^2 - e3*e4))*a*r3 + (1/(-e3))*a + r4,
 b*r1 + ((-1)/(-e3))*b*r2 + ((-2*c4*e2 - c4*e3 - e4)/(c4*e3^2 - e3*e4))*b*r3 + (1/(-e3))*b,
 m4*r1 + ((-1)/(-e3))*m4*r2 + ((-2*c4*e2 - c4*e3 - e4)/(c4*e3^2 - e3*e4))*m4*r3 - m1*r4 + (e4/(-c4*e3))*r2*r4 + ((2*c4*e2*e4 + c4*e3*e4 + e4^2)/(c4^2*e3^2 - c4*e3*e4))*r3*r4 + (1/(-e3))*m4 + ((-c4*e3 - e4)/(-c4*e3))*r4,
 r2^2 + ((c4*e3 - e4)/(c4*e2 + e4))*r2*s2 + ((-e4)/(c4*e2 + e4))*r2 + (e4/(c4*e2 + e4))*s2 + (-c4*e2)/(c4*e2 + e4),
 r2*r3 + ((c4^2*e2*e3 - 2*c4*e2*e4 - e4^2)/(c4^2*e2*e3 - c4*e2*e4 + c4*e3*e4 - e4^2))*r3*s3 + (e4/(c4*e3 - e4))*r3,
 r3^2 + ((c4*e3 - e4)/(c4*e2 + e4))*r3*s3,
 b*r4,
 a*s1 + ((-1)/(-e3))*a*s2 + ((-2*c4*e2 - c4*e3 - e4)/(c4*e3^2 - e3*e4))*a*s3 + ((2*c4*e2 + c4*e3 + e4)/(c4*e3^2 - e3*e4))*a + s4,
 b*s1 + ((-1)/(-e3))*b*s2 + ((-2*c4*e2 - c4*e3 - e4)/(c4*e3^2 - e3*e4))*b*s3 + ((2*c4*e2 + c4*e3 + e4)/(c4*e3^2 - e3*e4))*b,
 m4*s1 + ((-1)/(-e3))*m4*s2 + ((-2*c4*e2 - c4*e3 - e4)/(c4*e3^2 - e3*e4))*m4*s3 - m1*s4 + (e4/(-c4*e3))*r2*s4 + ((2*c4*e2*e4 + c4*e3*e4 + e4^2)/(c4^2*e3^2 - c4*e3*e4))*r3*s4 + ((2*c4*e2 + c4*e3 + e4)/(c4*e3^2 - e3*e4))*m4 + ((-c4*e3 - e4)/(-c4*e3))*s4,
 r4*s1 + ((-1)/(-e3))*r4*s2 + ((-2*c4*e2 - c4*e3 - e4)/(c4*e3^2 - e3*e4))*r4*s3 - r1*s4 + (1/(-e3))*r2*s4 + ((2*c4*e2 + c4*e3 + e4)/(c4*e3^2 - e3*e4))*r3*s4 + ((2*c4*e2 + c4*e3 + e4)/(c4*e3^2 - e3*e4))*r4 + ((-1)/(-e3))*s4,
 r3*s2 + r2*s3 + ((-2*c4^2*e2*e3 + 4*c4*e2*e4 + 2*e4^2 ...

(more)

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