Problem computing Grobner basis

asked 10 years ago

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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 10 years ago

nbruin
4153 ●3 ●45 ●91

updated 10 years ago

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 ...

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