# Problem computing Grobner basis This post is a wiki. Anyone with karma >750 is welcome to improve it.

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.

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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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