# Revision history [back]

You can use Singular's notion of a ring with parameters, but Sage's PolynomialRing interface to Singular doesn't understand this yet, so currently you have to do it by hand like so:

R = singular.ring('(0, p0, p1, p2, p3, p4, p5, p6, p7, p8, p9)', '(z0, z1, z2, z3, z4, z5, z6, z7)', 'dp')
I = singular.ideal('p0*z0*z1 - z2*z3', 'p1*z4 - z3*z5', 'p2*z1*z5 - z6', '-p3 - p4 - p5 + z4 + z5 + z6', '-p5 - p6 - p7 + z0 + z3 + z4', '-p3 - p8 - p9 + z1 + z2 + z6', '-p7 - p8 + z0 + z2', '-z6 + z7')
singular.option('redSB')
gb = singular.std(I)
S = singular.ring('(0, p0, p1, p2, p3, p4, p5, p6, p7, p8, p9)', '(z0, z1, z2, z3, z4, z5, z6, z7)', 'lp')
J = singular.ideal('fglm({}, {})'.format(R.name(), gb.name()))
J


It takes a few minutes but finally returns:

(-p0^2*p1*p2^2+p0^2*p2+2*p0*p1^2*p2^3-2*p0*p1*p2^2-p1^3*p2^4+p1^2*p2^3)*z7^5+(3*p0^2*p1*p2^2*p3+p0^2*p1*p2^2*p4+p0^2*p1*p2^2*p5-2*p0^2*p1*p2^2*p7+2*p0^2*p1*p2^2*p9+p0^2*p1*p2-2*p0^2*p2*p3-p0^2*p2*p4+p0^2*p2*p6+2*p0^2*p2*p7-p0^2*p2*p9-p0^2-p0*p1^3*p2^3-8*p0*p1^2*p2^3*p3-3*p0*p1^2*p2^3*p4-4*p0*p1^2*p2^3*p5-p0*p1^2*p2^3*p6+2*p0*p1^2*p2^3*p7-2*p0*p1^2*p2^3*p8-5*p0*p1^2*p2^3*p9-p0*p1^2*p2^2+6*p0*p1*p2^2*p3+3*p0*p1*p2^2*p4+2*p0*p1*p2^2*p5-p0*p1*p2^2*p6-2*p0*p1*p2^2*p7+2*p0*p1*p2^2*p8+3*p0*p1*p2^2*p9+2*p0*p1*p2+5*p1^3*p2^4*p3+2*p1^3*p2^4*p4+3*p1^3*p2^4*p5+p1^3*p2^4*p6+2*p1^3*p2^4*p8+3*p1^3*p2^4*p9+2*p1^3*p2^3-4*p1^2*p2^3*p3-2*p1^2*p2^3*p4-2*p1^2*p2^3*p5-2*p1^2*p2^3*p8-2*p1^2*p2^3*p9-2*p1^2*p2^2)*z7^4+(-3*p0^2*p1*p2^2*p3^2-2*p0^2*p1*p2^2*p3*p4-2*p0^2*p1*p2^2*p3*p5+4*p0^2*p1*p2^2*p3*p7-4*p0^2*p1*p2^2*p3*p9+2*p0^2*p1*p2^2*p4*p7-2*p0^2*p1*p2^2*p4*p9+2*p0^2*p1*p2^2*p5*p7-2*p0^2*p1*p2^2*p5*p9-p0^2*p1*p2^2*p7^2+2*p0^2*p1*p2^2*p7*p9-p0^2*p1*p2^2*p9^2-p0^2*p1*p2*p3+p0^2*p1*p2*p7-p0^2*p1*p2*p9+p0^2*p2*p3^2+p0^2*p2*p3*p4-p0^2*p2*p3*p6-2*p0^2*p2*p3*p7+p0^2*p2*p3*p9-p0^2*p2*p4*p7+p0^2*p2*p4*p9+p0^2*p2*p6*p7-p0^2*p2*p6*p9+p0^2*p2*p7^2-p0^2*p2*p7*p9+3*p0*p1^3*p2^3*p3+p0*p1^3*p2^3*p4+p0*p1^3*p2^3*p5-p0*p1^3*p2^3*p7+p0*p1^3*p2^3*p8+2*p0*p1^3*p2^3*p9+p0*p1^3*p2^2+12*p0*p1^2*p2^3*p3^2+9*p0*p1^2*p2^3*p3*p4+12*p0*p1^2*p2^3*p3*p5+3*p0*p1^2*p2^3*p3*p6-6*p0*p1^2*p2^3*p3*p7+6*p0*p1^2*p2^3*p3*p8+15*p0*p1^2*p2^3*p3*p9+p0*p1^2*p2^3*p4^2+3*p0*p1^2*p2^3*p4*p5+p0*p1^2*p2^3*p4*p6-3*p0*p1^2*p2^3*p4*p7+3*p0*p1^2*p2^3*p4*p8+7*p0*p1^2*p2^3*p4*p9+2*p0*p1^2*p2^3*p5^2+p0*p1^2*p2^3*p5*p6-4*p0*p1^2*p2^3*p5*p7+4*p0*p1^2*p2^3*p5*p8+9*p0*p1^2*p2^3*p5*p9-p0*p1^2*p2^3*p6*p7+p0*p1^2*p2^3*p6*p8+2*p0*p1^2*p2^3*p6*p9-2*p0*p1^2*p2^3*p7*p8-3*p0*p1^2*p2^3*p7*p9+3*p0*p1^2*p2^3*p8*p9+4*p0*p1^2*p2^3*p9^2+2*p0*p1^2*p2^2*p3+2*p0*p1^2*p2^2*p5+2*p0*p1^2*p2^2*p6+2*p0*p1^2*p2^2*p7+2*p0*p1^2*p2^2*p8+2*p0*p1^2*p2^2*p9-p0*p1^2*p2-6*p0*p1*p2^2*p3^2-6*p0*p1*p2^2*p3*p4-4*p0*p1*p2^2*p3*p5+2*p0*p1*p2^2*p3*p6+4*p0*p1*p2^2*p3*p7-4*p0*p1*p2^2*p3*p8-6*p0*p1*p2^2*p3*p9-p0*p1*p2^2*p4^2-2*p0*p1*p2^2*p4*p5+2*p0*p1*p2^2*p4*p7-2*p0*p1*p2^2*p4*p8-4*p0*p1*p2^2*p4*p9+2*p0*p1*p2^2*p5*p6+2*p0*p1*p2^2*p5*p7-2*p0*p1*p2^2*p5*p8-2*p0*p1*p2^2*p5*p9+p0*p1*p2^2*p6^2+2*p0*p1*p2^2*p6*p9+2*p0*p1*p2^2*p7*p8+2*p0*p1*p2^2*p7*p9-2*p0*p1*p2^2*p8*p9-p0*p1*p2^2*p9^2-2*p0*p1*p2*p3-p0*p1*p2*p4-2*p0*p1*p2*p5-p0*p1*p2*p6-2*p0*p1*p2*p7-2*p0*p1*p2*p8-p0*p1*p2*p9-10*p1^3*p2^4*p3^2-8*p1^3*p2^4*p3*p4-12*p1^3*p2^4*p3*p5-4*p1^3*p2^4*p3*p6-8*p1^3*p2^4*p3*p8-12*p1^3*p2^4*p3*p9-p1^3*p2^4*p4^2-4*p1^3*p2^4*p4*p5-2*p1^3*p2^4*p4*p6-4*p1^3*p2^4*p4*p8-6*p1^3*p2^4*p4*p9-3*p1^3*p2^4*p5^2-2*p1^3*p2^4*p5*p6-6*p1^3*p2^4*p5*p8-8*p1^3*p2^4*p5*p9-2*p1^3*p2^4*p6*p8-2*p1^3*p2^4*p6*p9-p1^3*p2^4*p8^2-4*p1^3*p2^4*p8*p9-3*p1^3*p2^4*p9^2-6*p1^3*p2^3*p3-2*p1^3*p2^3*p4-3*p1^3*p2^3*p5-p1^3*p2^3*p6-3*p1^3*p2^3*p8-4*p1^3*p2^3*p9-p1^3*p2^2+6*p1^2*p2^3*p3^2+6*p1^2*p2^3*p3*p4+6*p1^2*p2^3*p3*p5+6*p1^2*p2^3*p3*p8+6*p1^2*p2^3*p3*p9+p1^2*p2^3*p4^2+3*p1^2*p2^3*p4*p5+p1^2*p2^3*p4*p6+3*p1^2*p2^3*p4*p8+4*p1^2*p2^3*p4*p9+p1^2*p2^3*p5^2-p1^2*p2^3*p5*p6+4*p1^2*p2^3*p5*p8+3*p1^2*p2^3*p5*p9-p1^2*p2^3*p6^2+p1^2*p2^3*p6*p8-p1^2*p2^3*p6*p9+p1^2*p2^3*p8^2+3*p1^2*p2^3*p8*p9+p1^2*p2^3*p9^2+4*p1^2*p2^2*p3+2*p1^2*p2^2*p4+2*p1^2*p2^2*p5+2*p1^2*p2^2*p8+2*p1^2*p2^2*p9+p1^2*p2)*z7^3+(p0^2*p1*p2^2*p3^3+p0^2*p1*p2^2*p3^2*p4+p0^2*p1*p2^2*p3^2*p5-2*p0^2*p1*p2^2*p3^2*p7+2*p0^2*p1*p2^2*p3^2*p9-2*p0^2*p1*p2^2*p3*p4*p7+2*p0^2*p1*p2^2*p3*p4*p9-2*p0^2*p1*p2^2*p3*p5*p7+2*p0^2*p1*p2^2*p3*p5*p9+p0^2*p1*p2^2*p3*p7^2-2*p0^2*p1*p2^2*p3*p7*p9+p0^2*p1*p2^2*p3*p9^2+p0^2*p1*p2^2*p4*p7^2-2*p0^2*p1*p2^2*p4*p7*p9+p0^2*p1*p2^2*p4*p9^2+p0^2*p1*p2^2*p5*p7^2-2*p0^2*p1*p2^2*p5*p7*p9+p0^2*p1*p2^2*p5*p9^2-3*p0*p1^3*p2^3*p3^2-2*p0*p1^3*p2^3*p3*p4-2*p0*p1^3*p2^3*p3*p5+2*p0*p1^3*p2^3*p3*p7-2*p0*p1^3*p2^3*p3*p8-4*p0*p1^3*p2^3*p3*p9+p0*p1^3*p2^3*p4*p7-p0*p1^3*p2^3*p4*p8-2*p0*p1^3*p2^3*p4*p9+p0*p1^3*p2^3*p5*p7-p0*p1^3*p2^3*p5*p8-2*p0*p1^3*p2^3*p5*p9+p0*p1^3*p2^3*p7*p8+p0*p1^3*p2^3*p7*p9-p0*p1^3*p2^3*p8*p9-p0*p1^3*p2^3*p9^2-p0*p1^3*p2^2*p3-p0*p1^3*p2^2*p8-p0*p1^3*p2^2*p9-8*p0*p1^2*p2^3*p3^3-9*p0*p1^2*p2^3*p3^2*p4-12*p0*p1^2*p2^3*p3^2*p5-3*p0*p1^2*p2^3*p3^2*p6+6*p0*p1^2*p2^3*p3^2*p7-6*p0*p1^2*p2^3*p3^2*p8-15*p0*p1^2*p2^3*p3^2*p9-2*p0*p1^2*p2^3*p3*p4^2-6*p0*p1^2*p2^3*p3*p4*p5-2*p0*p1^2*p2^3*p3*p4*p6+6*p0*p1^2*p2^3*p3*p4*p7-6*p0*p1^2*p2^3*p3*p4*p8-14*p0*p1^2*p2^3*p3*p4*p9-4*p0*p1^2*p2^3*p3*p5^2-2*p0*p1^2*p2^3*p3*p5*p6+8*p0*p1^2*p2^3*p3*p5*p7-8*p0*p1^2*p2^3*p3*p5*p8-18*p0*p1^2*p2^3*p3*p5*p9+2*p0*p1^2*p2^3*p3*p6*p7-2*p0*p1^2*p2^3*p3*p6*p8-4*p0*p1^2*p2^3*p3*p6*p9+4*p0*p1^2*p2^3*p3*p7*p8+6*p0*p1^2*p2^3*p3*p7*p9-6*p0*p1^2*p2^3*p3*p8*p9-8*p0*p1^2*p2^3*p3*p9^2+p0*p1^2*p2^3*p4^2*p7-p0*p1^2*p2^3*p4^2*p8-2*p0*p1^2*p2^3*p4^2*p9+3*p0*p1^2*p2^3*p4*p5*p7-3*p0*p1^2*p2^3*p4*p5*p8-6*p0*p1^2*p2^3*p4*p5*p9+p0*p1^2*p2^3*p4*p6*p7-p0*p1^2*p2^3*p4*p6*p8-2*p0*p1^2*p2^3*p4*p6*p9+3*p0*p1^2*p2^3*p4*p7*p8+4*p0*p1^2*p2^3*p4*p7*p9-4*p0*p1^2*p2^3*p4*p8*p9-5*p0*p1^2*p2^3*p4*p9^2+2*p0*p1^2*p2^3*p5^2*p7-2*p0*p1^2*p2^3*p5^2*p8-4*p0*p1^2*p2^3*p5^2*p9+p0*p1^2*p2^3*p5*p6*p7-p0*p1^2*p2^3*p5*p6*p8-2*p0*p1^2*p2^3*p5*p6*p9+4*p0*p1^2*p2^3*p5*p7*p8+5*p0*p1^2*p2^3*p5*p7*p9-5*p0*p1^2*p2^3*p5*p8*p9-6*p0*p1^2*p2^3*p5*p9^2+p0*p1^2*p2^3*p6*p7*p8+p0*p1^2*p2^3*p6*p7*p9-p0*p1^2*p2^3*p6*p8*p9-p0*p1^2*p2^3*p6*p9^2+p0*p1^2*p2^3*p7*p8*p9+p0*p1^2*p2^3*p7*p9^2-p0*p1^2*p2^3*p8*p9^2-p0*p1^2*p2^3*p9^3-p0*p1^2*p2^2*p3^2-2*p0*p1^2*p2^2*p3*p5-2*p0*p1^2*p2^2*p3*p6-2*p0*p1^2*p2^2*p3*p7-2*p0*p1^2*p2^2*p3*p8-2*p0*p1^2*p2^2*p3*p9-p0*p1^2*p2^2*p4*p7-p0*p1^2*p2^2*p4*p8-p0*p1^2*p2^2*p5*p7-3*p0*p1^2*p2^2*p5*p8-2*p0*p1^2*p2^2*p5*p9-2*p0*p1^2*p2^2*p6*p8-2*p0*p1^2*p2^2*p6*p9-p0*p1^2*p2^2*p7*p8-p0*p1^2*p2^2*p7*p9-p0*p1^2*p2^2*p8*p9-p0*p1^2*p2^2*p9^2+2*p0*p1*p2^2*p3^3+3*p0*p1*p2^2*p3^2*p4+2*p0*p1*p2^2*p3^2*p5-p0*p1*p2^2*p3^2*p6-2*p0*p1*p2^2*p3^2*p7+2*p0*p1*p2^2*p3^2*p8+3*p0*p1*p2^2*p3^2*p9+p0*p1*p2^2*p3*p4^2+2*p0*p1*p2^2*p3*p4*p5-2*p0*p1*p2^2*p3*p4*p7+2*p0*p1*p2^2*p3*p4*p8+4*p0*p1*p2^2*p3*p4*p9-2*p0*p1*p2^2*p3*p5*p6-2*p0*p1*p2^2*p3*p5*p7+2*p0*p1*p2^2*p3*p5*p8+2*p0*p1*p2^2*p3*p5*p9-p0*p1*p2^2*p3*p6^2-2*p0*p1*p2^2*p3*p6*p9-2*p0*p1*p2^2*p3*p7*p8-2*p0*p1*p2^2*p3*p7*p9+2*p0*p1*p2^2*p3*p8*p9+p0*p1*p2^2*p3*p9^2-p0*p1*p2^2*p4^2*p7+p0*p1*p2^2*p4^2*p9-p0*p1*p2^2*p4*p5*p7+p0*p1*p2^2*p4*p5*p8+2*p0*p1*p2^2*p4*p5*p9+p0*p1*p2^2*p4*p6*p7+p0*p1*p2^2*p4*p6*p8-p0*p1*p2^2*p4*p7*p8+2*p0*p1*p2^2*p4*p8*p9+p0*p1*p2^2*p4*p9^2+p0*p1*p2^2*p5*p6*p7-p0*p1*p2^2*p5*p6*p8-2*p0*p1*p2^2*p5*p6*p9-2*p0*p1*p2^2*p5*p7*p8-p0*p1*p2^2*p5*p7*p9+p0*p1*p2^2*p5*p8*p9-p0*p1*p2^2*p6^2*p8-p0*p1*p2^2*p6^2*p9-p0*p1*p2^2*p6*p7*p8-p0*p1*p2^2*p6*p7*p9-p0*p1*p2^2*p6*p8*p9-p0*p1*p2^2*p6*p9^2-p0*p1*p2^2*p7*p8*p9-p0*p1*p2^2*p7*p9^2+10*p1^3*p2^4*p3^3+12*p1^3*p2^4*p3^2*p4+18*p1^3*p2^4*p3^2*p5+6*p1^3*p2^4*p3^2*p6+12*p1^3*p2^4*p3^2*p8+18*p1^3*p2^4*p3^2*p9+3*p1^3*p2^4*p3*p4^2+12*p1^3*p2^4*p3*p4*p5+6*p1^3*p2^4*p3*p4*p6+12*p1^3*p2^4*p3*p4*p8+18*p1^3*p2^4*p3*p4*p9+9*p1^3*p2^4*p3*p5^2+6*p1^3*p2^4*p3*p5*p6+18*p1^3*p2^4*p3*p5*p8+24*p1^3*p2^4*p3*p5*p9+6*p1^3*p2^4*p3*p6*p8+6*p1^3*p2^4*p3*p6*p9+3*p1^3*p2^4*p3*p8^2+12*p1^3*p2^4*p3*p8*p9+9*p1^3*p2^4*p3*p9^2+p1^3*p2^4*p4^2*p5+p1^3*p2^4*p4^2*p6+2*p1^3*p2^4*p4^2*p8+3*p1^3*p2^4*p4^2*p9+2*p1^3*p2^4*p4*p5^2+2*p1^3*p2^4*p4*p5*p6+8*p1^3*p2^4*p4*p5*p8+10*p1^3*p2^4*p4*p5*p9+4*p1^3*p2^4*p4*p6*p8+4*p1^3*p2^4*p4*p6*p9+2*p1^3*p2^4*p4*p8^2+8*p1^3*p2^4*p4*p8*p9+6*p1^3*p2^4*p4*p9^2+p1^3*p2^4*p5^3+p1^3*p2^4*p5^2*p6+6*p1^3*p2^4*p5^2*p8+7*p1^3*p2^4*p5^2*p9+4*p1^3*p2^4*p5*p6*p8+4*p1^3*p2^4*p5*p6*p9+3*p1^3*p2^4*p5*p8^2+10*p1^3*p2^4*p5*p8*p9+7*p1^3*p2^4*p5*p9^2+p1^3*p2^4*p6*p8^2+2*p1^3*p2^4*p6*p8*p9+p1^3*p2^4*p6*p9^2+p1^3*p2^4*p8^2*p9+2*p1^3*p2^4*p8*p9^2+p1^3*p2^4*p9^3+6*p1^3*p2^3*p3^2+4*p1^3*p2^3*p3*p4+6*p1^3*p2^3*p3*p5+2*p1^3*p2^3*p3*p6+6*p1^3*p2^3*p3*p8+8*p1^3*p2^3*p3*p9+p1^3*p2^3*p4*p5+p1^3*p2^3*p4*p6+3*p1^3*p2^3*p4*p8+4*p1^3*p2^3*p4*p9+p1^3*p2^3*p5^2+p1^3*p2^3*p5*p6+4*p1^3*p2^3*p5*p8+5*p1^3*p2^3*p5*p9+p1^3*p2^3*p6*p8+p1^3*p2^3*p6*p9+p1^3*p2^3*p8^2+3*p1^3*p2^3*p8*p9+2*p1^3*p2^3*p9^2+p1^3*p2^2*p3+p1^3*p2^2*p8+p1^3*p2^2*p9-4*p1^2*p2^3*p3^3-6*p1^2*p2^3*p3^2*p4-6*p1^2*p2^3*p3^2*p5-6*p1^2*p2^3*p3^2*p8-6*p1^2*p2^3*p3^2*p9-2*p1^2*p2^3*p3*p4^2-6*p1^2*p2^3*p3*p4*p5-2*p1^2*p2^3*p3*p4*p6-6*p1^2*p2^3*p3*p4*p8-8*p1^2*p2^3*p3*p4*p9-2*p1^2*p2^3*p3*p5^2+2*p1^2*p2^3*p3*p5*p6-8*p1^2*p2^3*p3*p5*p8-6*p1^2*p2^3*p3*p5*p9+2*p1^2*p2^3*p3*p6^2-2*p1^2*p2^3*p3*p6*p8+2*p1^2*p2^3*p3*p6*p9-2*p1^2*p2^3*p3*p8^2-6*p1^2*p2^3*p3*p8*p9-2*p1^2*p2^3*p3*p9^2-p1^2*p2^3*p4^2*p5-p1^2*p2^3*p4^2*p6-p1^2*p2^3*p4^2*p8-2*p1^2*p2^3*p4^2*p9-p1^2*p2^3*p4*p5^2-4*p1^2*p2^3*p4*p5*p8-4*p1^2*p2^3*p4*p5*p9+p1^2*p2^3*p4*p6^2-2*p1^2*p2^3*p4*p6*p8-p1^2*p2^3*p4*p8^2-4*p1^2*p2^3*p4*p8*p9-2*p1^2*p2^3*p4*p9^2+p1^2*p2^3*p5^2*p6-2*p1^2*p2^3*p5^2*p8-p1^2*p2^3*p5^2*p9+p1^2*p2^3*p5*p6^2+2*p1^2*p2^3*p5*p6*p9-2*p1^2*p2^3*p5*p8^2-4*p1^2*p2^3*p5*p8*p9-p1^2*p2^3*p5*p9^2+p1^2*p2^3*p6^2*p8+p1^2*p2^3*p6^2*p9-p1^2*p2^3*p6*p8^2+p1^2*p2^3*p6*p9^2-p1^2*p2^3*p8^2*p9-p1^2*p2^3*p8*p9^2-2*p1^2*p2^2*p3^2-2*p1^2*p2^2*p3*p4-2*p1^2*p2^2*p3*p5-2*p1^2*p2^2*p3*p8-2*p1^2*p2^2*p3*p9-p1^2*p2^2*p4*p5-p1^2*p2^2*p4*p6-p1^2*p2^2*p4*p8-2*p1^2*p2^2*p4*p9-p1^2*p2^2*p5^2-p1^2*p2^2*p5*p6-p1^2*p2^2*p5*p9+p1^2*p2^2*p6*p8+p1^2*p2^2*p6*p9-p1^2*p2^2*p8^2-p1^2*p2^2*p8*p9)*z7^2+(p0*p1^3*p2^3*p3^3+p0*p1^3*p2^3*p3^2*p4+p0*p1^3*p2^3*p3^2*p5-p0*p1^3*p2^3*p3^2*p7+p0*p1^3*p2^3*p3^2*p8+2*p0*p1^3*p2^3*p3^2*p9-p0*p1^3*p2^3*p3*p4*p7+p0*p1^3*p2^3*p3*p4*p8+2*p0*p1^3*p2^3*p3*p4*p9-p0*p1^3*p2^3*p3*p5*p7+p0*p1^3*p2^3*p3*p5*p8+2*p0*p1^3*p2^3*p3*p5*p9-p0*p1^3*p2^3*p3*p7*p8-p0*p1^3*p2^3*p3*p7*p9+p0*p1^3*p2^3*p3*p8*p9+p0*p1^3*p2^3*p3*p9^2-p0*p1^3*p2^3*p4*p7*p8-p0*p1^3*p2^3*p4*p7*p9+p0*p1^3*p2^3*p4*p8*p9+p0*p1^3*p2^3*p4*p9^2-p0*p1^3*p2^3*p5*p7*p8-p0*p1^3*p2^3*p5*p7*p9+p0*p1^3*p2^3*p5*p8*p9+p0*p1^3*p2^3*p5*p9^2+2*p0*p1^2*p2^3*p3^4+3*p0*p1^2*p2^3*p3^3*p4+4*p0*p1^2*p2^3*p3^3*p5+p0*p1^2*p2^3*p3^3*p6-2*p0*p1^2*p2^3*p3^3*p7+2*p0*p1^2*p2^3*p3^3*p8+5*p0*p1^2*p2^3*p3^3*p9+p0*p1^2*p2^3*p3^2*p4^2+3*p0*p1^2*p2^3*p3^2*p4*p5+p0*p1^2*p2^3*p3^2*p4*p6-3*p0*p1^2*p2^3*p3^2*p4*p7+3*p0*p1^2*p2^3*p3^2*p4*p8+7*p0*p1^2*p2^3*p3^2*p4*p9+2*p0*p1^2*p2^3*p3^2*p5^2+p0*p1^2*p2^3*p3^2*p5*p6-4*p0*p1^2*p2^3*p3^2*p5*p7+4*p0*p1^2*p2^3*p3^2*p5*p8+9*p0*p1^2*p2^3*p3^2*p5*p9-p0*p1^2*p2^3*p3^2*p6*p7+p0*p1^2*p2^3*p3^2*p6*p8+2*p0*p1^2*p2^3*p3^2*p6*p9-2*p0*p1^2*p2^3*p3^2*p7*p8-3*p0*p1^2*p2^3*p3^2*p7*p9+3*p0*p1^2*p2^3*p3^2*p8*p9+4*p0*p1^2*p2^3*p3^2*p9^2-p0*p1^2*p2^3*p3*p4^2*p7+p0*p1^2*p2^3*p3*p4^2*p8+2*p0*p1^2*p2^3*p3*p4^2*p9-3*p0*p1^2*p2^3*p3*p4*p5*p7+3*p0*p1^2*p2^3*p3*p4*p5*p8+6*p0*p1^2*p2^3*p3*p4*p5*p9-p0*p1^2*p2^3*p3*p4*p6*p7+p0*p1^2*p2^3*p3*p4*p6*p8+2*p0*p1^2*p2^3*p3*p4*p6*p9-3*p0*p1^2*p2^3*p3*p4*p7*p8-4*p0*p1^2*p2^3*p3*p4*p7*p9+4*p0*p1^2*p2^3*p3*p4*p8*p9+5*p0*p1^2*p2^3*p3*p4*p9^2-2*p0*p1^2*p2^3*p3*p5^2*p7+2*p0*p1^2*p2^3*p3*p5^2*p8+4*p0*p1^2*p2^3*p3*p5^2*p9-p0*p1^2*p2^3*p3*p5*p6*p7+p0*p1^2*p2^3*p3*p5*p6*p8+2*p0*p1^2*p2^3*p3*p5*p6*p9-4*p0*p1^2*p2^3*p3*p5*p7*p8-5*p0*p1^2*p2^3*p3*p5*p7*p9+5*p0*p1^2*p2^3*p3*p5*p8*p9+6*p0*p1^2*p2^3*p3*p5*p9^2-p0*p1^2*p2^3*p3*p6*p7*p8-p0*p1^2*p2^3*p3*p6*p7*p9+p0*p1^2*p2^3*p3*p6*p8*p9+p0*p1^2*p2^3*p3*p6*p9^2-p0*p1^2*p2^3*p3*p7*p8*p9-p0*p1^2*p2^3*p3*p7*p9^2+p0*p1^2*p2^3*p3*p8*p9^2+p0*p1^2*p2^3*p3*p9^3-p0*p1^2*p2^3*p4^2*p7*p8-p0*p1^2*p2^3*p4^2*p7*p9+p0*p1^2*p2^3*p4^2*p8*p9+p0*p1^2*p2^3*p4^2*p9^2-3*p0*p1^2*p2^3*p4*p5*p7*p8-3*p0*p1^2*p2^3*p4*p5*p7*p9+3*p0*p1^2*p2^3*p4*p5*p8*p9+3*p0*p1^2*p2^3*p4*p5*p9^2-p0*p1^2*p2^3*p4*p6*p7*p8-p0*p1^2*p2^3*p4*p6*p7*p9+p0*p1^2*p2^3*p4*p6*p8*p9+p0*p1^2*p2^3*p4*p6*p9^2-p0*p1^2*p2^3*p4*p7*p8*p9-p0*p1^2*p2^3*p4*p7*p9^2+p0*p1^2*p2^3*p4*p8*p9^2+p0*p1^2*p2^3*p4*p9^3-2*p0*p1^2*p2^3*p5^2*p7*p8-2*p0*p1^2*p2^3*p5^2*p7*p9+2*p0*p1^2*p2^3*p5^2*p8*p9+2*p0*p1^2*p2^3*p5^2*p9^2-p0*p1^2*p2^3*p5*p6*p7*p8-p0*p1^2*p2^3*p5*p6*p7*p9+p0*p1^2*p2^3*p5*p6*p8*p9+p0*p1^2*p2^3*p5*p6*p9^2-p0*p1^2*p2^3*p5*p7*p8*p9-p0*p1^2*p2^3*p5*p7*p9^2+p0*p1^2*p2^3*p5*p8*p9^2+p0*p1^2*p2^3*p5*p9^3-5*p1^3*p2^4*p3^4-8*p1^3*p2^4*p3^3*p4-12*p1^3*p2^4*p3^3*p5-4*p1^3*p2^4*p3^3*p6-8*p1^3*p2^4*p3^3*p8-12*p1^3*p2^4*p3^3*p9-3*p1^3*p2^4*p3^2*p4^2-12*p1^3*p2^4*p3^2*p4*p5-6*p1^3*p2^4*p3^2*p4*p6-12*p1^3*p2^4*p3^2*p4*p8-18*p1^3*p2^4*p3^2*p4*p9-9*p1^3*p2^4*p3^2*p5^2-6*p1^3*p2^4*p3^2*p5*p6-18*p1^3*p2^4*p3^2*p5*p8-24*p1^3*p2^4*p3^2*p5*p9-6*p1^3*p2^4*p3^2*p6*p8-6*p1^3*p2^4*p3^2*p6*p9-3*p1^3*p2^4*p3^2*p8^2-12*p1^3*p2^4*p3^2*p8*p9-9*p1^3*p2^4*p3^2*p9^2-2*p1^3*p2^4*p3*p4^2*p5-2*p1^3*p2^4*p3*p4^2*p6-4*p1^3*p2^4*p3*p4^2*p8-6*p1^3*p2^4*p3*p4^2*p9-4*p1^3*p2^4*p3*p4*p5^2-4*p1^3*p2^4*p3*p4*p5*p6-16*p1^3*p2^4*p3*p4*p5*p8-20*p1^3*p2^4*p3*p4*p5*p9-8*p1^3*p2^4*p3*p4*p6*p8-8*p1^3*p2^4*p3*p4*p6*p9-4*p1^3*p2^4*p3*p4*p8^2-16*p1^3*p2^4*p3*p4*p8*p9-12*p1^3*p2^4*p3*p4*p9^2-2*p1^3*p2^4*p3*p5^3-2*p1^3*p2^4*p3*p5^2*p6-12*p1^3*p2^4*p3*p5^2*p8-14*p1^3*p2^4*p3*p5^2*p9-8*p1^3*p2^4*p3*p5*p6*p8-8*p1^3*p2^4*p3*p5*p6*p9-6*p1^3*p2^4*p3*p5*p8^2-20*p1^3*p2^4*p3*p5*p8*p9-14*p1^3*p2^4*p3*p5*p9^2-2*p1^3*p2^4*p3*p6*p8^2-4*p1^3*p2^4*p3*p6*p8*p9-2*p1^3*p2^4*p3*p6*p9^2-2*p1^3*p2^4*p3*p8^2*p9-4*p1^3*p2^4*p3*p8*p9^2-2*p1^3*p2^4*p3*p9^3-2*p1^3*p2^4*p4^2*p5*p8-2*p1^3*p2^4*p4^2*p5*p9-2*p1^3*p2^4*p4^2*p6*p8-2*p1^3*p2^4*p4^2*p6*p9-p1^3*p2^4*p4^2*p8^2-4*p1^3*p2^4*p4^2*p8*p9-3*p1^3*p2^4*p4^2*p9^2-4*p1^3*p2^4*p4*p5^2*p8-4*p1^3*p2^4*p4*p5^2*p9-4*p1^3*p2^4*p4*p5*p6*p8-4*p1^3*p2^4*p4*p5*p6*p9-4*p1^3*p2^4*p4*p5*p8^2-12*p1^3*p2^4*p4*p5*p8*p9-8*p1^3*p2^4*p4*p5*p9^2-2*p1^3*p2^4*p4*p6*p8^2-4*p1^3*p2^4*p4*p6*p8*p9-2*p1^3*p2^4*p4*p6*p9^2-2*p1^3*p2^4*p4*p8^2*p9-4*p1^3*p2^4*p4*p8*p9^2-2*p1^3*p2^4*p4*p9^3-2*p1^3*p2^4*p5^3*p8-2*p1^3*p2^4*p5^3*p9-2*p1^3*p2^4*p5^2*p6*p8-2*p1^3*p2^4*p5^2*p6*p9-3*p1^3*p2^4*p5^2*p8^2-8*p1^3*p2^4*p5^2*p8*p9-5*p1^3*p2^4*p5^2*p9^2-2*p1^3*p2^4*p5*p6*p8^2-4*p1^3*p2^4*p5*p6*p8*p9-2*p1^3*p2^4*p5*p6*p9^2-2*p1^3*p2^4*p5*p8^2*p9-4*p1^3*p2^4*p5*p8*p9^2-2*p1^3*p2^4*p5*p9^3-2*p1^3*p2^3*p3^3-2*p1^3*p2^3*p3^2*p4-3*p1^3*p2^3*p3^2*p5-p1^3*p2^3*p3^2*p6-3*p1^3*p2^3*p3^2*p8-4*p1^3*p2^3*p3^2*p9-p1^3*p2^3*p3*p4*p5-p1^3*p2^3*p3*p4*p6-3*p1^3*p2^3*p3*p4*p8-4*p1^3*p2^3*p3*p4*p9-p1^3*p2^3*p3*p5^2-p1^3*p2^3*p3*p5*p6-4*p1^3*p2^3*p3*p5*p8-5*p1^3*p2^3*p3*p5*p9-p1^3*p2^3*p3*p6*p8-p1^3*p2^3*p3*p6*p9-p1^3*p2^3*p3*p8^2-3*p1^3*p2^3*p3*p8*p9-2*p1^3*p2^3*p3*p9^2-p1^3*p2^3*p4*p5*p8-p1^3*p2^3*p4*p5*p9-p1^3*p2^3*p4*p6*p8-p1^3*p2^3*p4*p6*p9-p1^3*p2^3*p4*p8^2-3*p1^3*p2^3*p4*p8*p9-2*p1^3*p2^3*p4*p9^2-p1^3*p2^3*p5^2*p8-p1^3*p2^3*p5^2*p9-p1^3*p2^3*p5*p6*p8-p1^3*p2^3*p5*p6*p9-p1^3*p2^3*p5*p8^2-3*p1^3*p2^3*p5*p8*p9-2*p1^3*p2^3*p5*p9^2+p1^2*p2^3*p3^4+2*p1^2*p2^3*p3^3*p4+2*p1^2*p2^3*p3^3*p5+2*p1^2*p2^3*p3^3*p8+2*p1^2*p2^3*p3^3*p9+p1^2*p2^3*p3^2*p4^2+3*p1^2*p2^3*p3^2*p4*p5+p1^2*p2^3*p3^2*p4*p6+3*p1^2*p2^3*p3^2*p4*p8+4*p1^2*p2^3*p3^2*p4*p9+p1^2*p2^3*p3^2*p5^2-p1^2*p2^3*p3^2*p5*p6+4*p1^2*p2^3*p3^2*p5*p8+3*p1^2*p2^3*p3^2*p5*p9-p1^2*p2^3*p3^2*p6^2+p1^2*p2^3*p3^2*p6*p8-p1^2*p2^3*p3^2*p6*p9+p1^2*p2^3*p3^2*p8^2+3*p1^2*p2^3*p3^2*p8*p9+p1^2*p2^3*p3^2*p9^2+p1^2*p2^3*p3*p4^2*p5+p1^2*p2^3*p3*p4^2*p6+p1^2*p2^3*p3*p4^2*p8+2*p1^2*p2^3*p3*p4^2*p9+p1^2*p2^3*p3*p4*p5^2+4*p1^2*p2^3*p3*p4*p5*p8+4*p1^2*p2^3*p3*p4*p5*p9-p1^2*p2^3*p3*p4*p6^2+2*p1^2*p2^3*p3*p4*p6*p8+p1^2*p2^3*p3*p4*p8^2+4*p1^2*p2^3*p3*p4*p8*p9+2*p1^2*p2^3*p3*p4*p9^2-p1^2*p2^3*p3*p5^2*p6+2*p1^2*p2^3*p3*p5^2*p8+p1^2*p2^3*p3*p5^2*p9-p1^2*p2^3*p3*p5*p6^2-2*p1^2*p2^3*p3*p5*p6*p9+2*p1^2*p2^3*p3*p5*p8^2+4*p1^2*p2^3*p3*p5*p8*p9+p1^2*p2^3*p3*p5*p9^2-p1^2*p2^3*p3*p6^2*p8-p1^2*p2^3*p3*p6^2*p9+p1^2*p2^3*p3*p6*p8^2-p1^2*p2^3*p3*p6*p9^2+p1^2*p2^3*p3*p8^2*p9+p1^2*p2^3*p3*p8*p9^2+p1^2*p2^3*p4^2*p5*p8+p1^2*p2^3*p4^2*p5*p9+p1^2*p2^3*p4^2*p6*p8+p1^2*p2^3*p4^2*p6*p9+p1^2*p2^3*p4^2*p8*p9+p1^2*p2^3*p4^2*p9^2+p1^2*p2^3*p4*p5^2*p8+p1^2*p2^3*p4*p5^2*p9+p1^2*p2^3*p4*p5*p8^2+2*p1^2*p2^3*p4*p5*p8*p9+p1^2*p2^3*p4*p5*p9^2-p1^2*p2^3*p4*p6^2*p8-p1^2*p2^3*p4*p6^2*p9+p1^2*p2^3*p4*p6*p8^2-p1^2*p2^3*p4*p6*p9^2+p1^2*p2^3*p4*p8^2*p9+p1^2*p2^3*p4*p8*p9^2-p1^2*p2^3*p5^2*p6*p8-p1^2*p2^3*p5^2*p6*p9+p1^2*p2^3*p5^2*p8^2+p1^2*p2^3*p5^2*p8*p9-p1^2*p2^3*p5*p6^2*p8-p1^2*p2^3*p5*p6^2*p9+p1^2*p2^3*p5*p6*p8^2-p1^2*p2^3*p5*p6*p9^2+p1^2*p2^3*p5*p8^2*p9+p1^2*p2^3*p5*p8*p9^2)*z7+(p1^3*p2^4*p3^5+2*p1^3*p2^4*p3^4*p4+3*p1^3*p2^4*p3^4*p5+p1^3*p2^4*p3^4*p6+2*p1^3*p2^4*p3^4*p8+3*p1^3*p2^4*p3^4*p9+p1^3*p2^4*p3^3*p4^2+4*p1^3*p2^4*p3^3*p4*p5+2*p1^3*p2^4*p3^3*p4*p6+4*p1^3*p2^4*p3^3*p4*p8+6*p1^3*p2^4*p3^3*p4*p9+3*p1^3*p2^4*p3^3*p5^2+2*p1^3*p2^4*p3^3*p5*p6+6*p1^3*p2^4*p3^3*p5*p8+8*p1^3*p2^4*p3^3*p5*p9+2*p1^3*p2^4*p3^3*p6*p8+2*p1^3*p2^4*p3^3*p6*p9+p1^3*p2^4*p3^3*p8^2+4*p1^3*p2^4*p3^3*p8*p9+3*p1^3*p2^4*p3^3*p9^2+p1^3*p2^4*p3^2*p4^2*p5+p1^3*p2^4*p3^2*p4^2*p6+2*p1^3*p2^4*p3^2*p4^2*p8+3*p1^3*p2^4*p3^2*p4^2*p9+2*p1^3*p2^4*p3^2*p4*p5^2+2*p1^3*p2^4*p3^2*p4*p5*p6+8*p1^3*p2^4*p3^2*p4*p5*p8+10*p1^3*p2^4*p3^2*p4*p5*p9+4*p1^3*p2^4*p3^2*p4*p6*p8+4*p1^3*p2^4*p3^2*p4*p6*p9+2*p1^3*p2^4*p3^2*p4*p8^2+8*p1^3*p2^4*p3^2*p4*p8*p9+6*p1^3*p2^4*p3^2*p4*p9^2+p1^3*p2^4*p3^2*p5^3+p1^3*p2^4*p3^2*p5^2*p6+6*p1^3*p2^4*p3^2*p5^2*p8+7*p1^3*p2^4*p3^2*p5^2*p9+4*p1^3*p2^4*p3^2*p5*p6*p8+4*p1^3*p2^4*p3^2*p5*p6*p9+3*p1^3*p2^4*p3^2*p5*p8^2+10*p1^3*p2^4*p3^2*p5*p8*p9+7*p1^3*p2^4*p3^2*p5*p9^2+p1^3*p2^4*p3^2*p6*p8^2+2*p1^3*p2^4*p3^2*p6*p8*p9+p1^3*p2^4*p3^2*p6*p9^2+p1^3*p2^4*p3^2*p8^2*p9+2*p1^3*p2^4*p3^2*p8*p9^2+p1^3*p2^4*p3^2*p9^3+2*p1^3*p2^4*p3*p4^2*p5*p8+2*p1^3*p2^4*p3*p4^2*p5*p9+2*p1^3*p2^4*p3*p4^2*p6*p8+2*p1^3*p2^4*p3*p4^2*p6*p9+p1^3*p2^4*p3*p4^2*p8^2+4*p1^3*p2^4*p3*p4^2*p8*p9+3*p1^3*p2^4*p3*p4^2*p9^2+4*p1^3*p2^4*p3*p4*p5^2*p8+4*p1^3*p2^4*p3*p4*p5^2*p9+4*p1^3*p2^4*p3*p4*p5*p6*p8+4*p1^3*p2^4*p3*p4*p5*p6*p9+4*p1^3*p2^4*p3*p4*p5*p8^2+12*p1^3*p2^4*p3*p4*p5*p8*p9+8*p1^3*p2^4*p3*p4*p5*p9^2+2*p1^3*p2^4*p3*p4*p6*p8^2+4*p1^3*p2^4*p3*p4*p6*p8*p9+2*p1^3*p2^4*p3*p4*p6*p9^2+2*p1^3*p2^4*p3*p4*p8^2*p9+4*p1^3*p2^4*p3*p4*p8*p9^2+2*p1^3*p2^4*p3*p4*p9^3+2*p1^3*p2^4*p3*p5^3*p8+2*p1^3*p2^4*p3*p5^3*p9+2*p1^3*p2^4*p3*p5^2*p6*p8+2*p1^3*p2^4*p3*p5^2*p6*p9+3*p1^3*p2^4*p3*p5^2*p8^2+8*p1^3*p2^4*p3*p5^2*p8*p9+5*p1^3*p2^4*p3*p5^2*p9^2+2*p1^3*p2^4*p3*p5*p6*p8^2+4*p1^3*p2^4*p3*p5*p6*p8*p9+2*p1^3*p2^4*p3*p5*p6*p9^2+2*p1^3*p2^4*p3*p5*p8^2*p9+4*p1^3*p2^4*p3*p5*p8*p9^2+2*p1^3*p2^4*p3*p5*p9^3+p1^3*p2^4*p4^2*p5*p8^2+2*p1^3*p2^4*p4^2*p5*p8*p9+p1^3*p2^4*p4^2*p5*p9^2+p1^3*p2^4*p4^2*p6*p8^2+2*p1^3*p2^4*p4^2*p6*p8*p9+p1^3*p2^4*p4^2*p6*p9^2+p1^3*p2^4*p4^2*p8^2*p9+2*p1^3*p2^4*p4^2*p8*p9^2+p1^3*p2^4*p4^2*p9^3+2*p1^3*p2^4*p4*p5^2*p8^2+4*p1^3*p2^4*p4*p5^2*p8*p9+2*p1^3*p2^4*p4*p5^2*p9^2+2*p1^3*p2^4*p4*p5*p6*p8^2+4*p1^3*p2^4*p4*p5*p6*p8*p9+2*p1^3*p2^4*p4*p5*p6*p9^2+2*p1^3*p2^4*p4*p5*p8^2*p9+4*p1^3*p2^4*p4*p5*p8*p9^2+2*p1^3*p2^4*p4*p5*p9^3+p1^3*p2^4*p5^3*p8^2+2*p1^3*p2^4*p5^3*p8*p9+p1^3*p2^4*p5^3*p9^2+p1^3*p2^4*p5^2*p6*p8^2+2*p1^3*p2^4*p5^2*p6*p8*p9+p1^3*p2^4*p5^2*p6*p9^2+p1^3*p2^4*p5^2*p8^2*p9+2*p1^3*p2^4*p5^2*p8*p9^2+p1^3*p2^4*p5^2*p9^3),
z6-z7,
...


Better yet would be using the libSingular interface.