ASKSAGE: Sage Q&A Forum - Latest question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Mon, 01 Jun 2020 13:12:06 -0500Variable elimination in Sagehttps://ask.sagemath.org/question/51683/variable-elimination-in-sage/ Besides `maxima.eliminate`, are there any other functions in Sage that can be used to eliminate variables in a system of equations? Eg. those that use algorithms other than `Maxima`?mathdude94Mon, 01 Jun 2020 13:12:06 -0500https://ask.sagemath.org/question/51683/Elimination of variables in polynomial equationhttps://ask.sagemath.org/question/32742/elimination-of-variables-in-polynomial-equation/Hi,
I'm trying to eliminate 5 variables from a system of 6 equations in 7 unknowns, to obtain a planar curve. Am I asking for too much?
This is what I tried:
R.<x,v,c1,c2,c3,c4,c5> = PolynomialRing(QQ)
p0 = -16*c1*c2*c3*c4*c5+16*v
p1 = 16*c1*c2*c3*c4-16*(-c1*c2*c3-(c1*c2-(-c1-c2)*c3)*c4)*c5+40*v
p2 = -16*c1*c2*c3-16*(c1*c2-(-c1-c2)*c3)*c4-16*(c1*c2-(-c1-c2)*c3-(-c1-c2-c3)*c4)*c5+25*v
p3 = 16*c1*c2-16*(-c1-c2)*c3-16*(-c1-c2-c3)*c4-16*(-c1-c2-c3-c4)*c5-25;
p4 = -16*c1-16*c2-16*c3-16*c4-16*c5-40
I = ideal((c1-c3)*(c2-c4)-x*(c1-c4)*(c2-c3),p0,p1,p2,p3,p4)
J = I.elimination_ideal([c1,c2,c3,c4,c5])
Note that the system is symmetric in permutations of c1...c5, except for one equation that says that x is the cross-ratio of c1...c4.
I'm all the more embarrassed because I already computed the solution some time ago, but forgot how: it should be a polynomial J of degree 30 in v and 16 in x.
Many thanks in advance! LaurentlaurentbartholdiWed, 09 Mar 2016 03:48:02 -0600https://ask.sagemath.org/question/32742/