
variable elimination from polynomial system (2)
Posted:
Apr 18, 2014 3:20 PM


I had to change my strategy, but am faced again with a hard (for Derive) to solve system of 9 polynomial equations (= 0 implied):
[x3*x5 + x6*x7 + x8^2  x9, x1*x5 + x4*x7 + x7*x8 + 1, x0*x5 + x2*x7 + x5*x8, x2*x3 + x4*x6 + x6*x8  x9, x1*x2 + x4^2 + x6*x7  x9 + 1, x0*x2 + x2*x4 + x5*x6 + 2, x0*x3 + x1*x6 + x3*x8, x0*x1 + x1*x4 + x3*x7  x9, x0^2 + x1*x2 + x3*x5  x9 + 2]
I am interested in bivariate polynomials containing only [x8, x9], but am having difficulties eliminating the variables [x0, x1, x2, x3, x4, x5, x6, x7] from this system.
A corresponding Mathematica command may be something like
GroebnerBasis[{...}, {x8, x9}, {x0, x1, x2, x3, x4, x5, x6, x7}, MonomialOrder > EliminationOrder] // First // Factor
where "..." represents the above system (without the surrounding brackets). The "First" would throw away all but the first basis element, and the "Factor" is hoped to reveal simple factors.
Martin.

