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Topic: variable elimination from polynomial system (2)
Replies: 4   Last Post: May 8, 2014 2:07 PM

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Posts: 1,245
Registered: 4/26/08
variable elimination from polynomial system (2)
Posted: Apr 18, 2014 3:20 PM
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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.


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