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How can I solve a system of polynomial equations?

Posted 9 years ago


First, I generate a set of coefficients Ann in an nxn, where n may vary. I then want to solve for equations in the form:

A11 X1 + A12X2 + A13X3 + ... + A1NXN = 0

A21 X1^2 + A22X2^2 + A23X3^2 + ... + A2NXN^2 = 0


An1 X1^n + An2X2^n + An3X3^n + ... + AnnXn^n = 0

Does anyone know a good way to do this? LinearSolve is close, but can't seem to handle the exponents. I've tried using Solve in Table form, but it's giving me problems. Any help would be appreciated.

POSTED BY: Cody Lamb
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POSTED BY: Simon Cadrin

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POSTED BY: Simon Cadrin

What input have you tried?

This really does not appear to be a question about Mathematica. A perusal of the Documentation Center page for Solve should give an indicatation of why I say that.

POSTED BY: Daniel Lichtblau
Posted 9 years ago

Thanks for the info! I was able to get it to work by creating a table of polynomial equations and setting them equal to their respective value (zero most of the time). Then I just used the Solve function on that table, with respect to a table of the different variables and it worked. In my case, there's a definite solution, but in general, they're numeric answers only.

POSTED BY: Cody Lamb

See Quintic function:

Solving linear, quadratic, cubic and quartic equations by factorization into radicals can always be done, no matter whether the roots are rational or irrational, real or complex; there are also formulae that yield the required solutions. However, there is no explicit formula for general quintic equations over the rationals in terms of radicals; this is known as the Abel–Ruffini theorem, first published in 1824, which was the main motivation of the introduction of group theory by Évariste Galois, a few years later. This result also holds for equations of higher degrees. An example of a quintic whose roots cannot be expressed in terms of radicals is $x^5-x+1=0$. This quintic is in Bring–Jerrard normal form. Some quintics may be solved in terms of radical. However the solution is generally too complex for being used in practice. Therefore, one commonly uses numerical approximations of the solutions, which can be provided by any root-finding algorithm, and in particular by any root-finding algorithm for polynomials.

POSTED BY: Sam Carrettie

In my experience, there are no closed-form solutions for such systems of equations. You might have to approach the problem numerically.

POSTED BY: S M Blinder
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