Re: Re: solving a system of polynomial equations

• To: mathgroup at smc.vnet.net
• Subject: [mg87262] Re: [mg87247] Re: solving a system of polynomial equations
• From: danl at wolfram.com
• Date: Sun, 6 Apr 2008 06:40:57 -0400 (EDT)
• References: <ft4nas\$43a\$1@smc.vnet.net>

>
>> Also, while NSolve intended primarily for polynomials,
>> Mathematica is not limited to solving polynomial equations. And
>> in fact, NSolve will solve some non-polynomial equations.
>
> but only one solution with non polynomial equations, right?
> The one closest to the starting guess?
> Do you know if Nsolve use any of the Groebner Theory?
>
> Thank you,
>
> Pluton

NSolve does not take a starting guess (FindRoot does).

If the system involves, say, transcendental functions, then NSolve will
just call Solve and numericize the results. Solve will typically do some
transformations in an attempt to find solutions using (possibly
multi-valued) inverse functions. You might obtain zero, one, or more
solutions in this way.

Regarding methods used, put NSolve into the Help browser, then follow

Related Links > Implementation notes: Numerical and Related Functions

You obtain:

"For systems of algebraic equations, NSolve computes a numerical Gröbner
basis using an efficient monomial ordering, then uses eigensystem methods
to extract numerical roots."

Daniel Lichtblau
Wolfram Research

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