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Re: Re: solving a system of polynomial equations

• To: mathgroup at smc.vnet.net
• Subject: [mg87271] Re: [mg87247] Re: solving a system of polynomial equations
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Sun, 6 Apr 2008 06:42:39 -0400 (EDT)
• References: <ft4nas$43a$1@smc.vnet.net> <200804050923.EAA12125@smc.vnet.net>

On 5 Apr 2008, at 10:23, pluton wrote:
>
>> 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
>

With systems of algebraic (polynomial) equations NSolve uses numerical  
Groebner basis implemented with Mathematica's "significance arithmetic".

Non-polynomial equations are passed to Solve which they tries to  
reduce them to polynomial  (or algebraic) ones by means of inverse  
fucntions. Only very special cases can be handled in this way.

Andrzej Kozlowski

• References:
  • Re: solving a system of polynomial equations
    • From: pluton <plutonesque@gmail.com>