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