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Re: which algorithms are used within Solve[]?

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  • Subject: [mg105705] Re: [mg105669] which algorithms are used within Solve[]?
  • From: "David Park" <djmpark at comcast.net>
  • Date: Wed, 16 Dec 2009 06:17:40 -0500 (EST)
  • References: <15138573.1260880287813.JavaMail.root@n11>

A core method that is used for polynomial equations is GroebnerBasis, which
also exists as an independent Mathematica function.

One place to learn more about Groebner Bases is 'Ideals, Varieties, and
Algorithms' by David Cox, John Little & Donal O'Shea.


David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/  


From: Sagrailo [mailto:sagrailo at gmail.com] 


Any insight on the exact procedure used by Solve[] for polynomial
equations (and systems of equations)?  Obviously, for several smaller
order polynomials, there exist explicit formulas, and then I remember
from my precalculus course of some methods of finding the range for
roots, then finding number of positive and negative roots, and then
finding possible rational root values for polynomials with integer
coefficients.  I guess there exist number of other specialized methods
that Mathematica is trying, any hints on these?




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