Re: which algorithms are used within Solve[]?
- To: mathgroup at smc.vnet.net
- 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?