Re: which algorithms are used within Solve[]?
- To: mathgroup at smc.vnet.net
- Subject: [mg105700] Re: [mg105669] which algorithms are used within Solve[]?
- From: Daniel Lichtblau <danl at wolfram.com>
- Date: Wed, 16 Dec 2009 06:16:43 -0500 (EST)
- References: <200912151224.HAA15012@smc.vnet.net>
Sagrailo wrote: > 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? The present version uses some flavor of Groebner bases to put the polynomial system into a "triangulated' form, similar to what happens in Gaussian elimination when all equations are linear. It then goes through a back substitution process. That is, it will have a univariate, solve for that, plug the roots into the next equation,... You can get further information from the documentation. See, for example, tutorial/ComplexPolynomialSystems in the Documentation Center. The notebook at the URL below will say a bit about what will be used in Solve in a future release of Mathematica. http://library.wolfram.com/infocenter/Conferences/7552/ Daniel Lichtblau Wolfram Research
- References:
- which algorithms are used within Solve[]?
- From: Sagrailo <sagrailo@gmail.com>
- which algorithms are used within Solve[]?