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which algorithms are used within Solve[]?

• To: mathgroup at smc.vnet.net
• Subject: [mg105669] which algorithms are used within Solve[]?
• From: Sagrailo <sagrailo at gmail.com>
• Date: Tue, 15 Dec 2009 07:24:37 -0500 (EST)

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?

• Follow-Ups:
  • Re: which algorithms are used within Solve[]?
    • From: Daniel Lichtblau <danl@wolfram.com>