AlgebraicRules

*To*: mathgroup at smc.vnet.net*Subject*: [mg127477] AlgebraicRules*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Sat, 28 Jul 2012 02:38:59 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*Reply-to*: murray at math.umass.edu

In a very recent post by Fred Simons, he cited his paper "Computer algebra in service courses", available as: http://alexandria.tue.nl/openaccess/Metis217845.pdf In it, he proves a certain trig identity. He begins by using TrigExpand to obtain a certain polynoial, call it "expanded", in Sin[x] and Cos[x]. Then he uses the function AlgebraicRules: expanded/.AlgebraicRules[{ Sin[x]^2 + Cos[x]^2 == 1, TrigExpand[Sin[3x]] == 1/2}] I only vaguely recall having seen AlgebraicRules back in Version 2.2 but have not come across it since. Although AlgebraicRules persists in the current version of Mathematica, the docs say that since Version 3.0, Algebraic Rules has been superseded by PolynomialReduce. Can PolynomialReduce in fact be used _directly_ on an expression that is not a polynomial in, say, a single variable x but rather in the pair of functions Sin[x] and Cos[x]? Or must one revert to the artifice of replacing Sin[x] and Cos[x] by new variable names, use PolynomialReduce, and finally reverse the replacement to get back to the original variable x? -- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305

**Follow-Ups**:**Re: AlgebraicRules***From:*Andrzej Kozlowski <akozlowski@gmail.com>