simplification rules

*To*: mathgroup at yoda.physics.unc.edu (Mathematica mailing list)*Subject*: simplification rules*From*: nachbar at merck.com*Date*: Thu, 3 Mar 1994 14:06:53 -0500 (EST)

Roman Maeder gives a nice exposition on using transformation rules to simplify trigonometric expressions in chapter 6 of his book "Programming in Mathematica, 2nd edition." i'm doing some work where i have the following identity ex^2 + ey^2 + ez^2 == 1 i would like to be able to use it, and its various equivalent forms (e.g., ez^2 == 1 - ex^2 - ey^2) to simplify expressions such as ex^2 - 2 ex^4 - 2 ex^2 ey^2 - 2 ex^2 ez^2 + Cos[delta] - 3 ex^2 Cos[delta] + 2 ex^4 Cos[delta] + ex^2 ey^2 Cos[delta] + 2 ex^2 ez^2 Cos[delta] (you can see the identity lurking there in two places!). Simplify[] does not change the above expression. i know part of the "problem" is that ex^4 is stored internally as Power[ex,4]. is there a *general* way of using Factor, Expand, Collect, ... along with ReplaceAll (/.) and ReplaceRepeated (//.) to simplify the above expression? by hand i get Cos[delta] - ex^2 Cos[delta] - ex^2 thanks in advance for any useful suggestions. bob -- Dr. Robert B. Nachbar | Merck Research Laboratories | 908/594-7795 nachbar at merck.com | R50S-100 | 908/594-4224 FAX | PO Box 2000 | | Rahway, NJ 07065 |