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            |

```

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