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MathGroup Archive 1994

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simplification rules

  • To: mathgroup at (Mathematica mailing list)
  • Subject: simplification rules
  • From: nachbar at
  • 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.


Dr. Robert B. Nachbar | Merck Research Laboratories | 908/594-7795
nachbar at     | R50S-100                    | 908/594-4224 FAX
                      | PO Box 2000                 |
                      | Rahway, NJ 07065            |

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