       Simplifying an expression - with my own definition of what "simple"

• To: mathgroup at smc.vnet.net
• Subject: [mg83441] Simplifying an expression - with my own definition of what "simple"
• From: user8472 <head_over_heels at freenet.de>
• Date: Tue, 20 Nov 2007 03:58:17 -0500 (EST)

```Hi,

I am using Mathematica 5.2 on i386 Linux and I have the following problem: I want to express a rational polynomial of trigonometric functions in terms of elementary polynomials that I have defined myself.

A simplified example of what I want to do is illustrated as follows: Suppose the elementary function is f[x_]:=Sin[x/2], then I want to obtain

Cos[x] becomes 1-2*f[x]^2

Sin[x]^2 becomes 4f[x]^2-4f[x]^4

and so on. So my own definition of "simple" is "in terms of f[x]".

Is there a straightforward way to do this?

My actual problem is a little harder since it involved multiple variables and rational trigonometric polynomials, but at least analytically I can show that it can always be rewritten in terms of the elementary functions. The question is if Mathematica can in principle solve such types of problems as illustrated above.