       Collect and manipulate subexpressions

• To: mathgroup at smc.vnet.net
• Subject: [mg53881] Collect and manipulate subexpressions
• From: "Goyder Dr HGD" <h.g.d.goyder at cranfield.ac.uk>
• Date: Tue, 1 Feb 2005 04:08:39 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```I am dealing with huge expressions that contain sums and products of trig functions as well as other terms. I wish to work with the expressions and make substitutions for various coefficients turning them into dimensionless groups. To help with this process I would like to replace the trig functions with symbols so I can see the overall form of the expression. As an example I give a very simple expression below and show how I replace the subexpressions made from trig functions by cutting and pasting. I wish to avoid cutting and pasting and do this automatically. Here is the expression.

e1 = (2 c q r w (-1 + Cos[k L2]))/(c S r w (4 Cos[k L1] - Cos[k (L1 - L2)] - 3 Cos[k (L1 + L2)]) + 2 M (w - w0) (w + w0) Sin[k (L1 + L2)]);

(* I cut and paste the trig functions avoiding all symbolic coefficients. How do I automate this? *)

ClearAll[f1, f2, f3];
subs = {f1 -> -1 + Cos[k L2],
f2 -> 4 Cos[k L1] - Cos[k (L1 - L2)] - 3 Cos[k (L1 + L2)],
f3 -> Sin[k (L1 + L2)]};

trigs = subs /. (a_ -> b_) :> (b -> a);

e2 = e1 /. trigs;

FullSimplify[e1 == e2 /. subs] (* check new expression *)

I can now work on this simpler expression, e2. The problem is how to make the subs, above, without resorting to cutting and pasting. I need to be able to identify any subexpression that contains sums or products of trig functions, but no other symbols, and turn this into a single symbol.

Thanks

Hugh Goyder

```

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