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Re: trying to "simplify" very large output

• To: mathgroup at smc.vnet.net
• Subject: [mg83096] Re: [mg83058] trying to "simplify" very large output
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Sat, 10 Nov 2007 03:45:51 -0500 (EST)
• References: <200711091011.FAA09888@smc.vnet.net>

Basjsmit wrote:
> Dear Reader,
> 
> When I used Mathematica to solve a certain expression, the output was 
> extremely large, somewhere around 10 000 characters. When I looked more 
> closely at the output, I noticed certain frases kept repeating. I havent 
> found anything in the help, but Im wondering if there is a function that can 
> replace those frases with a variable and set that variable once. An example:
> 
> t-> -(y z-v x Cos[k]^2-v x Sin[k]^2)/(z^2-x^2 Cos[k]^2-x^2 Sin[k]^2)-1/2 
> \[Sqrt]((4 (y z-v x Cos[k]^2-v x Sin[k]^2) ........
> 
> becomes:
> 
> A = y z-v x Cos[k]^2-v x Sin[k]^2
> B = z^2-x^2 Cos[k]^2-x^2 Sin[k]^2
> t-> -A / B -1/2 \[Sqrt]((4 A ........
> 
> Thanks in advance, Bas
> 
> PS: just curious, is there a name for the proces I described above? 
> 

It is usually referred to as common subexpression elimination (cse). 
Quite coincidently this same question came my way yesterday. Mathematica 
has some functionality for this in Experimental` context, thus it is a 
bit hidden (unfortunately, I should add). Here are some URLs to prior 
threads that indicate usage.

http://forums.wolfram.com/mathgroup/archive/2006/Sep/msg00300.html
http://forums.wolfram.com/mathgroup/archive/2005/Jan/msg00387.html
http://forums.wolfram.com/mathgroup/archive/2002/Jan/msg00369.htm

Whether the functionality in Experimental`OptimizeExpression will help 
for your particular type of examples might depend on option settings, 
etc. so you'll probably need to experiment.

Daniel Lichtblau
Wolfram Research

• References:
  • trying to "simplify" very large output
    • From: "Basjsmit" <basjsmit@wanadoo.nl>