trying to "simplify" very large output

[Basjsmit]

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?

[Jean-Marc Gulliet]

Basjsmit wrote:

Transformation rules and replacement operators are your friends here.
You should familiarize yourself with the following set of tutorials,
available in the documentation center

tutorial/TransformationRulesAndDefinitionsOverview

or online at

http://reference.wolfram.com/mathematica/tutorial/TransformationRulesAndDefinitionsOverview.html

Regards,
--
Jean-Marc

[Daniel Lichtblau]

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