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Re: Most efficient method of simplifying

  • To: mathgroup at smc.vnet.net
  • Subject: [mg16240] Re: Most efficient method of simplifying
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Fri, 5 Mar 1999 00:41:06 -0500
  • Organization: Universitaet Leipzig
  • References: <7bg2c6$5n9@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi Greg,

it depends strongly on your problem. It is very similar to the
calculation
by hand. You may
split then Numerator[] and Denominator[] and Simplify[] the expression
separately or
use CoefficientList[,someX] on Numerator[] and Denominator[] and
simplify the coefficients
separatly.

If you know : "The result must be a polynom in z" it is clever to
simplify
only the coefficients of the polynom instead of the full expression.
Finaly
you can revert your transformations and continue.

Or if you know:"This is a polynom of degree 3 and I search for the
zeros" it
is better to get the solution for a3*x^3+a2*x^2+a1*x+a0==0 and to insert
the
coeficients in the general solution.

You may search for common subexpressions that can't be simplifyed 
(say you have serveral versions of (1-mu)^n ), replace this
subexpressions
by some new symbols and try to simplify the remaining expression. 

How ever only you know what equations you have and so :
Buy the largest computer available and additional  512 MByte Ram 
and use FullSimplify[].


Hope that helps
  Jens

Greg Arnold wrote:
> 
> Hello all:
> 
> I realize this is not a well defined questions, but I'm working with some
> fairly nasty ratios of functions (generally ratios of polynomials, but not
> always).  At several points I do some substitutions and then I want to
> simplify the result such that (1) all variables are removed (cancelled) that
> can be, and (2) the result simplifies to zero if appropriate.
> 
> "Simplify" is the obvious choice, but I've had many cases where simplify did
> not cancel and/or find the zero solution.  So, I could use FullSimplify, but
> both versions can take days to run.  All I really need is to "expand", but
> again there are cases where expand doesn't cancel and/or produce the zero
> result.  "ExpandAll" can make even the simpliest expression exremely
> complicated.
> 
> So, I'm looking for any advice others may have for more efficient ways of
> doing Simplify[ Expand[ ]].  As I said, this is not a well defined question
> & I suppose the ultimate answer is to use FullSimplify and buy the largest
> computer available.
> 
> Thanks,
> 
> Greg


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