Re: Simplifying complicated expressions
- To: mathgroup at smc.vnet.net
- Subject: [mg110217] Re: Simplifying complicated expressions
- From: David Bailey <dave at removedbailey.co.uk>
- Date: Wed, 9 Jun 2010 07:18:56 -0400 (EDT)
- References: <hufu1o$eel$1@smc.vnet.net>
On 06/06/10 11:42, David Park wrote: > "The normal > /. and -> substitutions and patterns are not adequate for this." > > That sounds like a completely unfounded statement so why don't you > demonstrate it? > > > David Park > djmpark at comcast.net > http://home.comcast.net/~djmpark/ > > > From: S. B. Gray [mailto:stevebg at ROADRUNNER.COM] > > > Suppose I have a long complex expression in which terms like > (x^2+y^3-x^2y^2+Sqrt[z3+y2]) (for a simple example) appear many times > along with various powers and the reciprocals of it, etc. To make the > expression comprehensible and to make the computation faster, I would > like to substitute say "f1xyz" for it everywhere it appears. The normal > /. and -> substitutions and patterns are not adequate for this. Of > course at evaluation time I want to compute f1xyz only once and not have > the final formula revert to the original variables. How do I prevent that? > > Also a welcome addition to Mathematica would be the ability to find these > repeated expressions automatically and put them in, because doing it > manually is very error-prone and slow. > > Tips will be appreciated! > > Steve Gray > > > > In[10]:= x^2 + y^3 + b - x^2 y^2 + Sqrt[z3 + y2] + Sqrt[x^2 + y^3 - x^2 y^2 + Sqrt[z3 + y2]] //. x^2 + y^3 - x^2 y^2 + Sqrt[z3 + y2] -> flxyz Out[10]= b + Sqrt[flxyz] + flxyz Notice that Mathematica is not fooled by the fact that the 'b' term is embedded in one of the expressions that need to be replaced. Notice also that I used //. to obtain complete replacement. I was a little surprised that this was necessary, but the idea of //. (ReplaceAllRepeated) is that it looks again at subexpressions that have been changed. Extracting common sub expressions from a larger expression is a fairly tricky problem in general to do automatically, but you can get a fair way with /. and //. . The safest way to do this is to select the relevant subexpression using repeated clicking (or Control-.) so that you pick up a whole, valid expression, and then copy/paste it to the other side of the replacement operator. David Bailey www.dbaileyconsultancy.co.uk