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Re: Re: Polynomial rewriting question

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  • Subject: [mg101610] Re: [mg101525] Re: Polynomial rewriting question
  • From: Daniel Lichtblau <danl at>
  • Date: Fri, 10 Jul 2009 23:25:05 -0400 (EDT)
  • References: <>

AndrewTamra wrote:
> Thanks Daniel. You mentioned FullSimplify will SOMETIMES recognize the
 > factorization. Could you think of any other deterministic 
> I can implement in Mathematica for getting the simplification I am looking for?

Not offhand. The biggest impediment is in "factoring". I used the term 
loosely, to mean ability to isolate x-y as a reasonable-to-use common 
subexpression (CSE). I should have chosen a different term because 
factoring, an algorithmic process, is quite well defined.

> Even a probablistic numeric algorithm is OK as well, where I can test within
 > a reasonable probability, that there exists the factorization I am 
 > for; similar to the fast probablistic algorithms for Ideal membership 

Maybe I'm forgetting something important, but I'm not aware of fast 
probabalistic ideal membership algorithms. Regardless, I do not know a 
good way to deduce optimal CSEs, other than what you might find in CSE 
elimination literature.

> That way, first I can quickly determine the existence of such a simplification;
> then employ a slower (may be inefficient) algorithm to find the simplification
> (t=x-y in the example)
> Thanks

I think finding the simplification is the crux of the problem. You won't 
know one is there without explicitly finding it.


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