Re: Re: Re: Simplifying in Mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg71256] Re: [mg71247] Re: [mg71200] Re: Simplifying in Mathematica*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Sun, 12 Nov 2006 06:47:43 -0500 (EST)*References*: <eish5b$nq1$1@smc.vnet.net> <200611101138.GAA13711@smc.vnet.net> <200611110839.DAA27617@smc.vnet.net>

On 11 Nov 2006, at 17:39, Daniel Lichtblau wrote: > pierodancona at gmail.com wrote: >> Define a function (depending on the variables B,b,A,a,c,d...etc, >> all of them) equal to your expression, and compute it at many points. >> If the expression is 0, the result should always be 0. Notice that if >> your expression is a polynomial or rational and you choose your >> points in a "not too special" way, this gives actually a rigorous >> "proof" >> that the expression is 0. In general, this is an extrremely reliable >> heuristic (and of course a "proof" if you do not get 0 for some >> values). >> >> I encounter the same problem frequently, and this method works >> very well, also to test if two complicated expressions are the same >> or not (guess how :) >> >> Piero >> >> >> >> 330006 at gmail.com wrote: >> >>> I have a function which is a sum of many terms which look like this: >>> >>> (2*(B-b)^2 - 2*(A-a)*c*d^2)/(4*b^2*(1-c*2)*d^2) >>> >>> I think the function is actually equal to 0, but I have a hard >>> time in >>> trying to simplify it in Mathematica. Any ideas or commands I should >>> try? Any suggestions in general about simplifying formulas will also >>> be greatly appreciated! >>> >>> Thanks a lot! > > > Random point evaluation, and various other heuristics, are what lie > behind the Mathematica predicate Developer`ZeroQ. > > > Daniel Lichtblau > Wolfram Research > Another possible approach is to evaluate NMaximize[Abs[expr],vars], where expr is the expression suspected of being zero and vars the variables. Andrzej Kozlowski

**References**:**Re: Simplifying in Mathematica***From:*pierodancona@gmail.com

**Re: Re: Simplifying in Mathematica***From:*Daniel Lichtblau <danl@wolfram.com>