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Re: Simplify expression


On 6/8/05 at 3:21 AM, mbekkali at gmail.com (Mukhtar Bekkali) wrote:

>I need to solve system of equations f1[x1,x2]=0,f2[x1,x2]==0,
>however, some elements of these equation have the form
>Sqrt[(x1^2-x2^2)^2].  It takes really long time to solve.  If,
>however, I manually simplify those elements, for example,
>Sqrt[(x1^2-x2^2)^2]=x1^2-x2^2 then solve is fast.  Therefore, the
>question is how I can force mathematica simplify expressions of
>this sort (another elements are fractions that depend on x1 and x2
>in Mathematica's mind but in reality they cancel out and fraction
>becomes a number). I do not want to use FindRoot since I want to
>see all solutions. Thanks, Mukhtar Bekkali

I think PowerExpand is what you are looking for, i.e.

PowerExpand[Sqrt[(x1^2-x2^2)^2]] yields

x1^2 - x2^2

Solve doesn't use PowerExpand as one of the transforms to try since it will not yield valid results for all possible conditions.
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