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Re: Simplifying algebraic expressions


On 1 Jun 2006, at 19:54, Amitabha Roy wrote:

> Hello:
>
> I would like Mathematica to be able to take an expression, say,
>
> (-1)^{2 x  + 3 y} and be able to simplify to (-1)^y.
>
> Is there a way one can do this ?
>
> Thanks
>

Note that you are using {} instead of (). Different kind of brackets  
have completely different meaning in Mathematica.
I have found it amazingly hard to force Mathematica to perform this  
simplification. The best I could do is this. We need two rules. rule1  
will replace 2x by u and 3y by v. rule 2 does the opposite: it  
replaces u by 2x and v by 2y.

rule1 = {2x -> u, 3y -> v};rule2 = Map[Reverse, rule1];

Now:


Simplify[TrigFactor[
    FullSimplify[ExpToTrig[
      FullSimplify[
        ComplexExpand[
         (-1)^(2*x + 3*y) /.
          rule1], Mod[u, 2] ==
         0] /. rule2],
     y â?? Integers]],
   y â?? Integers]


(-1)^y

Uff... Surely, this ought to be easier...

Andrzej Kozlowski
Tokyo, Japan


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