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Re: Is it possible with Mathematica?big problem.thank you

• To: mathgroup at smc.vnet.net
• Subject: [mg102608] Re: [mg102602] Is it possible with Mathematica?big problem.thank you
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Mon, 17 Aug 2009 04:00:39 -0400 (EDT)
• References: <200908161041.GAA01276@smc.vnet.net>

On 16 Aug 2009, at 12:41, olfa wrote:

> hello mathematica community,
> is it possible with mathematica to simplify this expression:
> [(z == zP and x*y == xP*yP)or (z + x*y == zP + xP*yP)]
> into:
> (z + x*y == zP + xP*yP)
>
> in fact something in mathematica should detect automatically that (z
> == zP and x*y == xP*yP) implies (z + x*y == zP + xP*yP)and then
> simplify the expression above based on a theorem or rule that says
> when [a implies b] then [a or b] is simplified into b .
>
> hope my explanation is clear and thank you very much for your help.
>


You have asked similar questions before and I have answered them, but  
it seems that you are not satisfied although never explain why. Your  
question involves quantifier elimination and Mathematica will return  
the form you want only under the assumptions that you stay within the  
field of Real numbers:

Reduce[(z == zP && x*y == xP*yP) || (z + x*y == zP + xP*yP), Reals]
z ==  -x y + xP yP + zP

Whether the restriction to Reals is a limitation or not depends on the  
nature of your problem, but I don't think you will be able to avoid it  
as long as your expressions contain quantifiers.

Andrzej Kozlowski

• References:
  • Is it possible with Mathematica?big problem.thank you
    • From: olfa <olfa.mraihi@yahoo.fr>