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Re: Re: (x|y) \[element] Integers in Reduce function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg82590] Re: [mg82582] Re: (x|y) \[element] Integers in Reduce function
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Fri, 26 Oct 2007 05:09:02 -0400 (EDT)
  • References: <ffn0le$5sp$1@smc.vnet.net> <200710251009.GAA21790@smc.vnet.net>

On 25 Oct 2007, at 19:09, Jean-Marc Gulliet wrote:

> Steven Siew wrote:
>> Consider the following
>>
>> Reduce[x^2 - 2 y^2 == 1 && x>= 0 && y>=0 && (x|y) \[element]  
>> Integers,
>> {x,y} ]
>>
>> What does " (x|y) \[element] Integers "   mean?
>>
>> Does it mean:
>>
>> (a) x is an Integer  AND  y is an Integer
>>
>> (b) x is an Integer  OR  y is an Integer
>
> The correct answer is (b). The vertical bar | stands for  
> *Alternatives*
> in pattern matching (equivalent to the non-exclusive logical OR). See
> ref/Alternatives and also the tutorial "Patterns Involving  
> Alternatives"
> in the documentation center (tutorial/PatternsInvolvingAlternatives).
>
> Note that the correct syntax for \[element] is \[Element] (with a
> capital 'e').
>
> Regards,
> -- 
> Jean-Marc
>

No, the correct answer is (A)

FullSimplify[Im[a] + Im[b], Element[a | b, Reals]]
0

This only is correct when both a and b are real (given no other  
knowledge of a and b). For the explanation why the answer is A and  
not B see my first post in this thread.

Andrzej Kozlowski


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