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
- References:
- Re: (x|y) \[element] Integers in Reduce function
- From: Jean-Marc Gulliet <jeanmarc.gulliet@gmail.com>
- Re: (x|y) \[element] Integers in Reduce function