Re: (x|y) \[element] Integers in Reduce function
- To: mathgroup at smc.vnet.net
- Subject: [mg82596] Re: (x|y) \[element] Integers in Reduce function
- From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
- Date: Fri, 26 Oct 2007 05:12:07 -0400 (EDT)
- Organization: The Open University, Milton Keynes, UK
- References: <ffn0le$5sp$1@smc.vnet.net> <ffpqjg$lkk$1@smc.vnet.net>
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').
Please, disregard my above erroneous misleading comment. As other
posters have already pointed out, (a) is the correct answer.
In[1]:= Element[x | y, Integers] /. {x -> 1, y -> Pi}
Out[1]= False
In[2]:= Element[{x, y}, Integers] /. {x -> 1, y -> Pi}
Out[2]= False
In[3]:= Element[x, Integers] && Element[y, Integers] /. {x -> 1,
y -> Pi}
Out[3]= False
In[4]:= Element[x, Integers] || Element[y, Integers] /. {x -> 1,
y -> Pi}
Out[4]= True
Regards,
--
Jean-Marc