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Re: HoldAll for Integrate
*To*: mathgroup at smc.vnet.net
*Subject*: [mg98069] Re: HoldAll for Integrate
*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
*Date*: Sun, 29 Mar 2009 02:46:19 -0500 (EST)
*References*: <gqfknb$kht$1@smc.vnet.net> <gqia4g$oi0$1@smc.vnet.net> <gqkuoj$44r$1@smc.vnet.net>
Hi,
AFAIK Integrate[] is C/C++ code of the Mathematica Kernel
and only the CVS at Wolfram Reseach will know exacly
what have changed since 1996.
Regards
Jens
Tammo Jan Dijkema wrote:
> Hi,
>
> Thanks for the responses. I realize that I'm doing a strange thing
> here, the goal is not to compute the integral, but to understand a bit
> better how Integrate works with regards to evaluation orders.
>
> I hadn't tried using Trace, and for the indefinite integral it
> certainly explains the output 1000. Apparently, something in the code
> for Integrate has changed since 1996 and now (since it evaluated to
> 1000/3 then).
>
> However, I'm still curious about the output of the definite integral
> Integrate[ x^2, {x,0,1} ]
> There is no 'reasonable' way I can think of for this to yield the value 0.
>
> Regards,
> Tammo Jan
>
> Op 2009-03-27 11:34:56 +0100, zei Jens-Peer Kuska
> <kuska at informatik.uni-leipzig.de>:
>
>> Hi,
>>
>> compare
>> x = 10;
>> SetAttributes[Integrate, HoldAll];
>>
>> Trace[Block[{x}, Integrate[x^2, x]]]
>>
>> with
>>
>> Trace[Integrate[x^2, x]]
>>
>> and you see, that x^2 is evaluated to 100 but
>> x is preserved, than 100 dx is computed to 100*x
>> and than x->10 is substituted again to give
>> 1000
>>
>> Regards
>> Jens
>>
>> Tammo Jan Dijkema wrote:
>>> The following commands yield unexpected output:
>>>
>>> x=10;
>>> Integrate[x^2, {x,0,1}]
>>>
>>> That is because Integrate does not have attributes HoldAll, so that the
>>> second command will be interpreted as Integrate[100, {10,0,1}] which is
>>> not a command that Integrate can work with (so a warning message is
>>> returned).
>>>
>>> However, I can add the attribute HoldAll to Integrate myself:
>>>
>>> SetAttributes[Integrate, HoldAll];
>>>
>>> I'm not very sure what to expect when now trying the same experiment
>>> (the correct answer 1/3 would be nice), but the actual output surprised
>>> me:
>>>
>>> x=10;
>>> Integrate[x^2, {x,0,1}]
>>>
>>> Yields as output: 0 (without any warnings). Could anyone explain why I
>>> should have expected this result?
>>>
>>> On a side note, I found a similar in the Tech Support column of the
>>> Mathematica Journal Volume 6, Issue 2, by Carl Roy. He tried the
>>> integral without limits:
>>>
>>> x=10;
>>> SetAttributes[Integrate, HoldAll];
>>> Integrate[x^2, x]
>>>
>>> In the journal, the output 1000/3 is mentioned, whereas in Mathematica
>>> 7.0.1 this outputs 1000.
>>>
>>> Again, does anyone understand this?
>
>
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