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Re: HoldAll for Integrate

  • To: mathgroup at smc.vnet.net
  • Subject: [mg97974] Re: [mg97923] HoldAll for Integrate
  • From: "David Park" <djmpark at comcast.net>
  • Date: Fri, 27 Mar 2009 05:32:52 -0500 (EST)
  • References: <23611142.1238066136237.JavaMail.root@m02>

I would never write a statement like x = 10; x is too common a symbol to
give it a value and doing so just gets you into the kind of problem that you
did get into. Localize variables like x. For example make it an argument in
a function definition, f[x_] := something, or set it in a With statement
that contains expressions that use it.

But if you do give it a Global value, then localize it (with Block or
Module) where you don't want it to have a value.

x = 10;
Block[{x},
 Integrate[x^2, {x, 0, 1}]]
1/3


David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/  


From: Tammo Jan Dijkema [mailto:T.J.Dijkema at gmail.com] 

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?

Regards,

Tammo Jan Dijkema





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