MathGroup Archive 2001

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"just a bug" !; Mathematica 4


I've just noticed this issue : Integrate[Sqrt[(r - x)(r + x)], {x, -r, r}]

Okay - so version 3 works but version 4 doesn't. 

I've read all the eloquent remarks, but the bottom line is surely this:

 A maths package costing well over 1,000 pounds and written by some of the finest
mathematicians and programmers in the world - should be able to integrate

Integrate[Sqrt[(r - x)(r + x)], {x, -r, r}]

Pete Lindsay

> From: David Withoff <withoff at>
To: mathgroup at
> Date: Sun, 25 Feb 2001 00:53:20 -0500 (EST)
> To: mathgroup at
> Subject: [mg27435] [mg27396] [mg27396] Re: [mg27364] Re: A bug of Integrate[] in
> Mathematica 4.1 (and 4.0)
>>>> Thank you for the report. Integrate[] appears to be behaving
>>>> erroneously in all of the cases you present. I have notified
>>>> the the developers of the problems. Unfortunately, there does
>>>> not appear to be a workaround.
>>>> Unfortunately, there are no bug lists available, and I will
>>>> not be informed of the status of the bug until it is fixed.
>>>> Most likely, a patch will not be made available.
>> I think this behaviour of Wolfram Research should be made public
>> somewhere on the web! Why do these guys not care about BUGS? A software
>> developer should fix his bugs and make this bug fixes available to the
>> users of his product.
> The unfortunate misstatements quoted above from technical support are
> at best misleading, and basically are just plain wrong.  For that, we
> certainly apologize. Unfortunately, now that this misinformation is on
> the web, it has a life of its own.
> It is of course abundantly false that there are no bug lists, no bug
> workarounds, that people are never notified of bug fixes, and so forth.
> Many if not most of the items in the web site
> (the bug list) describe bugs or other behaviors that people find
> troublesome, and many of those items include fixes and workarounds.
> This and other information is also frequently distributed in other ways,
> both to technical support people and to users.
> In fact, if one strips away the generalizations and takes a close
> look at the specific examples that have been raised here, it turns
> out that in all of these cases solutions have already been provided
> and/or the problems are already discussed in the bug list and/or
> the reported behaviors are not really bugs at all.
> Regarding the following particular examle:
>> Another annoying bug in Integrate is its handling of branch cuts in real
>> integrals. A "nice" example is the area of a half circle. You may try if
>> there has something changed in version 4.1 compared to 3.0 or 4.0.
>> Reporting this bug they did not admit that it is one at all because
>> Integrate would do "complex integrals". After my reply that then there
>> should be a possibility to define the path of integration in the complex
>> plane I never got a convincing answer ;-(. So here is my example:
>> Correct is the following:
>> In[1]:== Integrate[Sqrt[r^2-x^2],{x,-r,r},Assumptions->{r>0}]
>>              2
>>          Pi r
>> Out[1]== -----   (correct area of a half circle!)
>>            2
>> Now doing the same integral with a mathematically identical integrand:
>> In[1]:== Integrate[Sqrt[(r-x)(r+x)],{x,-r,r},Assumptions->{r>0}]
>>                    2
>>         Pi r Sqrt[r ]
>> Out[1]== -------------
>>               4
>> In[2]:== Simplify[%,r>0]
>>              2
>>          Pi r
>> Out[2]== ----- (WRONG factor 1/2)
>>           4
>> The reason is that Mathematica simply puts the boundaries which are on
>> the branch points of the integrand in the indefinite integrals which are
>> along branchcuts without proper I epsilon-descriptions (well known in
>> quantum theory)
> that class of bugs is described in the bug list
> (
> If someone didn't want to admit that this was a bug it was probably
> because they weren't sure, and didn't want to admit to something
> without knowing if it was true.  If someone said specifically that
> this wasn't a bug, or tried to offer some explanation involving
> complex integrals (or quantum theory) then they were mistaken.
> It's just a bug.  Probably it will be fixed in the next major release.
> Development of algorithms to do this sort of thing is a very difficult
> problem in mathematics, and yes it can be annoying that this problem
> has not yet been solved.  As soon as all problems have been solved
> then we can all go on vacation.
> Dave Withoff
> Wolfram Research

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