Re: "just a bug" !; Mathematica 4
- To: mathgroup at smc.vnet.net
- Subject: [mg27804] Re: "just a bug" !; Mathematica 4
- From: Lawrence Walker <lwalker701 at earthlink.net>
- Date: Fri, 16 Mar 2001 04:38:02 -0500 (EST)
- Organization: Morgan State University: COMSARE
- References: <N6mm6.17728$0r1.43475@ralph.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi Peter,
Try changing the limits of integration variables to be different from any variables
you called out within the integrand. That is, you can try
sol=Integrate[Sqrt[(r - x)(r + x)], {x, -a, a}] instead of
sol=Integrate[Sqrt[(r - x)(r + x)], {x, -r, r}]
and then
Limit[sol, r -> a] (* this step took a while to execute on my machine *)
This should give the expected solution in versions 4.0 and 4.1.
Lawrence
pl10-mac wrote:
> Hi,
>
> 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 wolfram.com>
To: mathgroup at smc.vnet.net
> > Date: Sun, 25 Feb 2001 00:53:20 -0500 (EST)
> > To: mathgroup at smc.vnet.net
> > Subject: [mg27804] [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 support.wolfram.com 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
> > (http://support.wolfram.com/Kernel/Symbols/System/Integrate.html).
> >
> > 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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-----`"" ""`------------------------------------------------
Lawrence A. Walker Jr., M.Eng./Ph.D. Candidate
Morgan State University
Clarence M. Mitchell School of Engineering
COMSARE (Center Of Microwave/Satellite And RF Engineering)
(443)885-1453
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