"just a bug" !; Mathematica 4

*To*: mathgroup at smc.vnet.net*Subject*: [mg27435] "just a bug" !; Mathematica 4*From*: pl10-mac <pl10 at st-and.ac.uk>*Date*: Sun, 25 Feb 2001 20:55:38 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

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: [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 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 > >