Re: Re: Nasty bug in Integrate (version 5.0)

*To*: mathgroup at smc.vnet.net*Subject*: [mg45993] Re: [mg45958] Re: Nasty bug in Integrate (version 5.0)*From*: Dr Bob <drbob at bigfoot.com>*Date*: Mon, 2 Feb 2004 05:20:28 -0500 (EST)*References*: <200401281019.FAA18530@smc.vnet.net> <bvapk6$aat$1@smc.vnet.net> <200401300917.EAA05062@smc.vnet.net> <68A351B5-5333-11D8-94B3-00039311C1CC@mimuw.edu.pl> <opr2mc5zdhamtwdy@smtp.cox-internet.com> <7159C05C-53B8-11D8-9076-00039311C1CC@mimuw.edu.pl>*Reply-to*: drbob at bigfoot.com*Sender*: owner-wri-mathgroup at wolfram.com

Don't put me in that category; I'm using Mathematica, not debugging it. And I like Mathematica -- a lot. I'm simply saying the answer to errors with a small problem isn't, "Don't use it for small problems." And of course people come to the Group when they think they've found a bug or a gap in documentation. They don't need to come there when everything works fine. Bobby On Sat, 31 Jan 2004 07:41:04 +0100, Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote: > > On 31 Jan 2004, at 03:57, Dr Bob wrote: > >>>> if you are going to use it only for problems that are trivial to do >>>> by hand what is the point of using it at all? >> >> Why use it only for the ones that are too big to check? That way, we >> don't know whether we're wrong or not. We wouldn't know about this bug, >> for instance. > > From reading the Mathgroup I get the impression that more people are > "debugging" Mathematica than using it. This may not bad thing for those > who are actually using it, since it presumably helps to improve the > program, but I am surprised that so many find this sort of thing worth > their while. > > Andrzej > > > >> >> Bobby >> >> On Fri, 30 Jan 2004 15:48:47 +0100, Andrzej Kozlowski >> <akoz at mimuw.edu.pl> wrote: >> >>> But then if you are going to use it only for problems that are trivial >>> to do by hand what is the point of using it at all? Computers are >>> supposed to be good at computing, we are supposed to be good at >>> thinking. >>> >>> Andrzej >>> >>> >>> On 30 Jan 2004, at 10:17, Bobby R. Treat wrote: >>> >>>> The only reason we know the answer is wrong is BECAUSE it's trivial by >>>> hand. It makes no sense to trust Mathematica for problems that are >>>> too hard to >>>> check. >>>> >>>> Bobby >>>> >>>> Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote in message >>>> news:<bvapk6$aat$1 at smc.vnet.net>... >>>>> Mathematica seems to get lost in the large number of checks that it >>>>> attempts to perform to find the exact conditions (in the complex >>>>> plane) for the convergence of this integral. Even if a and b are >>>>> assumed to be real there is a problem that 0 may lie in between them. >>>>> Only in the case when you specify that the limits are both positive >>>>> or >>>>> both negative you get the correct answers because Mathematica can >>>>> quickly deal with this problem. >>>>> If you really want to see how much checking Mathematica attempts to >>>>> do >>>>> just evaluate: >>>>> >>>>> Trace[Integrate[1/x + x^c, {x, a, b}], TraceInternal->True] >>>>> >>>>> and be prepared to wait and obtain a huge output. >>>>> >>>>> Anyway, this is clearly a bug. However, it is in general a good idea >>>>> not to ask a computer program to do what is trivial to do by hand, >>>>> which in this case means evaluating a definite rather than an >>>>> indefinite integral. Note that >>>>> >>>>> >>>>> Integrate[1/x + x^c, x] >>>>> >>>>> x^(c + 1)/(c + 1) + Log[x] >>>>> >>>>> and the answer is obtained instantly. If this is what you really were >>>>> after (you can substitute in the limits for example by using: >>>>> >>>>> >>>>> Subtract @@ (Integrate[1/x + x^c, x] /. x -> #1 & ) /@ {b, a} >>>>> >>>>> >>>>> -(a^(c + 1)/(c + 1)) - Log[a] + Log[b] + b^(c + 1)/(c + 1) >>>>> >>>>> >>>>> Of course this now makes sense only under certain conditions on a,b >>>>> and >>>>> c which you now have to determine yourself. >>>>> >>>>> >>>>> On 28 Jan 2004, at 11:19, Math User wrote: >>>>> >>>>>> Hi, >>>>>> >>>>>> Sorry if this has been discussed before. Could anyone explain why >>>>>> Mathematica 5.0 is ignoring the term 1/x in the first and second >>>>>> answers? >>>>>> >>>>>> Thanks! >>>>>> >>>>>> >>>>>> In[1]:= Integrate[1/x + x^c, {x, a, b}] >>>>>> >>>>>> Out[1]= (-a^(1 + c) + b^(1 + c))/(1 + c) >>>>>> >>>>>> In[2]:= Integrate[1/x + x^c, {x, a, b}, Assumptions -> {Element[a, >>>>>> Reals], Element[b, Reals]}] >>>>>> >>>>>> Out[2]= (-a^(1 + c) + b^(1 + c))/(1 + c) >>>>>> >>>>>> In[3]:= Integrate[1/x + x^c, {x, a, b}, Assumptions -> {a > 0, b > >>>>>> 0}] >>>>>> >>>>>> Out[3]= (-a^(1 + c) + b^(1 + c))/(1 + c) + Log[b/a] >>>>>> >>>>>> >>>> >>>> >>> >> >> >> >> >