Re: Re: Need a better Integrate
- To: mathgroup at smc.vnet.net
- Subject: [mg43054] Re: [mg43019] Re: [mg42976] Need a better Integrate
- From: Dr Bob <drbob at bigfoot.com>
- Date: Sun, 10 Aug 2003 01:46:44 -0400 (EDT)
- References: <8FE7F32E-CA23-11D7-8D38-00039311C1CC@platon.c.u-tokyo.ac.jp> <oprtmlmenaamtwdy@smtp.cox-internet.com>
- Reply-to: drbob at bigfoot.com
- Sender: owner-wri-mathgroup at wolfram.com
>> and that's when its derivative has a multiple root Sorry, I think I should have said "when its derivative has a real root". But the method doesn't always help in either situation (as you already said). For instance, g = Expand[(x^2 - 1)^3]. D[g,x] has two double roots, and all its roots are real, but MyIntegrate doesn't improve things. Please straighten me out if I still have it wrong. Bobby On Sat, 09 Aug 2003 01:57:40 -0500, Dr Bob <drbob at bigfoot.com> wrote: > "Just mathematics" covers a lot of territory, Andrzej. As evidence of > that, I completed over 70 graduate courses in Mathematics and Operations > Research at five graduate schools, yet I didn't study all the same things > you did! Amazing, isn't it? I think I may have wasted some time on > topology, network optimization algorithms, pseudodifferential equations, > stochastic processes, and probability (as opposed to statistics). These > topics don't come up in the group much. > > So, your method can be expected to help when the integrand can be made to > have multiple roots by adding a constant, and that's when its derivative > has a multiple root. Probably everybody else in MathGroup knew that > intuitively. > > Thanks for the clarification. My integration rule isn't nearly as > general as yours, and often gets the wrong answer, too. But it was a > first try; I can live with that. > > Bobby > > On Sat, 9 Aug 2003 06:40:11 +0200, Andrzej Kozlowski <andrzej at platon.c.u- > tokyo.ac.jp> wrote: > >> >> On Saturday, August 9, 2003, at 01:32 AM, Dr Bob wrote: >> >>>>> This is of course not true. >>> >>> It may not be true, but it's not "of course" untrue, unless >>> >>> (a) there's an obvious reason it's not true or >>> (b) you've made some slight attempt, at least, to explain why your >>> method should work and when. (Or would that spoil your fun?) >>> >>> >>> Congratulations on finding an example that isn't of the form D[g, x] >>> g^n, but don't strain a muscle patting yourself on the back. >> >>> >>> Bobby >> >> >> I did not find this example. It's just mathematics. Discriminant[f]==0 >> if an only if f has a multiple (repeated) root. So the method will work >> not just for powers of polynomials but also for products of powers. One >> can look up the discriminant in various places (suchas the famous book >> by Van Der Vaerden on Algebra) or on Eric Eric Weisstein's MathWorld. >> Daniel Lichtblau told me that that is where he took his implementation >> from. >> >> Andrzej >> >> > > > -- majort at cox-internet.com Bobby R. Treat