Re: Re: Need a better Integrate
- To: mathgroup at smc.vnet.net
- Subject: [mg43053] 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>
- Reply-to: drbob at bigfoot.com
- Sender: owner-wri-mathgroup at wolfram.com
"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