On Fri, Jul 10, 2009 at 9:13 AM, rjf<fate...@gmail.com> wrote: > > > > On Jun 23, 7:29 am, Golam Mortuza Hossain <gmhoss...@gmail.com> wrote: > > >> >> +1, I agree, this is badly needed. We should ask maxima/sympy to >> compute an integral when algorithm within Sage fails. That way >> one can implement the integration algorithm within Sage which are >> not yet implemented in maxima/sympy. > > Just a warning. If the algorithm within Sage gets an answer, but it > is in wrong, or in a much inferior form than you would get in Maxima, > then Sage will have some unnecessary deficiencies. Probably more than > any other feature in Maxima, its integration code accesses the > underlying algorithms for simplification, changes in representation, > rational function manipulation such as partial fractions, factoring, > algebraic function simplification, limits, knowledge of special > functions, calculations with assumptions, pattern matching, the Risch- > based programs, (which depend on construction of differential fields), > etc. > > Consequently, it would be a challenge to do as effective an > "integration" program without subroutines similar in power to those in > Maxima (or superior). > > Note also that Maxima's integration program continues to be improved, > so that programming Sage symbolics to replace Maxima integration > places you in the same situation as Lewis Carroll's Red Queen who > points out.. > " Now, here, you see, it takes all the running you can do, to keep in > the same place. If you want to get somewhere else, you must run at > least twice as fast as that!" > > You can do quite a few easy integrals (including ones that "look" > complicated) with simple methods. Norvig's Paradigms of AI Programming > has a chapter on the topic. You shouldn't let the success of simple > methods fool you into thinking your demo program just needs a few > finishing touches. Look at the sizes of the ambitious integration > programs in 3M's and Axiom -- it would be unreasonable to think that > they are all large because all the programmers were incompetent. >
Thanks for your constant encouragement. It's been really inspiring over the last 4 years of Sage development. -- William --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
