From: Andreas.Eder@t-online.de (Andreas Eder) Subject: Re: Risch Algorithm Date: 04 Mar 1999 10:45:53 +0100 Newsgroups: sci.math.symbolic Keywords: Pointers on symbolic integration jemfinch02@aol.com (Jemfinch02) writes: > What is the Risch Algorithm? Answers, Websites, anything is welcome. THanks If you look for a good book an symbolic integration, I would have a look in: Manuel Bronstein 'Symbolic Integration I : transcendental functions' Spinger-Verlag Berlin Heidelberg New York 1997 ISBN 3-540-60521-5 There, you will also find the original Risch papers in the bibliography. Andreas -- Wherever I lay my .emacs, there's my $HOME ============================================================================== From: Carlos Bazzarella Subject: Re: how can i find information on symbolic integration Date: Thu, 04 Mar 1999 10:26:57 -0400 Newsgroups: sci.math.symbolic > i'm wondering how hard it is to write a program to integrate elementary > functions symbolically. If you can point me to a place where i can find > info or tell me more about the algorithms involved, i would appreciate > it. It just seems like everybody nowadays wants to do this... So here it goes again. There are two main approaches : Pattern Matching or Algorithmic. For a good description of the Pattern Matching approach get a hold of the following paper. "Symbolic Integration: The Stormy Decade Joel Moses Project MAC, MIT, Cambridge, Massachusetts Communications of the ACM, August 1971, Volume 14 Number 8 Page 548 " For a good description of the Algorithmic approach get a hold of the following book. "Algorithms for Computer Algebra Keith O. Geddes Stephen R. Czapor George Labahn Kluwer Academic Publishers ISBN 0-7923-9259-0 " Carlos. ============================================================================== From: fateman@peoplesparc.cs.berkeley.edu (Richard J. Fateman) Subject: Re: how can i find information on symbolic integration Date: 4 Mar 1999 15:43:42 GMT Newsgroups: sci.math.symbolic In article <36DE14C2.E31947B7@lynx.neu.edu>, Mark Logan wrote: >i'm wondering how hard it is to write a program to integrate elementary >functions symbolically. If you can point me to a place where i can find >info or tell me more about the algorithms involved, i would appreciate >it. > >Thanks in advance, >Mark > Not very hard to write a heuristic program to do some of this. See Norvig's "Paradigms of Artificial Intelligence Programming" (Morgan Kaufman Publ.) for a complete listing with explanations. A complete mathematical analysis and algorithmic approach is much harder. A recent monograph on the topic is by Manuel Bronstein .. That's a good deal harder. There is no particular reason for you to write a program, of course. You can get one free, or buy one. -- Richard J. Fateman fateman@cs.berkeley.edu http://http.cs.berkeley.edu/~fateman/ ============================================================================== From: Boudewijn Moonen Subject: Re: Integral Algorithm? Date: Thu, 02 Sep 1999 14:42:04 +0200 Newsgroups: sci.math To: neenag@cableol.co.uk neenag@cableol.co.uk wrote: > > Is there like an algorithm for finding out whether a function is > integrable or not? > > E.g. functions like cos(x^2), sin(x^2), x^x, e^(x^2) are not integrable > (or is it integratable?), but I only know those examples, because I have > been told that they cannot be integrated. > > Neenag@cableol.co.uk ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1992/92-66.ps.gz -- Boudewijn Moonen Institut fuer Photogrammetrie der Universitaet Bonn Nussallee 15 D-53115 Bonn GERMANY e-mail: Boudewijn.Moonen@ipb.uni-bonn.de Tel.: GERMANY +49-228-732910 Fax.: GERMANY +49-228-732712