From: Manuel Bronstein Subject: Re: Risch algorithm? Date: Fri, 05 May 2000 11:07:56 +0200 Newsgroups: sci.math.symbolic Summary: [missing] "F. Xavier Noria" wrote: > I am a graduate in maths (University degree) and would like > to have some clue on how the Risch algorithm works. Could you > please give an outline, which are the main ideas involved? > Are there standard proofs of the non-existence of primitives > in closed form of the known functions x^x, e^(-x^2), ... or > is it established using the algorithm and seeing the output? > > Regards, > > -- Xavier I'm distributing a symbolic integration tutorial from my home page (see the URL below). It's a compact description of all the cases of the Risch algorithm (including algebraic and mixed functions) with examples and essentially no proofs. There is also my textbook, which goes deeper into the transcendental cases, but it's distributed by Springer (pointer on my home page). The easiest way to prove the non-existence of some classical primitives such as x^x or e^(-x^2) is to simulate the algorithm by hand on them, the proof of non-elementary integrability comes quickly. There are "historical" proofs (rather than standard) that predate the algorithm, for example in Liouville's papers. -- Manuel Bronstein -- Manuel.Bronstein@sophia.inria.fr -- http://www.inria.fr/cafe/Manuel.Bronstein/ ============================================================================== From: "Atul Sharma" Subject: Re: INTRGRATION ALGORITHM Date: Wed, 19 Jul 2000 16:54:02 GMT Newsgroups: sci.math.symbolic Summary: [missing] Michael Bronstein has a nice tutorial on the Risch algorthm, in postscript format available on his website: http://www-sop.inria.fr/cafe/Manuel.Bronstein/bronstein-eng.html More detail in his book, Springer Verlaag, 1996: Symbolic Integration I Transcendental Functions This first volume in the series "Algorithms and Computation in Mathematics", is destined to become the standard reference work in the field. Professor Bronstein is the number-one expert on this topic and his book is the first to treat the subject both comprehensively and in sufficient detail - incorporating new results along the way. The book addresses mathematicians and computer scientists interested in symbolic computation, developers and programmers of computer algebra systems as well as users of symbolic integration methods. Many algorithms are given in pseudocode ready for immediate implementation, making the book equally suitable as a textbook for lecture courses on symbolic integration. 1996 . Approx. 250 pp., Hardcover ISBN 3-540-60521-5 AS The_Mandelbrot_Set wrote in message <8l4jqo$b4e$1@pegasus.tiscalinet.it>... >Hi all > >Does anybody know how do the integration algorithm work?? >I am building a equation interpreter and i would add this option... > > Thanks