W dniu wtorek, 28 lutego 2017 09:03:52 UTC użytkownik Dima Pasechnik napisał: > > The problem with Risch "algorithm" is that's not very implementable. > No system ever had a complete implementation; it's true that results and > implementations by Manuel Bronstein > <https://www-sop.inria.fr/cafe/Manuel.Bronstein/bronstein-fr.html> (this > is a memorial page, for he died 12 years ago), > who authored a lot of results towards making Risch more practical, are > most completely represented in Axiom. > In 2006 Axiom had "most complete" implementation. But there were several holes. Some missing parts are implemented in FriCAS and there are extensions. Currently more than 25% of integration code in FriCAS is new. AFAIK FriCAS is the only system which can reasonably claim to have full implementation of transcendental part of Risch algorithm. To complete what was in Axiom I had to add a sizable subsytem to integration code. Testing seem to indicate that commercial competion (Maple and Mathematica) did not implement this part. Maxima has part called Risch, but AFAIK this is heuristic using ideas from early Risch papers (part may be original). AFAIK Maxima Risch misses most of what is now considered Risch algorithm. To get some idea of scope of various implementations you may wish to look at examples on: http://axiom-wiki.newsynthesis.org/FriCASIntegration or at FriCAS integration test suite: https://sourceforge.net/p/fricas/code/HEAD/tree/trunk/src/input/integ.input
You may be also interested in extensions of Risch algorithm to special functions: http://www.math.uni.wroc.pl/~hebisch/other/icms.pdf -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
