Maxima's version of Risch is about 13 pages of code, not counting some material that may reside in other files having to do with finding appropriate algebraic or transcendental extensions. I suspect no one has looked at it seriously in 40 years.
On Wednesday, March 1, 2017 at 1:26:04 PM UTC-8, heb...@math.uni.wroc.pl wrote: > > > > 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.
