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.
On Tuesday, February 28, 2017 at 8:45:27 AM UTC, Ralf Stephan wrote: > > Fricas was forked from Axiom, according to > https://en.wikipedia.org/wiki/Axiom_(computer_algebra_system)#History > and Axiom had the complete Risch algorithm implemented. > > On Tue, Feb 28, 2017 at 9:01 AM Thierry Dumont <tdu...@math.univ-lyon1.fr > <javascript:>> wrote: > >> Following https://en.wikipedia.org/wiki/Risch_algorithm ,the Risch >> algorithm is able to find an antiderivative of: >> >> x |-> x/sqrt(x^4+10*x^2-96*x-71) >> >> but not of: >> >> x |-> x/sqrt(x^4+10*x^2-96*x-72) . >> >> What can do Sage? >> >> #-------------------------------------------------------- >> fok(x)=x/sqrt(x^4+10*x^2-96*x-71) >> fnot_ok(x)=x/sqrt(x^4+10*x^2-96*x-72) >> # >> algs=["maxima","sympy","fricas"] >> # >> for alg in algs: >> print alg,integral(fok,x,algorithm=alg) >> # >> for alg in algs: >> print alg,integral(fnot_ok,x,algorithm=alg) >> #--------------------------------------------------------- >> >> For fnot_ok no primitive is found (may be an other algorithm could find >> it -it exists in terms of elliptic integrals-) >> >> For f_ok, *only* *fricas* finds the primitive: >> >> maxima x |--> integrate(x/sqrt(x^4 + 10*x^2 - 96*x - 71), x) >> sympy x |--> integrate(x/sqrt(x^4 + 10*x^2 - 96*x - 71), x) >> fricas x |--> 1/8*log(x^8 + 20*x^6 - 128*x^5 + 54*x^4 - 1408*x^3 + >> 3124*x^2 + (x^6 + 15*x^4 - 80*x^3 + 27*x^2 - 528*x + 781)*sqrt(x^4 + >> 10*x^2 - 96*x - 71) + 10001) >> >> The wikipedia paper says that Risch algorithm was implemented in Macsyma >> (and thus I think in maxima!). So, iffricas and maxima use Risch >> algorithm, the implementation in fricas is better, or may be fricas uses >> some other method. >> >> What about maple and mathematica ? As far as I remember maple can >> integrate f_ok. I have no more access to maple to look at this :-) . >> >> t. >> >> >> >> -- >> You received this message because you are subscribed to a topic in the >> Google Groups "sage-devel" group. >> To unsubscribe from this topic, visit >> https://groups.google.com/d/topic/sage-devel/7OO_VyMC1Ts/unsubscribe. >> To unsubscribe from this group and all its topics, send an email to >> sage-devel+...@googlegroups.com <javascript:>. >> To post to this group, send email to sage-...@googlegroups.com >> <javascript:>. >> Visit this group at https://groups.google.com/group/sage-devel. >> For more options, visit https://groups.google.com/d/optout. >> > -- 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.
