Fricas does some integrals very well (also, gives more compact form, as it does not introduce as many field extensions as other packages), and some pretty badly. IMHO one first has to classify the integrals and only then choose a good backend.
On Tuesday, February 28, 2017 at 9:21:35 AM UTC, Ralf Stephan wrote: > > Assuming the Fricas implementation is as good as Axiom's, would this alone > not be enough reason to make Fricas a standard package (and call it first > when integrating)? > > On Tue, Feb 28, 2017 at 10:03 AM Dima Pasechnik <dim...@gmail.com > <javascript:>> wrote: > >> 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> 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. >>>> To post to this group, send email to sage-...@googlegroups.com. >>> >>> >>>> 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 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.
