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 <tdum...@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+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. > -- 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.
