Bill, Sagemath cloud complains that your worksheet does not exist. Anyway :
sage: integrate(sqrt(cot(x)^2),x).trig_reduce().trig_simplify().log_expand() log(sin(x)) sage: integrate(sqrt(cot(x)^2), x,algorithm="fricas").trig_reduce(). trig_simplify().log_expand() log(sin(x)) sage: integrate(sqrt(cot(x)^2),x, algorithm="mathematica_free") sqrt(cot(x)^2)*log(sin(x))*tan(x) The expressions given by sage (i. e. maxima) and fricas can't be computed as reals (i. e. plotted), whereas the expression given by Mathematica can. If staying in reals, this expression is : log(sin(x))*tan(x)/sqrt(1/tan(x)^2)=log(sin(x))*tan(x)/abs(tan(x))=log(sin(x ))*sign(tan(x)) But there is something else : plotting log(sin(x) fails for x>pi/2, an so does plotting of log(sin(x))*sign(tan(x)) or log(sin(x)*sign(tan(x)), whereas the expression given by mathematica somehow evaluates to a real. sage: plot(log(sin(x)*sign(tan(x))) ,[x, pi/4, 3*pi/4]) verbose 0 (2716: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 100 points. verbose 0 (2716: plot.py, generate_plot_points) Last error message: 'can't convert complex to float' Launched png viewer for Graphics object consisting of 1 graphics primitive sage: plot(sqrt(cot(x)^2)*log(sin(x))*tan(x), [x, pi/4, 3*pi/4]) Launched png viewer for Graphics object consisting of 1 graphics primitive I do not (yet) understand why the Mathematica expression can be evaluated as a real, whereas Sage/Fricas expressions cannot. Any ideas ? HTH, -- Emmanuel Charpentier Le mercredi 3 juin 2015 19:47:52 UTC+2, Bill Page a écrit : > > Yes. > > > https://cloud.sagemath.com/projects/b04b5777-e269-4c8f-a4b8-b21dbe1c93c6/files/integral.sagews > > > On 3 June 2015 at 13:31, Samuel Lelievre <samuel....@gmail.com > <javascript:>> wrote: > > Can fricas do this integral? > > > > -- > > 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+...@googlegroups.com <javascript:>. > > To post to this group, send email to sage-...@googlegroups.com > <javascript:>. > > Visit this group at http://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 http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
