> atan((exp(x) + x + 1)/(exp(x) - x - 1)) > > There are two kernels here (exp(x) and x). I am not sure > if Rioboo is used here, but at least some simplification > is done.
I checked this example, the "Rioboo" (aka log2atan) is not used here, for rewriting "i*log((A+i*B)/(A-i*B))" to sums of arc-tangents, it returns "2*atan(A/B)" because A and B are not both polynomials of x. >> I get it that x and sqrt(x) can both appear as kernels; is it possible >> that there are three or more kernels? My answer to my question: in general, if there are more than 2 non-constant kernels, the log2atan function just return "2*atan(A/B)", and the selection of kernel is not relevant. The exception is that when kernels are [x,sqrt(x)] (or [g(x),sqrt(g(x))], because "univariate(x,first kernels sqrt x)" doesn't return "?^2". How to solve this problem? Examples are compose rational function f with other function g: f := (2560*x^3 - 400*x^2 - 576*x - 84)/(320*x^4 + 80*x^3 - 12*x^2 + 24*x + 9) g x == sqrt x -- or g x == sqrt exp x h == eval(f, x= g x)*D(g x , x) integrate(h,x) -- if there's only one atan in the result, then it's not continuous. -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
