Hi, >> Somebody should check (re-check ?) branch cuts and singularities with this >> patch. >> > > (for convenience, I include the patch below) > > I guess the right place to check branch cuts and singularities is in > src/input/elemnum.input. I looked at the common lisp hyperspec, the > definition > of branchcuts is quite clear there, so I suggest that we take it as > definition, > unless you have a better reference. >
I don't understand. Do you change asin z == atan (z/(1-z^2)^(1/2)) to asin z == -i log(iz+(1-z^2)^(1/2)) ? I prefer the atan definition because real number remains real number. > so we need to test: > > real < -1 error > > +1 error > = -1 -%pi/2 > = +1 -%pi/2 > Yes this test is necessary for the atan definition, with the denominator (1-z^2)^(1/2). No this test isn't useful for the log definition : log (e*%i) == e*%pi / 2 almost everywhere for e=1 and e=-1. > complex x + 0*%i, x < -1 close to x + 0.1*%i > complex x + 0*%i, x > 1 close to x - 0.1*%i > > Is this correct? What definition do you call ? with the log definition I see no sigularity arroud x+/-0%i for x >=1. x^2-1 is (c+) +/- 0%i : a positive constant (c+), and imaginary part is arround 0. sqrt(1-x^2) is arround (c+)*%i then (%i*z+sqrt(1-z^2)) = (c+)*%i and -i log (iz+sqrt(1-z^2)) = pi/2 +/- %i*0... If asin is defined from the complex atan, what definition do you use for atan ? I suppose you start from : http://www.lispworks.com/documentation/HyperSpec/Body/f_asin_.htm i (log (1-iz)-log(1+iz)) / 2 = -i log ((1+iz)/(1+z^2)^(1/2)) François --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/fricas-devel?hl=en -~----------~----~----~----~------~----~------~--~---
