Waldek Hebisch <[EMAIL PROTECTED]> writes: | The problem here is that sin asin(7.0::COMPLEX FLOAT) give something | close to -7. This is due to wrong bunch cuts during evaliation. | Namely in trigcat we have: | | asin x == atan(x/sqrt(1-x**2)) | | this formula for asin has wrong branch cuts. When x is real and bigger | then 1 sqrt(1-x**2) is imaginary with positive imaginary part. So | x/sqrt(1-x**2) is imaginary with _negative_ imaginary part. atan has | branch cut on %i*[-1, %minusInfinity], with jump discontinuity when | real part goes to 0 trough positve values. This discontinuity means | that values of asin are wrong (of opposite sign) for big real x. | | There is an easy workaround, put: | | asin x == -atan(-x/sqrt(1-x**2)) | | However, the problem with asin is just one special case. We | would like to support many multivalued special functions (which in | numerical version require branch cuts). Tracking that we get | "correct" values on cuts may well take significant portion of | effert to implements those functions. OTOH computing with | values on branch cuts does not seem very useful. So I am tempted | to declare that arguments branch cuts are errors (like divison | by 0).
I'm concerned with that approach. After all, this is a mathematical computational platform. If we go that way, how else can we expect other people to take branch cuts seriously? -- Gaby _______________________________________________ Axiom-developer mailing list Axiom-developer@nongnu.org http://lists.nongnu.org/mailman/listinfo/axiom-developer
