Karim BELABAS on Sat, 12 Oct 2002 18:34:25 +0200 (MEST) |
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Re: gp: x^(1/2) and (1/x)^(1/2) and sqrt(x) |
On Sat, 5 Oct 2002, Michael Somos wrote: > ? (1/x)^(1/2) > *** log is not analytic at 0. > ? x^(1/2) > *** not an integer exponent for non invertible series in gpow. > ? sqrt(x) > *** odd exponent in gsqrt > > It seems to me that this is a confusing variety of error messages. > Perhaps there might be a way to make them more comparable? It > is further interesting that : > > ? (1/x^2)^(1/2) > *** log is not analytic at 0. > ? (x^2)^(1/2) > *** not an integer exponent for non invertible series in gpow. > ? sqrt(x^2) > %3 = x + O(x^15) > > Perhaps it would be easy to make these comparable also? I have written a common driver for sqrt, sqrtn and x^(a/b) [a,b integers]. I now get (\ps 16) (18:24) gp > (1/x)^(1/2) *** 2 should divide valuation (= -1) in sqrtn. (18:24) gp > x^(1/2) *** 2 should divide valuation (= 1) in sqrtn. (18:24) gp > sqrt(x) *** 2 should divide valuation (= 1) in sqrtn. (18:24) gp > (1/x^2)^(1/2) %1 = x^-1 + O(x^15) (18:24) gp > (x^2)^(1/2) %2 = x + O(x^17) (18:24) gp > sqrt(x^2) %3 = x + O(x^17) [ note I get the requested 16 significant terms now ] Cheers, Karim. -- Karim Belabas Tel: (+33) (0)1 69 15 57 48 Dép. de Mathematiques, Bat. 425 Fax: (+33) (0)1 69 15 60 19 Université Paris-Sud Email: Karim.Belabas@math.u-psud.fr F-91405 Orsay (France) http://www.math.u-psud.fr/~belabas/ -- PARI/GP Home Page: http://www.parigp-home.de/