Karim BELABAS on Thu, 18 Apr 2002 19:02:22 +0200 (MEST) |
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Re: GP algdep() bug? |
On Thu, 18 Apr 2002, Michael Somos wrote: > On Thu, 18 Apr 2002, Karim BELABAS wrote: > > > > > > > Could something have changed in the last few weeks for 'algdep()'? > > > > The current CVS version uses PSLQ instead of LLL / HJLS to find integral > > relations [ undocumented for now, the code is in a _very_ unstable state ]. > > > > The output means that PSLQ failed and any relation (in algdep context: a > > minimal polynomial) has height > 20837... I believe the current output is > > more useful than the former one. > > > Perhaps there is a difference of opinion here? Would it be possible to > have the option of using the old behavior? It would be very useful. Already there: (18:57) gp > ??algdep algdep(x,k,{flag = 0}): [...] If flag is non-zero, use a standard LLL. flag then indicates a precision, which should be between 0.5 and 1.0 times the number of decimal digits to which x was computed. =============================================================================== So if you want a "more or less random" polynomial, which is close to 0 at x, you can use the optional flag. (18:58) gp > algdep(sin(1),2, 10) time = 0 ms. %1 = 258*x^2 - 2*x - 181 (18:58) gp > algdep(sin(1),2, 20) time = 10 ms. %2 = 78594*x^2 + 1425003*x - 1254749 (18:58) gp > algdep(sin(1),2, 30) time = 0 ms. %3 = 509248885*x^2 - 2125480139*x + 1427944267 The original call (no flag) already tells that these are most probably artefacts, and not genuine relations. 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/