Gerhard Niklasch on Sat, 30 Oct 1999 22:24:26 +0200 (MET DST) |
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Re: sqr() bug and acos bug. |
In response to: > Message-Id: <199910301454.QAA03593@sadir.math.u-bordeaux.fr> > Date: Sat, 30 Oct 1999 16:54:31 +0200 (MET DST) > From: Bill Allombert <Bill.Allombert@math.u-bordeaux.fr> > > If you like 2-adics, check if the sqrt function is correct (remember > there is 4 square roots for 2-adics and PARI returns only one). No, that would be horrible. (There ain't no zero divisors in fields or integral domains...) (22:20) gp > a=17+O(2^11) 1 + 2^4 + O(2^11) (22:20) gp > sqrt(a) 1 + 2^3 + 2^5 + 2^6 + 2^7 + 2^9 + O(2^10) (22:20) gp > We return one of the two square roots to the best possible precision based on our knowledge of the input. (There would be four if we kept working in Z/(2^11 Z), but the obvious thing to do here is indeed to undo what sqr() is doing). Off-topic question: I guess most readers here don't know what the allusion to Blaise Pascal was about; could you elaborate? Thanks, Gerhard