Re: sqr() bug and acos bug.

[Gerhard Niklasch <nikl@mathematik.tu-muenchen.de>]

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