Re: precision peculiarity

[Karim BELABAS <Karim.Belabas@math.u-psud.fr>]

[Igor:]
> ? f(x, n) = setrand(x);return(quadclassunit(N)[4])
> ? N=139619637069004;
> ? f(1,N)-f(628697742,N)
> 0.000000007731182653209892135624526494
> 
> I think the difference is somewhat significant, considering \p28.
> Or is internal precision different for these computations?  

The significant quantity is

? ( f(1,N) - f(628697742,N) ) / f(1,N)
%1 = 3.369471553850136186628266618 E-16

to be compared with E-28, which is still bad, but a bit more acceptable.

The bnfinit/quadclassunit computation don't guarantee anything about the
actual precision of the output. They use an internal (much higher) precision
using heuristics with the goal to get an exact class group, not an exact
regulator. It should be relatively easy, given the bnf data and a crude
approximation to the regulator as above, to improve it to any desired
accuracy (using Shanks infrastructure), but this is not part of the current
routines.

  Karim.
__
Karim Belabas                    email: Karim.Belabas@math.u-psud.fr
Dep. de Mathematiques, Bat. 425
Universite Paris-Sud             Tel: (00 33) 1 69 15 57 48
F-91405 Orsay (France)           Fax: (00 33) 1 69 15 60 19
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