Re: algdep broken in CVS?

[Walter Neumann <neumann@cpw.math.columbia.edu>]

There still seems to be a bug in algdep:

Some time ago Karim wrote

>2.2.5 uses PSLQ which either
>  * returns a polynomial which evaluates to 0 at the input precision [ I
>have just changed that. It used to be "at realprecision" which led to
>weird results if you changed the precision after approximating your
>algebraic number. Now PSLQ is insensitive to realprecision
>
>or
>
>  * returns a real number B and guarantees that no polynomial of height
>less than B can evaluate to 0.

The following example contradicts this:

? \p 50
   realprecision = 57 significant digits (50 digits displayed)
?  a=sqrt(2)+sqrt(3)-5^(1/3)
%1 = 1.4362884232652753529760261931717103356444220186443
? algdep(a,12)
%2 = 235*x^12 - 479*x^11 + 361*x^10 - 278*x^9 + 1252*x^8 - 1922*x^7 +
337*x^6 + 204*x^5 - 549*x^4 - 1096*x^3 + 1491*x^2 - 113*x + 1361
? x=a
%3 = 1.4362884232652753529760261931717103356444220186443
? eval(%2)
%4 = 2.171420994059481315 E-37

--walter