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PSLQ implementation?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg34206] PSLQ implementation?
  • From: Ronald Bruck <bruck at math.usc.edu>
  • Date: Thu, 9 May 2002 05:16:17 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Is there an implementation of the PSLQ algorithm in Mathematica?  For
my purposes, it would be enough to be able to find the minimal
polynomial of a decimal approximation r of an algebraic number z, to
within a given degree d.  (That is, to find the polynomial p(x) of
smallest degree <= d with integer coefficients for which |p(r)| is
smallest.)

Currently, I have to do such computations in Maple, which is **not**
convenient.  In Maple you must first set the precision; Mathematica has
the ability of adapting to the precision of the given approximation r. 
Furthermore, Maple 7 **still** does not run native in Mac OS X.

Best of all would be a special-purpose implementation using the Gnu
Multiprecision Library, or equivalent.  It would be interesting to
compare the speed to that of a Mathematica implementation.

I don't want to reinvent the wheel.  Is there such a package?  (My
numbers often seem to have degree > 32, but I know them to a couple of
thousand digits; Maple takes forever.  Probably Mathematica will too,
but I want to try an alternative.)

--Ron Bruck


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