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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