PSLQ technical

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Description of PSLQ
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Proceedings of the
Organic Mathematics
Workshop

Recognizing Numerical Constants
David H. Bailey and Simon Plouffe

The PSLQ Integer Relation Algorithm

http://www.cecm.sfu.ca/organics/papers/bailey/paper/html/node3-an.shtml

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PDF original paper on PSLQ
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Analysis of PSLQ, an Integer Relation Finding Algorithm
Helaman R.P. Ferguson, David H. Bailey, and Steve Arno

http://www.nas.nasa.gov/Research/Reports/Techreports/1996/PDF/nas-96-005.pdf

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Implementation of PSLQ
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From Newsgroups: sci.math.symbolic

Serge Zlobin wrote:

<< I want to know is there PSLQ algorithm realized in maple
(or in Mathematica)? Maybe there is such library. The
algorithm finds integer relation between real numbers with
some precision. >>

Raymond Manzoni wrote (23 Oct 1999):

<< An implementation is available in Mathematica :
R.E. Crandall, Topics in Advanced Scientific Computation,
Springer/TELOS, New York
http://www.telospub.com/catalog/MATHEMATICS/TASC.html >>

<< I wrote an implementation in mupad myself (available on
request)(*). I wrote C code too (for limited search in
double or quadruple precision) >>

<< But both implementations are of limited interest now
since the LLL implementation is proposed in the quick and
free (with C sources) pari/gp number theory package. It is
order of magnitudes quicker!! >>

http://www.parigp-home.de/

(*) Manzoni implementation : see my post "PSLQ in Yacas and MuPAD"

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Bibliography
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Jonathan M. Borwein, Peter B. Borwein and David H. Bailey, "Ramanujan,
Modular Equations, and Approximations to Pi", American Mathematical
Monthly, Mar. 1989, pg. 201-219. This paper was cited for both the
Chauvenet Prize and the Merten Hesse Prize.

David H. Bailey, Jonathan M. Borwein, Peter B. Borwein and Simon Plouffe,
"The Quest for Pi", Mathematical Intelligencer, vol. 19, no. 1 (Jan. 1997),
pg. 50-57.

David H. Bailey, Peter B. Borwein and Simon Plouffe, "On The Rapid
Computation of Various Polylogarithmic Constants", Mathematics of
Computation, vol. 66, no. 218 (Apr. 1997), pg. 903-913. This paper has
been accessed thousands of times from various web sites, and it is
mentioned on numerous web sites and in other references dealing with the
computation of pi. See for example
http://www.mathsoft.com/asolve/plouffe/plouffe.html

Helaman R. P. Ferguson, David H. Bailey and Stephen Arno, "Analysis of
PSLQ, An Integer Relation Finding Algorithm", Mathematics of Computation,
vol. 68 (Jan. 1999), pg. 351-369.