Computer Algebra Systems for Experimental Mathematics (especially Integer Relations with PSLQ)

Question

I would like to use a computer algebra system to do some experimental mathematics, particularly Integer Relation problems using the PSLQ algorithm.

I know that Maple has a PSLQ implementation, but I'd rather not pay for the entire Maple suite just to do Integer Relation problems. I've noticed that Sage links to a python library that does PSLQ, but that library is very limited in that it doesn't give the range of arguments for precision and tolerance that I'd like to be able to explore. Bailey has a GNU C++ library that does PSLQ with arbitrary precision, but I'd rather not be forced to use a command-line interface for experimentation. I like the cleaner presentation available in most CAS products.

I'm especially interested in PSLQ and not LLL simply because PSLQ gives you bounds on the norm of any possible integer relation even when it fails to find one, and this is a useful property. I'd like to explore some approximations to $\pi$ as well as play with some other integer relations among other constants that show up a lot in geometry.

Do you know of any CAS products (free or not) that have a good PSLQ implementation I can use, or are there other alternatives I may have overlooked?

Answer 1

I have a reasonable implementation in GAP using the Float package that IU wrote a few weeks ago. It's not world-class, but it should be OK for reasonable sized problems. Contact me or reply to this if you'd like to try it.

Answer 2

For simple or rather mechanical tasks i'm always using sympy, PSLQ is included in a package called "mpmath". LLL is available, too, either as a wrapper around FPLLL, or (implemented somewhat awkwardly) as a part of a package called "liblll". In that neighborhood, there's also a cute package "diophantine", which can provide minimal solutions to linear diophantine equations in a way I have never seen before spelled out. In more complex cases, where for example differential calculus is needed, I prefer the (gargantuan, but nearly perfect) axiom.