* Fred Lunnon <fred.lunnon@gmail.com> [Aug 26. 2015 07:49]:
[...]
QUERY: Given dimension (ie. presumed polynomial degree) m , what precision is necessary to ensure successful lattice basis reduction?
Pari/GP's help on algdep() points to http://www.sciencedirect.com/science/article/pii/S0012365X99002563 Since that paper appeared the performance of the function (which is LLL in it's core) is said to have been sped up by a factor of 200. I'd be surprised if _practical_ bounds for either precision or run-time are known. Observationally a good implementation of LLL works "surprisingly often and surprisingly fast". There is a paper about hard instances, search for hard instances for LLL Pari/GP's help on lindep() says that by default "the accuracy is chosen internally using a crude heuristic". This appears to back up what I said above. Best regards, jj
Fred Lunnon
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun