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Old 2020-12-07, 15:39   #10
charybdis's Avatar
Apr 2020

263 Posts

Originally Posted by jasonp View Post
Try asking the developers in the cado-nfs mailing list, they are very responsive and I know they have thought pretty deeply about cofactorization strategies.

For extra credit: given a rational and algebraic pair of numbers to factorize, determine as fast as possible if it is worth the effort to try factorizing both.
I figured in the end that it wasn't worth it. The time spent on 2LP cofactorization is tiny, so the savings from having mfb below 2*lpb actually come from reducing the number of relations needed to build a matrix. But the larger norms on the algebraic side mean that yield drops much more if you drop algebraic mfb by one bit than if you drop rational mfb by one bit (and this will apply to the hypothetical algebraic 2LP bound too).

One useful thing that we do seem to have discovered is that it can be optimal to set the mfb bounds asymmetrically (algebraic higher than rational) even when both lpbs are the same; Curtis has run some tests in the c100-c120 range that show this to be the case.

Last fiddled with by charybdis on 2020-12-07 at 15:40
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