Improved ozman sieve #95
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I found a way to simplify the Ozman sieve computationally, also in the more general case where N is no longer assumed to be prime. One of course still needs the complete splitting condition in the Hilbert class field. But the existence of a residue field 1 degree one prime above p in B can be made easier. Namely we just need p to split in all real quadratic fields inside the HilbertClass field. And actually genus theory gives a quite nice description of all quadratic fields in the Hilbert class field. So that the upshot is that for N prime we only need to check if p splits in Q(sqrt( N )) if -N is not a fundamental discriminant, in the case that -N is a fundamental discriminant, there is no extra condition we need to check.
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Only commit 1610795 actually needs review. The other commits contain either changes that were automatically made by black, or just contain some small tweaking to the makefile so that it works again with sage 9.7 on os x. |
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p.s. I recently found out that our recent upgrade of black together with this pr in black psf/black#2726 are the reason for a lot of reformatting. I do agree that in most code that we write not having spaces around ** is an improvement, since this makes it easier to spot individual monomials in math expressions. |
BarinderBanwait
approved these changes
Jan 26, 2023
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