Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Jump to bottom

Improved ozman sieve #95

Merged
merged 3 commits into from Jan 26, 2023
Merged

Improved ozman sieve #95

merged 3 commits into from Jan 26, 2023

Commits on Nov 2, 2022

  1. Automated black reformatting

    @koffie
    koffie committed Nov 2, 2022
    Configuration menu
    Copy the full SHA
    dc3a7d7 View commit details
    Browse the repository at this point in the history

  2. Fix automated testing on OS X

    @koffie
    koffie committed Nov 2, 2022
    Configuration menu
    Copy the full SHA
    219018e View commit details
    Browse the repository at this point in the history

  3. Improve the ozman sieve 

    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.
    @koffie
    koffie committed Nov 2, 2022
    Configuration menu
    Copy the full SHA
    1610795 View commit details
    Browse the repository at this point in the history