Opened 4 years ago

Last modified 3 years ago

#24098 closed enhancement

S_hilbert_symbol() helper function to find integer with negative Hilbert symbol for primes in a set S — at Version 8

Reported by: annahaensch Owned by:
Priority: minor Milestone: sage-8.8
Component: basic arithmetic Keywords: sd90
Cc: mroy, sbrudzin, jduque Merged in:
Authors: Anna Haensch, Manami Roy, Juanita Duque, Sandi Rudzinski Reviewers: Simon Brandhorst
Report Upstream: N/A Work issues:
Branch: u/annahaensch/_s_hilbert_symbol___helper_function_to_find_integer_with_negative_hilbert_symbol_for_primes_in_at_set_s (Commits, GitHub, GitLab) Commit: ec55c0d42702b1bf86f12e9e0cdb13f3c76949d2
Dependencies: Stopgaps:

Status badges

Description (last modified by sbrandhorst)

This is an implementation of algorithm 3.4.1 from Markus Kirschmer's "Definite quadratic and hermitian forms with small class number." Given a non-square b and a set of primes S, the function returns a number a which has negative Hilbert symbol with respect to b at precisely the primes in S.

This is a function in service to algorithm 3.4.3, quadratic_form_form_local_invariants(), ticket #24108.

Change History (8)

comment:1 Changed 4 years ago by annahaensch

  • Description modified (diff)
  • Summary changed from _S_hilbert_symbol() helper function to find integer with negative Hilbert symbol for primes in at set S to S_hilbert_symbol() helper function to find integer with negative Hilbert symbol for primes in at set S

comment:2 Changed 4 years ago by annahaensch

  • Branch set to u/annahaensch/_s_hilbert_symbol___helper_function_to_find_integer_with_negative_hilbert_symbol_for_primes_in_at_set_s

comment:3 Changed 4 years ago by annahaensch

  • Commit set to ec55c0d42702b1bf86f12e9e0cdb13f3c76949d2
  • Status changed from new to needs_review

New commits:

ec55c0dAdds function S_hilbert_symbol
Last edited 4 years ago by annahaensch (previous) (diff)

comment:4 Changed 4 years ago by annahaensch

  • Cc manami.roy.90@… sbrudzin@… jduque@… added

comment:5 Changed 4 years ago by annahaensch

  • Cc mroy sbrudzin jduque added; manami.roy.90@… sbrudzin@… jduque@… removed

comment:6 Changed 4 years ago by annahaensch

  • Component changed from quadratic forms to basic arithmetic

comment:7 Changed 4 years ago by annahaensch

  • Keywords sd90 added; #sd90 removed
  • Summary changed from S_hilbert_symbol() helper function to find integer with negative Hilbert symbol for primes in at set S to S_hilbert_symbol() helper function to find integer with negative Hilbert symbol for primes in a set S

comment:8 Changed 4 years ago by sbrandhorst

  • Description modified (diff)
  • Reviewers set to Simon Brandhorst
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