Opened 2 years ago

Last modified 4 weeks ago

#28113 new defect

List of completely split primes is incomplete

Reported by: ehlen Owned by:
Priority: major Milestone: sage-9.5
Component: number fields Keywords: number fields, splitting of primes
Cc: Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

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Description

For number fields, the method completely_split_primes may be incomplete.

Example

  K.<a> = QuadraticField(17)
  K.completely_split_primes(20)
  [13, 19]

However,

  K.<a> = QuadraticField(17)
  K.ideal(2).factor()
  (Fractional ideal (-1/2*a - 3/2)) * (Fractional ideal (-1/2*a + 3/2))

The reason is that the factorization of the defining polynomial mod p does not always give the correct answer. It does in all but finitely many cases, the exception being primes that divide the index of ZZ[a] in the ring of integers of K.

A possible solution would be to use the function K.ideal(p).factor() and determine the length of the splitting (at least for those finitely many primes in case we can easily determine those primes).

Change History (5)

comment:1 Changed 21 months ago by embray

  • Milestone changed from sage-8.9 to sage-9.1

Ticket retargeted after milestone closed

comment:2 Changed 17 months ago by mkoeppe

  • Milestone changed from sage-9.1 to sage-9.2

Moving tickets to milestone sage-9.2 based on a review of last modification date, branch status, and severity.

comment:3 Changed 11 months ago by mkoeppe

  • Milestone changed from sage-9.2 to sage-9.3

comment:4 Changed 5 months ago by mkoeppe

  • Milestone changed from sage-9.3 to sage-9.4

Moving to 9.4, as 9.3 has been released.

comment:5 Changed 4 weeks ago by mkoeppe

  • Milestone changed from sage-9.4 to sage-9.5
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