Opened 3 years ago

Last modified 3 months ago

#28113 new defect

List of completely split primes is incomplete

Reported by: ehlen Owned by:
Priority: major Milestone: sage-9.7
Component: number fields Keywords: number fields, splitting of primes
Cc: mderickx, slelievre, mwest Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

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Description (last modified by slelievre)

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 them).

Change History (10)

comment:1 Changed 3 years ago by embray

  • Milestone changed from sage-8.9 to sage-9.1

Ticket retargeted after milestone closed

comment:2 Changed 2 years 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 22 months ago by mkoeppe

  • Milestone changed from sage-9.2 to sage-9.3

comment:4 Changed 15 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 12 months ago by mkoeppe

  • Milestone changed from sage-9.4 to sage-9.5

comment:6 Changed 8 months ago by mderickx

  • Cc mderickx added

comment:7 Changed 8 months ago by slelievre

  • Cc slelievre added
  • Description modified (diff)

Reported again at #32982. The example there might serve as a doctest here.

comment:8 Changed 7 months ago by mkoeppe

  • Milestone changed from sage-9.5 to sage-9.6

comment:9 Changed 4 months ago by dimpase

  • Cc mwest added

CC-ing the code author

comment:10 Changed 3 months ago by mkoeppe

  • Milestone changed from sage-9.6 to sage-9.7
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