Opened 3 years ago

Last modified 2 months ago

#28113 new defect

List of completely split primes is incomplete — at Version 7

Reported by: Stephan Ehlen Owned by:
Priority: major Milestone: sage-9.8
Component: number fields Keywords: number fields, splitting of primes
Cc: Maarten Derickx, Samuel Lelièvre, Mckenzie West Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

Status badges

Description (last modified by Samuel Lelièvre)

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 (7)

comment:1 Changed 3 years ago by Erik Bray

Milestone: sage-8.9sage-9.1

Ticket retargeted after milestone closed

comment:2 Changed 3 years ago by Matthias Köppe

Milestone: sage-9.1sage-9.2

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

comment:3 Changed 2 years ago by Matthias Köppe

Milestone: sage-9.2sage-9.3

comment:4 Changed 19 months ago by Matthias Köppe

Milestone: sage-9.3sage-9.4

Moving to 9.4, as 9.3 has been released.

comment:5 Changed 16 months ago by Matthias Köppe

Milestone: sage-9.4sage-9.5

comment:6 Changed 12 months ago by Maarten Derickx

Cc: Maarten Derickx added

comment:7 Changed 12 months ago by Samuel Lelièvre

Cc: Samuel Lelièvre added
Description: modified (diff)

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

Note: See TracTickets for help on using tickets.