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: |
Description (last modified by )
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
Milestone: | sage-8.9 → sage-9.1 |
---|
comment:2 Changed 3 years ago by
Milestone: | sage-9.1 → 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 2 years ago by
Milestone: | sage-9.2 → sage-9.3 |
---|
comment:4 Changed 19 months ago by
Milestone: | sage-9.3 → sage-9.4 |
---|
Moving to 9.4, as 9.3 has been released.
comment:5 Changed 16 months ago by
Milestone: | sage-9.4 → sage-9.5 |
---|
comment:6 Changed 12 months ago by
Cc: | Maarten Derickx added |
---|
comment:7 Changed 12 months ago by
Cc: | Samuel Lelièvre added |
---|---|
Description: | modified (diff) |
Reported again at #32982. The example there might serve as a doctest here.
Ticket retargeted after milestone closed