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: |
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 (10)
comment:1 Changed 3 years ago by
- Milestone changed from sage-8.9 to sage-9.1
comment:2 Changed 2 years ago by
- 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
- Milestone changed from sage-9.2 to sage-9.3
comment:4 Changed 15 months ago by
- 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
- Milestone changed from sage-9.4 to sage-9.5
comment:6 Changed 8 months ago by
- Cc mderickx added
comment:7 Changed 8 months ago by
- 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
- Milestone changed from sage-9.5 to sage-9.6
comment:10 Changed 3 months ago by
- Milestone changed from sage-9.6 to sage-9.7
Ticket retargeted after milestone closed