Opened 15 years ago
Closed 15 years ago
#1183 closed defect (fixed)
[with patch, with positive review] Residue fields are broken
| Reported by: | roed | Owned by: | was |
|---|---|---|---|
| Priority: | major | Milestone: | sage-2.9 |
| Component: | number theory | Keywords: | |
| Cc: | Merged in: | ||
| Authors: | Reviewers: | ||
| Report Upstream: | Work issues: | ||
| Branch: | Commit: | ||
| Dependencies: | Stopgaps: |
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Description
The current implementation of residue fields for number fields is broken. It just takes the defining polynomial for the number field, factors it over Z/pZ, picks one factor and creates an extension using that factor. This breaks because elements of the ring of integers, when expressed in terms of the power basis of the number field can have denominators divisible by p.
The solution is to create a p-maximal order and do some linear algebra to come up with a map that doesn't break on denominators divisible by p. Pari's nfinit has a way to give it a partial factorization of the discriminant that will produce a p-maximal order.
If you want to implement this, talk to William Stein or David Roe for more details.
Attachments (5)
Change History (10)
comment:1 Changed 15 years ago by
Changed 15 years ago by
Changed 15 years ago by
comment:2 Changed 15 years ago by
NOT ready to be released yet.
comment:3 Changed 15 years ago by
NOTE!! Be sure to also apply
Changed 15 years ago by
Changed 15 years ago by
comment:4 Changed 15 years ago by
- Summary changed from Residue fields are broken to [with patch, with positive review] Residue fields are broken
comment:5 Changed 15 years ago by
- Resolution set to fixed
- Status changed from new to closed
Merged in 2.9.rc0.
Ifti did open #1185 for his specific problem. So in case this is solved and the status of #1183 remains unchanged please resolve that ticket, also.
Cheers,
Michael