Opened 5 years ago
Closed 5 years ago
#23780 closed enhancement (fixed)
Modify p-adic Gauss sum to allow working directly in Q_p
| Reported by: | kedlaya | Owned by: | |
|---|---|---|---|
| Priority: | major | Milestone: | sage-8.1 |
| Component: | padics | Keywords: | Gauss sums, Gross-Koblitz formula |
| Cc: | Merged in: | ||
| Authors: | Kiran Kedlaya | Reviewers: | David Roe, Frédéric Chapoton |
| Report Upstream: | N/A | Work issues: | |
| Branch: | 45da482 (Commits, GitHub, GitLab) | Commit: | 45da48281b575794afe1e83f2378f80418c5c7d8 |
| Dependencies: | Stopgaps: |
Status badges
Description
The Gross-Koblitz formula for p-adic computation of Gauss sums was implemented in #23456. The formula involves working in the ramified extension of Q_p generated by an element pi for which pi^(p-1) == -p; however, the formula actually is written as a power of pi times an element of Z_p, and for some applications (e.g., hypergeometric motives; see #23671) it would be helpful to be able to access the unramified factor without going through the extension ring (for efficiency when p is large). That is, one should have the option to request the output in the form (e, z) where e is a nonnegative integer, z is an element of Z_p, and the real answer is pi^e*z for pi as above. And in this case, the extension field should not be formed at all.
Change History (13)
comment:1 Changed 5 years ago by
- Branch set to u/kedlaya/modify_p_adic_gauss_sum_to_allow_working_directly_in_q_p
comment:2 Changed 5 years ago by
- Commit set to 50cd8bf9f3ea296f3894a550f91cc99e33cdeb98
comment:3 Changed 5 years ago by
- Status changed from new to needs_review
Commit added, with a doctest to match. I also fixed the mathematical issue with the docstring reported in #23671.
This should be an easy review, except possibly for formatting issues.
comment:4 Changed 5 years ago by
- Reviewers set to David Roe
Looks good to me; positive review once tests pass.
comment:5 Changed 5 years ago by
- Commit changed from 50cd8bf9f3ea296f3894a550f91cc99e33cdeb98 to 6cc03a1bc2f4e116854e9243d229b7998ab5789a
Branch pushed to git repo; I updated commit sha1. New commits:
| 6cc03a1 | Correct docstring formatting, handling of r=0 case
|
comment:6 Changed 5 years ago by
Fixed docstring formatting in my mathematical correction; and forced the answer to be cast into the p-adic ring even when r=0 (otherwise errors may result down the line).
comment:7 Changed 5 years ago by
does not apply on the latest beta, needs rebase
comment:8 Changed 5 years ago by
- Commit changed from 6cc03a1bc2f4e116854e9243d229b7998ab5789a to ef1626f70212fd236a888e874a644fcb8cb1f4ea
Branch pushed to git repo; I updated commit sha1. New commits:
| ef1626f | Merge branch 'develop' into t/23780/modify_p_adic_gauss_sum_to_allow_working_directly_in_q_p
|
comment:9 Changed 5 years ago by
Sorry, that should be fixed now.
comment:11 Changed 5 years ago by
- Branch changed from u/kedlaya/modify_p_adic_gauss_sum_to_allow_working_directly_in_q_p to public/23780
- Commit changed from ef1626f70212fd236a888e874a644fcb8cb1f4ea to 45da48281b575794afe1e83f2378f80418c5c7d8
comment:12 Changed 5 years ago by
- Reviewers changed from David Roe to David Roe, Frédéric Chapoton
- Status changed from needs_review to positive_review
ok, let it be.
comment:13 Changed 5 years ago by
- Branch changed from public/23780 to 45da48281b575794afe1e83f2378f80418c5c7d8
- Resolution set to fixed
- Status changed from positive_review to closed
Branch pushed to git repo; I updated commit sha1. New commits:
Fixed typo in doctest