#23456 closed enhancement (fixed)
Compute Gauss sums with GrossKoblitz formula
Reported by:  asteele  Owned by:  

Priority:  minor  Milestone:  sage8.1 
Component:  padics  Keywords:  sd87 gamma padic 
Cc:  Merged in:  
Authors:  Adriana Salerno, Ander Steele  Reviewers:  Adele Bourgeois, Frédéric Chapoton 
Report Upstream:  N/A  Work issues:  
Branch:  95a100a (Commits)  Commit:  
Dependencies:  Stopgaps: 
Description
This code uses the GrossKoblitz formula to compute Gauss sums as products of padic Gamma functions. The result is an element of a totally ramified extension of Q_p. This can be much faster than computing gauss sums in the naive way. References: Benedict Gross & Neil Koblitz, "Gauss sums and the $p$adic $\Gamma$function", 1979 Alain Robert, "The GrossKoblitz formula revisited", 2001
Change History (27)
comment:1 Changed 2 years ago by
 Branch set to u/asteele/compute_gauss_sums_with_gross_koblitz_formula
comment:2 Changed 2 years ago by
 Commit set to 45b56d0cd0ae65795ce9da3d42b43c22bee4c3a3
comment:3 Changed 2 years ago by
 Commit changed from 45b56d0cd0ae65795ce9da3d42b43c22bee4c3a3 to b77e34f83d4c50ca8517abc66e2e333aad3600f0
Branch pushed to git repo; I updated commit sha1. New commits:
b77e34f  fix import on doctests

comment:4 Changed 2 years ago by
 Commit changed from b77e34f83d4c50ca8517abc66e2e333aad3600f0 to cb21c90a1ed8e169c2f71237fe9f3573b1805c49
Branch pushed to git repo; I updated commit sha1. New commits:
cb21c90  Fix whitespace problems with documentation

comment:5 Changed 2 years ago by
 Commit changed from cb21c90a1ed8e169c2f71237fe9f3573b1805c49 to 1c3d06ab244343f2f3c6ce956d1ca502f3b6eef2
Branch pushed to git repo; I updated commit sha1. New commits:
1c3d06a  prettify documentation with latex tags

comment:6 Changed 2 years ago by
 Commit changed from 1c3d06ab244343f2f3c6ce956d1ca502f3b6eef2 to f5583f680a031dd20544a3dea950f700538d6bc8
Branch pushed to git repo; I updated commit sha1. New commits:
f5583f6  Add documentation

comment:7 Changed 2 years ago by
 Status changed from new to needs_review
comment:8 Changed 2 years ago by
 Reviewers set to Adele Bourgeois
 Status changed from needs_review to positive_review
Looks good.
comment:9 Changed 2 years ago by
 Commit changed from f5583f680a031dd20544a3dea950f700538d6bc8 to 88b954e7c2bc522f4cf5d0d04de424f8296bff76
 Status changed from positive_review to needs_review
Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. New commits:
88b954e  Fix modulus for argument a, which depends only on residue class mod(p^f1)

comment:10 Changed 2 years ago by
 Status changed from needs_review to positive_review
comment:11 Changed 2 years ago by
 Status changed from positive_review to needs_work
I am happy to see this available; this will come handy for some code I am working on right now.
But the documentation is not properly formatted. I am going now to make a quick reviewer commit to fix that.
comment:12 Changed 2 years ago by
 Branch changed from u/asteele/compute_gauss_sums_with_gross_koblitz_formula to public/23456
 Commit changed from 88b954e7c2bc522f4cf5d0d04de424f8296bff76 to dd10796b0bece236bd8381627cb7dcba897088c9
 Reviewers changed from Adele Bourgeois to Adèle Bourgeois, Frédéric Chapoton
 Status changed from needs_work to needs_review
comment:13 Changed 2 years ago by
The patchbot is morally green. Please one of you set this ticket to positive !
comment:14 Changed 2 years ago by
 Status changed from needs_review to positive_review
comment:15 Changed 2 years ago by
 Status changed from positive_review to needs_work
Docbuild fails (merge in 8.1.beta1)
comment:16 Changed 2 years ago by
 Commit changed from dd10796b0bece236bd8381627cb7dcba897088c9 to c6536fd1a1a52971065118975e8ccde534277b50
comment:17 Changed 2 years ago by
 Status changed from needs_work to needs_review
I moved the imports inside the function, and documentation builds now.
comment:18 Changed 2 years ago by
 Commit changed from c6536fd1a1a52971065118975e8ccde534277b50 to 5c7db5d54bf07a7ec5194ea3041a27a2ce4b5dc1
Branch pushed to git repo; I updated commit sha1. New commits:
5c7db5d  trac 23456 one doc detail

comment:19 Changed 2 years ago by
 Status changed from needs_review to positive_review
I changed a detail in the doc, and checked that doc builds. I am setting back to positive review.
comment:20 Changed 2 years ago by
 Commit changed from 5c7db5d54bf07a7ec5194ea3041a27a2ce4b5dc1 to 68dedc74951ee49ea4684b14e550d4ef940a3782
 Status changed from positive_review to needs_review
Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. New commits:
68dedc7  trac 23456 fixing pdf documentation

comment:21 Changed 2 years ago by
There was a r"""
missing at the beginning of the file.
comment:22 Changed 2 years ago by
 Commit changed from 68dedc74951ee49ea4684b14e550d4ef940a3782 to 95a100a63d3d75cbaea714b4f2dce2c071ac84bb
Branch pushed to git repo; I updated commit sha1. New commits:
95a100a  trac 23456 missing capital for Gauss

comment:23 Changed 2 years ago by
 Status changed from needs_review to positive_review
I was fixing details and pdf doc, now setting back to positive
comment:24 Changed 2 years ago by
 Branch changed from public/23456 to 95a100a63d3d75cbaea714b4f2dce2c071ac84bb
 Resolution set to fixed
 Status changed from positive_review to closed
comment:25 followup: ↓ 26 Changed 2 years ago by
 Commit 95a100a63d3d75cbaea714b4f2dce2c071ac84bb deleted
Silly question maybe, but are we completely sure of the correctness of the code here ? I am asking because I have some problems in #23671 that could possibly come from here.
comment:26 in reply to: ↑ 25 Changed 2 years ago by
Replying to chapoton:
Silly question maybe, but are we completely sure of the correctness of the code here ? I am asking because I have some problems in #23671 that could possibly come from here.
There is a code snippet on #23671 that checks the padic computation against the computation by roots of unity. Perhaps that could be added as a doctest, but not on this ticket since it's already closed.
comment:27 Changed 22 months ago by
 Reviewers changed from Adèle Bourgeois, Frédéric Chapoton to Adele Bourgeois, Frédéric Chapoton
Branch pushed to git repo; I updated commit sha1. New commits:
Add documentation