Opened 5 years ago
Closed 5 years ago
#19060 closed defect (fixed)
Fix gauss_sum() for Dirichlet characters over cyclotomic fields
Reported by:  pbruin  Owned by:  

Priority:  major  Milestone:  sage6.9 
Component:  number theory  Keywords:  Dirichlet character Gauss sum 
Cc:  Merged in:  
Authors:  Peter Bruin  Reviewers:  Frédéric Chapoton 
Report Upstream:  N/A  Work issues:  
Branch:  ad61452 (Commits)  Commit:  ad6145286b8bae19ac6f3f7d7078a7cb8b4dd41b 
Dependencies:  #19056  Stopgaps: 
Description
In SageMath 6.9.beta2:
sage: K.<z> = CyclotomicField(8) sage: G = DirichletGroup(13, K) sage: chi = G([z^2]) sage: chi.gauss_sum() Traceback (most recent call last): ... TypeError: Cannot coerce zeta52 into Cyclotomic Field of order 8 and degree 4
This arises because chi
is actually defined over a smaller cyclotomic field. It can be fixed by letting gauss_sum()
minimize the base ring.
Change History (17)
comment:1 Changed 5 years ago by
 Branch set to u/pbruin/19060gauss_sum_cyclotomic_field
 Commit set to 6ea900bbe4ea86533daacdadec083a3f2db5c893
 Status changed from new to needs_review
comment:2 Changed 5 years ago by
 Commit changed from 6ea900bbe4ea86533daacdadec083a3f2db5c893 to 95b5401cf55f8650dfcc222d32da081c32ba1044
comment:3 Changed 5 years ago by
 Commit changed from 95b5401cf55f8650dfcc222d32da081c32ba1044 to c5f0a8a1e5186d160c22f933a97b9d41b82bc70b
comment:4 Changed 5 years ago by
 Dependencies set to #19056
Added #19056 as a dependency because it has positive review and there is a merge conflict.
comment:5 Changed 5 years ago by
 Status changed from needs_review to needs_work
two failing doctest, problem of complex conjugate
comment:6 Changed 5 years ago by
 Commit changed from c5f0a8a1e5186d160c22f933a97b9d41b82bc70b to 4236cdce5113b9a732db96b21cf7f9d38d1c7682
Branch pushed to git repo; I updated commit sha1. New commits:
4236cdc  Trac 19060: make doctests less sensitive to numerical noise

comment:7 Changed 5 years ago by
 Status changed from needs_work to needs_review
comment:8 followup: ↓ 10 Changed 5 years ago by
Hmm. Precision seems too high to me.. Maybe 1e15 would be better ?
and maybe replace the very small imaginary part in the doctest by 0.0*I ?
comment:9 Changed 5 years ago by
 Commit changed from 4236cdce5113b9a732db96b21cf7f9d38d1c7682 to 4cd66fddb6fd862b665c78d95e6b506b79ac201e
Branch pushed to git repo; I updated commit sha1. New commits:
4cd66fd  Trac 19060: increase doctest tolerance

comment:10 in reply to: ↑ 8 Changed 5 years ago by
Replying to chapoton:
Hmm. Precision seems too high to me.. Maybe 1e15 would be better ?
You are right, done.
and maybe replace the very small imaginary part in the doctest by 0.0*I ?
I prefer to have the doctest output reflect the actual output (on some system) as closely as possible, and I have never seen 0.0*I
in these tests (of course it would be the ideal answer).
comment:11 Changed 5 years ago by
 Status changed from needs_review to needs_work
one failing doctest, need to relax the tolerance a little bit, see patchbot report
comment:12 Changed 5 years ago by
 Commit changed from 4cd66fddb6fd862b665c78d95e6b506b79ac201e to ad6145286b8bae19ac6f3f7d7078a7cb8b4dd41b
Branch pushed to git repo; I updated commit sha1. New commits:
ad61452  Trac 19060: further increase doctest tolerance

comment:13 Changed 5 years ago by
 Status changed from needs_work to needs_review
comment:14 Changed 5 years ago by
 Status changed from needs_review to positive_review
ok, looks good to me
comment:15 Changed 5 years ago by
 Status changed from positive_review to needs_work
Reviewer name missing
comment:16 Changed 5 years ago by
 Reviewers set to Frédéric Chapoton
 Status changed from needs_work to positive_review
sorry for that.
comment:17 Changed 5 years ago by
 Branch changed from u/pbruin/19060gauss_sum_cyclotomic_field to ad6145286b8bae19ac6f3f7d7078a7cb8b4dd41b
 Resolution set to fixed
 Status changed from positive_review to closed
Branch pushed to git repo; I updated commit sha1. New commits:
Trac 19060: fix doctests