Opened 3 years ago

Closed 3 years ago

#28404 closed defect (fixed)

Sign of hypergeometric motives is sometimes wrong

Reported by: kedlaya Owned by:
Priority: major Milestone: sage-8.9
Component: modular forms Keywords: hypergeometric motives
Cc: Merged in:
Authors: Kiran Kedlaya Reviewers: Frédéric Chapoton
Report Upstream: N/A Work issues:
Branch: 37fda46 (Commits, GitHub, GitLab) Commit: 37fda46afe7e05a2fac93ec6a6e6edfd5b67ad4d
Dependencies: Stopgaps:

Status badges


The sign method of HypergeometricData sometimes returns answers that do not agree with Magma:

sage: from sage.modular.hypergeometric_motive import HypergeometricData as Hyp
sage: H = Hyp(cyclotomic=([6,2],[1,1,1]))
sage: [H.sign(1/4,p) for p in [5,7,11,13,17,19]] #correct
[1, 1, -1, -1, 1, 1]
sage: H = Hyp(cyclotomic=([1,1,1],[6,2]))
sage: [H.sign(4,p) for p in [5,7,11,13,17,19]] #should agree but doesn't
[-1, -1, -1, -1, -1, -1]

I believe this is because Magma's formula is not valid when 0 in alpha. Note that this does not affect the padic_H_value or euler_factor methods because these do an alpha-beta swap to avoid this case (just as in Magma).

I have a fix for this coded up locally. Will post a patch shortly.

Change History (8)

comment:1 Changed 3 years ago by kedlaya

  • Branch set to u/kedlaya/sign_of_hypergeometric_motives_is_sometimes_wrong

comment:2 Changed 3 years ago by chapoton

  • Commit set to 8bbce1f713dfec2971a14433d3e629195bbeb1dd

Maybe we should instead always switch when creating the object (in the __init__) when 0 in alpha ?

New commits:

61f3c25Fix sign of hypergeometric motives
8bbce1fDocstring edit


But maybe this is not a good idea, because the user will not get what he wants..

Last edited 3 years ago by chapoton (previous) (diff)

comment:3 Changed 3 years ago by kedlaya

Right, it is probably a bad idea to not return what is asked for. I understand that Magma originally did this and it caused all sorts of headaches.

A better idea might be, at creation time, if 0 in alpha, instantiate the swapped data and save it in H._swap. Then one can access this attribute when sign is called (or for that matter padic_H_value or H_value or euler_factor).

comment:4 Changed 3 years ago by git

  • Commit changed from 8bbce1f713dfec2971a14433d3e629195bbeb1dd to 68eeea1a521543804b1f8636e877199d6fd5be30

Branch pushed to git repo; I updated commit sha1. New commits:

68eeea1Add _swap attribute to HypergeometricData

comment:5 Changed 3 years ago by kedlaya

  • Authors set to Kiran Kedlaya
  • Status changed from new to needs_review

While implementing this last suggestion, I discovered I was getting strange irreproducible errors if I didn't perform

t = QQ(t)

before doing the swap (the value of t was sometimes getting cast to 0).

comment:6 Changed 3 years ago by chapoton

  • Branch changed from u/kedlaya/sign_of_hypergeometric_motives_is_sometimes_wrong to public/ticket/28404
  • Commit changed from 68eeea1a521543804b1f8636e877199d6fd5be30 to 37fda46afe7e05a2fac93ec6a6e6edfd5b67ad4d
  • Reviewers set to Frédéric Chapoton
  • Status changed from needs_review to positive_review

I have changed a few details. I am setting to positive.

New commits:

37fda46trac 28404 fix details

comment:7 Changed 3 years ago by kedlaya

Looks good, thanks.

comment:8 Changed 3 years ago by vbraun

  • Branch changed from public/ticket/28404 to 37fda46afe7e05a2fac93ec6a6e6edfd5b67ad4d
  • Resolution set to fixed
  • Status changed from positive_review to closed
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