Opened 10 years ago
Closed 10 years ago
#12166 closed defect (fixed)
Elliptic curves: improve documentation of period_lattice
Reported by: | johanbosman | Owned by: | cremona |
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Priority: | minor | Milestone: | sage-4.8 |
Component: | elliptic curves | Keywords: | |
Cc: | Merged in: | sage-4.8.alpha5 | |
Authors: | Johan Bosman | Reviewers: | John Cremona |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description
sage: E = EllipticCurve([1,2,3,4,5]) sage: E.period_lattice? ... Docstring: Returns the period lattice of the elliptic curve. INPUT: * "embedding" - ignored (for compatibility with the period_lattice function for elliptic_curve_number_field) OUTPUT: (period lattice) The PeriodLattice_ell object associated to this elliptic curve (with respect to the natural embedding of QQ into RR). ...
The documentation speaks of "the" period lattice of E, but to define a period lattice one needs an invariant differential as well. From the documentation, it is not clear to me which differential is chosen here.
Attachments (1)
Change History (6)
comment:1 follow-up: ↓ 2 Changed 10 years ago by
- Summary changed from Elliptic curves: improve documentation of documentation of period_lattice to Elliptic curves: improve documentation of period_lattice
comment:2 in reply to: ↑ 1 Changed 10 years ago by
Replying to cremona:
How pedantic you are! Of course it means dx/(2y+a1*x+a3), what else?
It could be either that or a Néron differential, or perhaps people use other normalizations. I really didn't know which one was chosen or what is considered to be "standard" here. Thanks for clarifying!
Changed 10 years ago by
comment:3 Changed 10 years ago by
- Status changed from new to needs_review
comment:4 Changed 10 years ago by
- Reviewers set to John Cremona
- Status changed from needs_review to positive_review
Looks good! (Applies fine to 4.8.alpha4)
comment:5 Changed 10 years ago by
- Merged in set to sage-4.8.alpha5
- Resolution set to fixed
- Status changed from positive_review to closed
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How pedantic you are! Of course it means dx/(2y+a1*x+a3), what else? But feel free to change that (just as I have corrected the title of this ticket). Don't forget to also look at the function for elliptic curves over number fields (where there is a lot about choosing the real or complex embedding).