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Period lattice: fix documentation error #38561

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merged 1 commit into from
Sep 3, 2024
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@user202729 user202729 commented Aug 25, 2024

That's what the code appear to be doing.

The existing example in _compute_periods_real also show it:

sage:             sage: # needs sage.rings.number_field
....:             sage: x = polygen(ZZ, 'x')
....:             sage: K.<a> = NumberField(x^3 - 2)
....:             sage: E = EllipticCurve([0,1,0,a,a])
....:             sage: embs = K.embeddings(CC)
....:             sage: Ls = [E.period_lattice(e) for e in embs]
....:             sage: [L.is_real() for L in Ls]
....: 
[False, False, True]
sage:             sage: Ls[2]._compute_periods_real(100)
....: 
(3.8145297721785450936365098936,
 1.9072648860892725468182549468 + 1.3404778596244020196600112394*I)

Then do

sage: ω1, ω2 = _
sage: ω2/ω1
0.50000000000000000000000000000 + 0.35141365769412556448697319411*I
sage: ω1/ω2
1.3387183410189190672591156778 - 0.94088781767934015952275257142*I

📝 Checklist

  • The title is concise and informative.
  • The description explains in detail what this PR is about.
  • I have linked a relevant issue or discussion.
  • I have created tests covering the changes.
  • I have updated the documentation and checked the documentation preview.

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Documentation preview for this PR (built with commit 2215319; changes) is ready! 🎉
This preview will update shortly after each push to this PR.

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@kwankyu kwankyu left a comment

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Nice catch. LGTM.

vbraun pushed a commit to vbraun/sage that referenced this pull request Aug 27, 2024
    
That's what the code appear to be doing.

The existing example in `_compute_periods_real` also show it:

```sage
sage:             sage: # needs sage.rings.number_field
....:             sage: x = polygen(ZZ, 'x')
....:             sage: K.<a> = NumberField(x^3 - 2)
....:             sage: E = EllipticCurve([0,1,0,a,a])
....:             sage: embs = K.embeddings(CC)
....:             sage: Ls = [E.period_lattice(e) for e in embs]
....:             sage: [L.is_real() for L in Ls]
....:
[False, False, True]
sage:             sage: Ls[2]._compute_periods_real(100)
....:
(3.8145297721785450936365098936,
 1.9072648860892725468182549468 + 1.3404778596244020196600112394*I)

```
Then do
```sage
sage: ω1, ω2 = _
sage: ω2/ω1
0.50000000000000000000000000000 + 0.35141365769412556448697319411*I
sage: ω1/ω2
1.3387183410189190672591156778 - 0.94088781767934015952275257142*I
```



### 📝 Checklist

<!-- Put an `x` in all the boxes that apply. -->

- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
- [ ] I have linked a relevant issue or discussion.
- [ ] I have created tests covering the changes.
- [x] I have updated the documentation and checked the documentation
preview.

### ⌛ Dependencies

<!-- List all open PRs that this PR logically depends on. For example,
-->
<!-- - sagemath#12345: short description why this is a dependency -->
<!-- - sagemath#34567: ... -->
    
URL: sagemath#38561
Reported by: user202729
Reviewer(s): Kwankyu Lee
@vbraun vbraun merged commit 35e0c66 into sagemath:develop Sep 3, 2024
21 of 22 checks passed
@mkoeppe mkoeppe added this to the sage-10.5 milestone Sep 3, 2024
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4 participants