Implement analytic modular symbols for elliptic curves

[williamstein]

Apply attachment: trac_6666-rebased-5.12.patch

CC: @pjbruin @JohnCremona

Component: modular forms

Keywords: period, modular symbol

Author: William Stein, Peter Bruin

Branch/Commit: dcaefdc

Reviewer: Frédéric Chapoton, Peter Bruin

Issue created by migration from https://trac.sagemath.org/ticket/6666

[loefflerd]

comment:1

Attachment: trac_6666-part1.patch.gz

[fchapoton]

comment:3

Here is a rebased patch.

apply trac_6666-rebased-5.12.patch

[fchapoton]

Changed keywords from none to period, modular symbol

[williamstein]

comment:5

Frédéric Chapoton -- whoever you are -- I'm extremely happy seeing all the work you're doing on modular forms related functionality in Sage!!!!!!

+1000

-- William Stein

[fchapoton]

comment:6

Thanks William. I am in algebra and combinatorics, not a number theorist, but I am trying to help nevertheless.

for the patchbot:

apply trac_6666-rebased-5.12.patch

[williamstein]

comment:7

Replying to @fchapoton:

Thanks William. I am in algebra and combinatorics, not a number theorist, but I am trying to help nevertheless.

Thanks. I'm in number theory, not algebra/combinatorics, but I hope Sage has been helpful to people in algebra/combinatorics :-)

[fchapoton]

comment:8

ok, the bot has turned green. Needs review

[fchapoton]

comment:9

new patch, rebased on 5.13.beta1

apply trac_6666-rebased-5.12.patch

[fchapoton]

comment:10

So there is numerical noise. Could somebody remind me what is the proper way to handle that ?

Use ... or use # rel tol or use # abs tol ?

[fchapoton]

comment:11

new patch, with numerical tolerance

apply trac_6666-rebased-5.12.patch

[fchapoton]

comment:12

apply trac_6666-rebased-5.12.patch

[fchapoton]

Attachment: trac_6666-rebased-5.12.patch.gz

[fchapoton]

comment:13

new patch, with lazy import

apply trac_6666-rebased-5.12.patch

[fchapoton]

Commit: 1986947

[fchapoton]

Branch: u/chapoton/6666

[fchapoton]

New commits:

[1986947](https://github.com/sagemath/sagetrac-mirror/commit/1986947)

trac #6666 -- implement analytic modular symbols algorithm and cusp transformation matrix

[sagetrac-git]

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

2e06ddb

trac #6666 -- implement analytic modular symbols algorithm and cusp transformation matrix

[sagetrac-git]

Changed commit from 1986947 to 2e06ddb

[sagetrac-git]

Changed commit from 2e06ddb to 91eb78f

[sagetrac-git]

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

28666a8	Merge branch 'u/chapoton/6666' of trac.sagemath.org:sage into 6.5.b3
91eb78f	trac #6666 minor formatting (towards pep8)

[pjbruin]

Author: William Stein, Peter Bruin

[pjbruin]

comment:21

The most important part of this ticket (periods of newforms) was implemented in a more general context (and with better precision handling) in #11215. The new commit reorganises the code, moves it to a more logical place (in my opinion) and uses the period() method of #11215.

[pjbruin]

Changed commit from 91eb78f to b50bec1

[pjbruin]

Reviewer: Frédéric Chapoton, Peter Bruin

[pjbruin]

Changed branch from u/chapoton/6666 to u/pbruin/6666-modular_symbol_numerical

[fchapoton]

Changed branch from u/pbruin/6666-modular_symbol_numerical to public/6666

[fchapoton]

comment:22

Looks good to me.

I allowed myself a few minor changes.

---

New commits:

4ba47c6	Merge branch 'u/pbruin/6666-modular_symbol_numerical' into 6.5.b5
dcaefdc	trac #6666 some pep8 details + crossref

[fchapoton]

Changed commit from b50bec1 to dcaefdc

[pjbruin]

comment:23

Replying to @fchapoton:

Looks good to me.

Thanks for the review!

I allowed myself a few minor changes.

I'm not disputing your changes to the whitespace here, but note that PEP 8 does not say that there should be spaces around all operators, only the relational ones. From https://www.python.org/dev/peps/pep-0008/:

If operators with different priorities are used, consider adding whitespace around the operators with the lowest priority(ies). Use your own judgment; however, never use more than one space, and always have the same amount of whitespace on both sides of a binary operator.
Yes:

i = i + 1
submitted += 1
x = x*2 - 1
hypot2 = x*x + y*y
c = (a+b) * (a-b)

No:

i=i+1
submitted +=1
x = x * 2 - 1
hypot2 = x * x + y * y
c = (a + b) * (a - b)

Actually, in the case of c = ..., I would personally prefer the "no" option or even (a + b)*(a - b), which is closer to standard mathematical typesetting, but in any case this is a matter of taste.

[vbraun]

Changed branch from public/6666 to dcaefdc