Solution of S-unit equations over Q

[JohnCremona]

Angelos Koutsianas has written code to solve general 3-term S-unit equations over Q, i.e. to find all solutions to x+y=1 where x,y are rationals supported on the primes in a given finite set S. This is based on de Weger's thesis.

The code is currently being tested, and will be made into a new branch here.

CC: @sagetrac-akoutsianas

Component: number theory

Keywords: S-unit equation

Author: Angelos Koutsianas, John Cremona

Branch/Commit: u/mwest/19887 @ 1f4de5b

Issue created by migration from https://trac.sagemath.org/ticket/19887

[JohnCremona]

Branch: u/cremona/19887

[JohnCremona]

Commit: 64b0e74

[sagetrac-git]

Changed commit from 64b0e74 to f97b22f

[sagetrac-git]

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

b1709e9	Merge branch 'develop' into S_unit
f97b22f	remove redundant import from S_unit.py which caused startup crash

[JohnCremona]

comment:4

The above commit (f97b22f) includes 7.1.beta1, and the new file passes its tests.

[JohnCremona]

comment:5

I think we need to added the new file S_unit_equation.py to the reference manual, and I will try to do that. Also, the file aith.py was moved and I am not sure that the reference manual has been adjusted correctly.

[sagetrac-git]

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

42d9788

progress on documentation of S-unit code

[sagetrac-git]

Changed commit from f97b22f to 42d9788

[JohnCremona]

comment:7

Docs now build without errors, I will work on the text a bit.

[sagetrac-git]

Changed commit from 42d9788 to d0fb02b

[sagetrac-git]

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

d0fb02b

fix some docstring formatting in S-unit eqn code

[JohnCremona]

comment:9

The docstrings now look OK, though perhaps not all functions are explained adequately (and the specific reference should be checked as I was not sure which were to Smart and which to de Weger). I am finished with this code for now.

[mckenziewest]

Changed branch from u/cremona/19887 to u/mwest/19887

[JohnCremona]

Changed commit from d0fb02b to 1f4de5b

[JohnCremona]

comment:12

This ticket became obsolete as the work was done at #22148, merged in version 8.5.

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New commits:

3934d22	updated code moved to number_field directory
1f4de5b	remove solver from arith directory