Implement reconstruction of binary quintics

[jnoordsij]

Implement a function that given a set of values of invariants of a binary quintic, finds a quintic that attains these values up to scaling.

A general framework for reconstruction is implemented for quintics defined over fields of characteric different from 2, 3 and 5. This is placed in the new invariants folder created in ticket #26370.

For fields of characteristic 2, 3 and 5, see ticket #26786.

This ticket requires binary quintics for computations and doctests, so depends on #25395.

CC: @mstreng @pjbruin

Component: algebra

Keywords: invariant_theory

Author: Jesper Noordsij

Branch/Commit: ff11a5d

Reviewer: Frédéric Chapoton

Issue created by migration from https://trac.sagemath.org/ticket/25508

[jnoordsij]

Branch: u/jnoordsij/binary_quintics_reconstruction

[sagetrac-git]

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

3247dc5	Fixed spaces and imports.
b62525a	Changed invariants output & added reduced flag for output.
b80da8c	Some more fixes & added files to documentation.

[sagetrac-git]

Commit: b80da8c

[sagetrac-git]

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

480180a

Fixed a bug with infinite loop when using reduced flag.

[sagetrac-git]

Changed commit from b80da8c to 480180a

[sagetrac-git]

Changed commit from 480180a to fd21650

[sagetrac-git]

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

775e8cb	Merge branch 'develop' into binary_quintics_reconstruction
fd21650	Fixes to ensure documentation builds after merge.

[jnoordsij]

Author: Jesper Noordsij

[sagetrac-git]

Changed commit from fd21650 to 8460b3d

[sagetrac-git]

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

e6646ad	Removing invariant_theory.py before merge.
8460b3d	Merge branch 'develop' into binary_quintics_reconstruction.

[sagetrac-git]

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

30be42f	Removing invariant_theory.py before merge.
78a30ed	Adjusted to fix slower startup time.
b935917	Merge branch 'develop' into t/25395/binary_quintics
dc81ba3	Documentation fixes.
872f8d2	Merge branch 't/25395/binary_quintics' into t/25508/binary_quintics_reconstruction
0236fed	Small corrections.
8ddfe30	More documentation fixes & adjusting transvectant.

[sagetrac-git]

Changed commit from 8460b3d to 8ddfe30

[sagetrac-git]

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

fd6719d

Minor documentation fixes.

[sagetrac-git]

Changed commit from 8ddfe30 to fd6719d

[sagetrac-git]

Changed commit from fd6719d to 85a8383

[sagetrac-git]

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

85a8383

Fixed pyflakes and failing doctests.

[jnoordsij]

Work Issues: fix doctests where deprecation errors appear

[sagetrac-git]

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

ff5f1b9	Changed import to lazy_import and moved two imports.
2501a4e	Adjusted imports of invariant_theory to new file location.

[sagetrac-git]

Changed commit from 85a8383 to 2501a4e

[jnoordsij]

Changed work issues from fix doctests where deprecation errors appear to none

[sagetrac-git]

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

0e27dc1

Final doctest fixed.

[fchapoton]

comment:39

back to needs review ?

[fchapoton]

comment:40

ok, I will assume so.. but you should rather react yourself..

[jnoordsij]

comment:41

I will implement a more general binary_form_from_invariants method, with an additional binary_quintic_coefficients_from_invariants method.

[sagetrac-git]

Changed commit from e514138 to 56a0d79

[sagetrac-git]

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

c713632	Adjust coefficients scaling
56a0d79	Adjust reconstruction methods so Form objects are returned by default

[fchapoton]

comment:43

needs review ?

[jnoordsij]

comment:44

I intend to do a last check if there are sufficient doctests and references later this week; after that I will change to needs review again.

[sagetrac-git]

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

383cd48

Update doctests and documentation of several methods

[sagetrac-git]

Changed commit from 56a0d79 to 383cd48

[fchapoton]

comment:47

looks almost good.

Error messages should not end with a dot and should not start with a capital. They should look something like

IncredibleError: this banana is blue

[sagetrac-git]

Changed commit from 383cd48 to ff11a5d

[sagetrac-git]

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

ff11a5d

Update format of error messages

[fchapoton]

comment:49

ok, let it be.

[fchapoton]

Reviewer: Frédéric Chapoton

[vbraun]

Changed branch from u/jnoordsij/binary_quintics_reconstruction_2 to ff11a5d