Shioda invariants for hyperelliptic curves with genus 3

[anna-somoza]

Sorina Ionica, Elisa Lorenzo Garcia and I implemented the computation of Shioda invariants for a given hyperelliptic curve of genus 3.

Following the implementation of the constructors of genus 2 curves over various fields we have added the corresponding classes for genus 3 hyperelliptic curves.

Depends on #26462
Depends on #27633

CC: @sagetrac-christelle @sagetrac-elorenzogarcia @sagetrac-ionisorus @mstreng @sagetrac-kohel @sagetrac-florian @JRSijsling @jnoordsij

Component: number theory

Keywords: days82, hyperelliptic curves, shioda invariants, days98

Author: Sorina Ionica, Elisa Lorenzo Garcia, Anna Somoza

Branch/Commit: public/22173 @ ca3b22c

Reviewer: Vincent Delecroix, Jean-Pierre Flori

Issue created by migration from https://trac.sagemath.org/ticket/22173

[anna-somoza]

Branch: u/annasomoza/22173-shiodainv

[sagetrac-git]

Commit: 2bc9d8e

[sagetrac-git]

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

87e7c25	work in progress
5a83cd4	Merge branch 'develop' into local-g3invariants
2bc9d8e	Add doctests

[sagetrac-git]

Changed commit from 2bc9d8e to 153178f

[sagetrac-git]

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

153178f

Fix extra empty lines

[fchapoton]

comment:5

missing "of" in

Compute invariants genus 2 and 3 hyperelliptic curves via 'Ueberschiebung'

[sagetrac-git]

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

4f8d45f	Fix output type
955cc72	Fix minor doc error

[sagetrac-git]

Changed commit from 153178f to 955cc72

[fchapoton]

comment:9

doc still does not build:

+[dochtml] [curves   ] /home/u1/chapoton/sage/local/lib/python2.7/site-packages/sage/schemes/hyperelliptic_curves/invariants.py:docstring of sage.schemes.hyperelliptic_curves.invariants.shioda_invariants:7: WARNING:
 Duplicate explicit target name: "sh".
+[dochtml] [curves   ] /home/u1/chapoton/sage/local/lib/python2.7/site-packages/sage/schemes/hyperelliptic_curves/invariants.py:docstring of sage.schemes.hyperelliptic_curves.invariants.shioda_invariants:7: WARNING:
 duplicate citation Sh, other instance in /home/u1/chapoton/sage/src/doc/en/reference/curves/sage/schemes/hyperelliptic_curves/invariants.rst

[sagetrac-git]

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

1da5c7e

Add Shioda computation for h neq 0. Doc builds.