Global function fields

[kwankyu]

Function fields part of Sage has long been neglected and has little significant functionality besides basic arithmetic and frameworks. This ticket improves the situation by two tasks:

1. Add global function fields (with complete functionality for the theory of AG codes)

2. Clean existing code (mostly revising docstrings)

A pdf for a short introduction to global function fields in Sage is attached.

---

Now the long-term process to merge the global function field machinery to Sage has finished. This ticket played the role of meta-ticket that tracks the multi-step process:

Step	Ticket	Comments
0	#24591	Trim the existing code. Add several classes that are now just stubs.
1	#25435	Add orders and ideals.
2	#26616	Add places.
3	#27121	Add divisors.
4	#27370	Add differentials.
5	#27418	Add completions.
6	#27558	Last fixes and additions.

---

The author was supported by Chosun University 2016 and by NRF of Korea 2017, 2018, 2019

CC: @johanrosenkilde @sagetrac-danielaugot @BrentBaccala

Component: algebra

Keywords: global function field, algebraic geometry code

Author: Kwankyu Lee

Issue created by migration from https://trac.sagemath.org/ticket/22982

[kwankyu]

Branch: u/klee/22982

[sagetrac-git]

Commit: 269da47

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

4bb538e	Improve docstrings
2847da0	Trim code and docstrings
939fda6	Refine docstrings
2ee70bd	Merge branch 'derivations_trac16561'
a910bfa	Improve docstrings
931c72c	Merge branch 'develop'
665f508	Add new features and revise docstrings
b1d1efd	Merge branch 'develop'
4b5d8aa	Raise doctest coverage by adding lots of them
269da47	Add more maps

[sagetrac-git]

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

6fa87ce

Remove redundant a or an

[sagetrac-git]

Changed commit from 269da47 to 6fa87ce

[sagetrac-git]

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

1a0414c	Merge branch 'develop'
da7cb4d	Improve _test_derivative test
7ef1bec	Merge branch 'trac16561'

[sagetrac-git]

Changed commit from 6fa87ce to 7ef1bec

[kwankyu]

Dependencies: #22841

[sagetrac-git]

Changed commit from 7ef1bec to 1034aac

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. Last 10 new commits:

b292fb2	Use reverse_rows_and_columns
df8ce31	Fixes in docstrings and code
0e57cc1	Improve docstrings
ad9a8c4	Fix a bug in include_zero_rows
1894770	Relocate _hermite_form_euclidean
bf6b339	Fix a bug; add an example for ZZ
464f6de	Fix a docstring failure
734c862	Merge branch 'develop' into hermite_trac22841
268f049	Compute U also by low level operations
1034aac	Merge branch 'hermite_trac22841' into function_fields_trac22982

[sagetrac-git]

Changed commit from 1034aac to a5ceb84

[sagetrac-git]

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

a5ceb84

Merge branch 'develop' into function_fields_trac22982

[kwankyu]

Changed keywords from none to global function field, algebraic geometry code

[sagetrac-git]

Changed commit from a5ceb84 to ae89ab2

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

4cd0abc	Merge branch 'develop' into hermite_trac22841
a96c3be	Remove reversed hermite form methods
f1c8202	Set hermite form immutable consistently
9c8408f	More static typing and setting immutable
3d7fd03	Fix EXAMPLE to EXAMPLES
ff0b73e	Improve normalization
bc890de	Merge branch 'hermite_trac22841' into function_fields_trac22982
1b4881b	Fix reverse hermite form code
e59bd0d	Merge branch 'develop' into function_fields_trac22982
ae89ab2	Fix richcmp deprecation warnings

[kwankyu]

Changed dependencies from #22841 to none

[sagetrac-git]

Changed commit from ae89ab2 to 8143ac6

[sagetrac-git]

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

d893d55	Merge branch 'develop' into function_fields_trac22982
d12fd77	Merge branch 'develop' into hermite_trac22841
dd0d065	Add an example using normalization argument
7933860	Merge branch 'develop' into hermite_trac22841
032ee67	Merge branch 'hermite_trac22841' into function_fields_trac22982
8143ac6	Fix a doctest failure

[sagetrac-git]

Changed commit from 8143ac6 to 40af34a

[kwankyu]

comment:85

Replying to @BrentBaccala:

Some of #25494's code should probably be merged into #22982. The commit labeled "refactor divisor methods" moves the divisor, divisor_of_zeros, and divisor_of_poles methods into superclasses. Is there a reason not to do this? It avoids some code duplication.

As you see, this ticket is just a meta ticket. You comment should be addressed to a (not yet created) sub ticket of this ticket, merging divisor part of the code. I am still waiting for a review of the ticket #25435 dealing with orders and ideals before I create a ticket for divisors.

[BrentBaccala]

comment:86

Replying to @kwankyu:

Replying to @BrentBaccala:

Would you like to add a link to #25494 on this ticket's description?

No, it should be the other way around. I mean that #25494 should contain a link to this ticket if it depends on this ticket.

#25494 does contain a link to #22982 in its "dependencies".

I suggest putting a link in this ticket (just like you have links to the sub tickets) so that people will know that we've got a version of this code that works over QQ.

[dimpase]

comment:87

I don't think working on kash makes sense - it's basically dead, it seems.
The last release was 10 years ago, and it's binary only!

[kwankyu]

comment:88

Replying to @dimpase:

I don't think working on kash makes sense - it's basically dead, it seems.
The last release was 10 years ago, and it's binary only!

You read wrong some previous comments. This ticket is not about kash at all!