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

[kwankyu]

Description changed:

--- 
+++ 
@@ -4,4 +4,4 @@
 
 2. Improve docstrings for existing code
 
-There are two dependencies: #16561, #22841.
+There are two dependencies: #16561, #22841, which were merged to this ticket.

[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]

Description changed:

--- 
+++ 
@@ -2,6 +2,6 @@
 
 1. Add global function fields with lots of useful functionality 
 
-2. Improve docstrings for existing code
+2. Clean existing code (mostly revising docstrings)
 
 There are two dependencies: #16561, #22841, which were merged to this ticket.

[kwankyu]

Description changed:

--- 
+++ 
@@ -1,6 +1,6 @@
 Function fields part of Sage has long been neglected and lacks any significant functionality besides basic arithmetic and frameworks. This ticket improves the situation by doing two things:
 
-1. Add global function fields with lots of useful functionality 
+1. Add global function fields with complete functionality for the theory of AG codes 
 
 2. Clean existing code (mostly revising docstrings)
 

[kwankyu]

Description changed:

--- 
+++ 
@@ -1,7 +1,7 @@
 Function fields part of Sage has long been neglected and lacks any significant functionality besides basic arithmetic and frameworks. This ticket improves the situation by doing two things:
 
-1. Add global function fields with complete functionality for the theory of AG codes 
+1. Add global function fields (with complete functionality for the theory of AG codes) 
 
 2. Clean existing code (mostly revising docstrings)
 
-There are two dependencies: #16561, #22841, which were merged to this ticket.
+There are two dependencies: #16561, #22841, which were merged to this patch. The author was supported by research fund from Chosun University 2016.