gh-35026: Drinfeld modules

    
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### 📚 Description

Fixes #33713.

We implement Drinfeld $\mathbb{F}_q[T]$-modules with a focus towards
finite Drinfeld modules. We also implement isogenies of Drinfeld
modules. More details in the issue.

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None.
    
URL: #35026
Reported by: Antoine Leudière
Reviewer(s): David Ayotte, Xavier Caruso

src/doc/en/reference/drinfeld_modules/conf.py

@@ -0,0 +1 @@
+../conf_sub.py

src/doc/en/reference/drinfeld_modules/index.rst

@@ -0,0 +1,42 @@
+Drinfeld modules
+====================================
+
+SageMath include facilities to manipulate Drinfeld modules and their morphisms. The
+main entry point is the class
+:class:`sage.rings.function_field.drinfeld_modules.drinfeld_module.DrinfeldModule`.
+
+Drinfeld modules
+----------------
+
+.. toctree::
+   :maxdepth: 2
+
+   sage/rings/function_field/drinfeld_modules/drinfeld_module
+   sage/rings/function_field/drinfeld_modules/finite_drinfeld_module
+
+Morphisms and isogenies
+-----------------------
+
+.. toctree::
+   :maxdepth: 2
+
+   sage/rings/function_field/drinfeld_modules/morphism
+   sage/rings/function_field/drinfeld_modules/homset
+
+The module action induced by a Drinfeld module
+----------------------------------------------
+
+.. toctree::
+   :maxdepth: 2
+
+   sage/rings/function_field/drinfeld_modules/action
+
+The category of Drinfeld modules
+--------------------------------
+
+.. toctree::
+   :maxdepth: 2
+
+   sage/categories/drinfeld_modules
+
+.. include:: ../footer.txt

src/doc/en/reference/index.rst

@@ -115,6 +115,7 @@ Number Fields, Function Fields, and Valuations
 * :doc:`Number Fields <number_fields/index>`
 * :doc:`Function Fields <function_fields/index>`
 * :doc:`Discrete Valuations <valuations/index>`
+* :doc:`Drinfeld Modules <drinfeld_modules/index>`
 
 Number Theory
 -------------

src/doc/en/reference/references/index.rst

@@ -2608,6 +2608,9 @@ REFERENCES:
             TR-737-05, (2005).
             ftp://ftp.cs.princeton.edu/reports/2005/737.pdf
 
+.. [Gek1991] \E.-U. Gekeler. On finite Drinfeld modules. Journal of
+             algebra, 1(141):187–203, 1991.
+
 .. [GG2012] Jim Geelen and Bert Gerards, Characterizing graphic
             matroids by a system of linear equations,
             submitted, 2012. Preprint:
@@ -2771,6 +2774,9 @@ REFERENCES:
 .. [Gos1972] Bill Gosper, "Continued Fraction Arithmetic"
              https://perl.plover.com/classes/cftalk/INFO/gosper.txt
 
+.. [Gos1998] \D. Goss. Basic structures of function field arithmetic. Springer,
+             1998.
+
 .. [Gor1980] Daniel Gorenstein, Finite Groups (New York: Chelsea
              Publishing, 1980)
 
@@ -4642,6 +4648,11 @@ REFERENCES:
             Int. Math. Res. Not. (2015).
             :doi:`10.1093/imrn/rnv194`, :arxiv:`1408.0320`.
 
+.. [MS2019] \Y. Musleh and \'E. Schost. Computing the characteristic polynomial
+            of a finite rank two Drinfeld module. In Proceedings of the 2019
+            ACM on International Symposium on Symbolic and Algebraic
+            Computation, pages 307–314. ACM, 2019.
+
 .. [MSSY2001] Mateescu, A., Salomaa, A., Salomaa, K. and Yu, S., *A
               sharpening of the Parikh mapping*. Theoret. Informatics Appl. 35
               (2001) 551-564.
@@ -5222,6 +5233,8 @@ REFERENCES:
 .. [Ros2002] Rosenfeld, Vladimir Raphael, 2002: Enumerating De Bruijn
              Sequences. *Communications in Math. and in Computer Chem.*
 
+.. [Rosen2002] \M. Rosen. Number theory in function fields. Springer, 2022.
+
 .. [Rot2001] Gunter Rote, *Division-Free Algorithms for the
              Determinant and the Pfaffian: Algebraic and Combinatorial
              Approaches*, H. Alt (Ed.): Computational Discrete
@@ -6093,6 +6106,9 @@ REFERENCES:
 .. [Voi2012] \J. Voight. Identifying the matrix ring: algorithms for
              quaternion algebras and quadratic forms, to appear.
 
+.. [VS06]   \G.D. Villa Salvador. Topics in the Theory of Algebraic Function
+            Fields. Birkh\"auser, 2006.
+
 .. [VW1994] Leonard Van Wyk. *Graph groups are biautomatic*. J. Pure
             Appl. Alg. **94** (1994). no. 3, 341-352.