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New algorithms to compute the characteristic polynomial of the Frobenius endomorphism of a Drinfeld module #38174

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Sep 22, 2024
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3dbf839
Add CL23 to the master bibliography
kryzar Jun 7, 2024
560d446
Update DrinfeldModule_finite.frobenius_charpoly docstring
kryzar Jun 7, 2024
9c4a302
Implement CSA and gekeler algorithms
kryzar Jun 8, 2024
e1bb7fb
Fix frobenius_norm
kryzar Jun 8, 2024
cdd6380
Fix whitespace on empty line
kryzar Jun 8, 2024
0b8bdde
Change \FF to \mathbb F
kryzar Jun 8, 2024
504f044
Update src/sage/rings/function_field/drinfeld_modules/finite_drinfeld…
kryzar Jun 11, 2024
290e7f8
Merci David (remove backslash)
kryzar Jun 11, 2024
86b2b31
Fix a reference
kryzar Jun 28, 2024
a6ae5ba
Fix algorithm flag
kryzar Jun 28, 2024
8e85d71
Merge branch 'develop' into charpoly-csa
kryzar Jun 30, 2024
da1629b
Merge branch 'develop' into charpoly-csa
kryzar Aug 1, 2024
730d0e7
Do not use cached charpoly when `algorithm` is specified
kryzar Aug 2, 2024
68112b8
Fix previous fix
kryzar Aug 2, 2024
bd8ae68
DAMMIT (forgot to commit previously)
kryzar Aug 2, 2024
00d1b16
[Test] Choose Frobenius trace algorithm
kryzar Aug 2, 2024
143a5fd
Fix a few lint typos
kryzar Aug 2, 2024
8b19e29
Manage merge conflict
kryzar Aug 5, 2024
01e5889
Fix algorithm=None for frobenius_trace
kryzar Aug 9, 2024
b632a75
Update src/sage/rings/function_field/drinfeld_modules/finite_drinfeld…
kryzar Aug 9, 2024
a801502
Change phi_T to f in the CSA loop
kryzar Aug 9, 2024
a77165f
Remove useless comment
kryzar Aug 9, 2024
c06482d
Remove var keyword in _frobenius_charpoly_* methods
kryzar Aug 9, 2024
b50fd21
Remove @cached_function for frobenius_trace and frobenius_norm
kryzar Aug 9, 2024
a1c9106
Remove @cached_function for charpoly and matrix computations
kryzar Aug 9, 2024
fef5d05
Call getattr
kryzar Aug 9, 2024
856c965
Fix phi_T -> f
kryzar Aug 9, 2024
f676556
Remove useless import
kryzar Aug 10, 2024
9d162d1
Fix a f -> phi_T
kryzar Aug 10, 2024
4ee14ea
Remove useless var keywords
kryzar Aug 10, 2024
66926d1
Revert "Remove useless var keywords"
kryzar Aug 10, 2024
a6d38aa
Merge branch 'charpoly-csa' of github:kryzar/sage into charpoly-csa
xcaruso Aug 11, 2024
9a627ec
fix trace computation with CSA algorithm
xcaruso Aug 11, 2024
f121bad
Add Gek2008 reference
kryzar Aug 26, 2024
0ddc130
Merge branch 'develop' into charpoly-csa
kryzar Sep 6, 2024
3dd3c04
Merge branch 'develop' into charpoly-csa
kryzar Sep 18, 2024
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7 changes: 7 additions & 0 deletions src/doc/en/reference/references/index.rst
Original file line number Diff line number Diff line change
Expand Up @@ -1716,6 +1716,9 @@ REFERENCES:
Yokonuma-Hecke algebras and the HOMFLYPT
polynomial*. (2015) :arxiv:`1204.1871v4`.

.. [CL2023] Xavier Caruso and Antoine Leudière.
*Algorithms for computing norms and characteristic polynomials on general Drinfeld modules*, (2023) :arxiv:`2307.02879`.

.. [Cle1872] Alfred Clebsch, *Theorie der binären algebraischen Formen*,
Teubner, 1872.

Expand Down Expand Up @@ -2814,6 +2817,10 @@ REFERENCES:
.. [Gek1991] \E.-U. Gekeler. On finite Drinfeld modules. Journal of
algebra, 1(141):187–203, 1991.

.. [Gek2008] \E.-U. Gekeler. Frobenius Distributions of Drinfeld Modules over
Finite Fields. Transactions of the American Mathematical Society,
Volume 360 (2008), no. 4.

.. [Gek2017] \E.-U. Gekeler. On Drinfeld modular forms of higher rank.
Journal de théorie des nombres de Bordeaux,
Volume 29 (2017) no. 3, pp. 875-902. :doi:`10.5802/jtnb.1005`
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