added function all_possible_global_periods

[Saher-Amasha]

for several primes P with good reduction, find the list of possible global periods of a Dynamical System

CC: @bhutz

Component: dynamics

Author: Saher Amasha,Safa Amasha

Branch/Commit: u/gh-Saher-Amasha/added_function_all_possible_global_periods @ c8af081

Issue created by migration from https://trac.sagemath.org/ticket/31872

[Saher-Amasha]

Branch: u/gh-Saher-Amasha/added_function_all_possible_global_periods

[Saher-Amasha]

Commit: c8af081

[Saher-Amasha]

New commits:

3373f9f	added the function all_possible_global_periods
903bc3b	added the function is_prime_of_good_reduction:
3a8008b	removed the mod function because it allready has a ticket
00a32f2	mod function for Dynamical Systems, the function takes as a parameter a prime p and returns the Dynamical System modulo p
ac0b2ec	Merge branch 't/31399/mod_function_for_dynamicalsystem' into t/31464/add_the_function_is_prime_of_good_reduction
08cab12	fixed style issues
f453ffd	fixed style issues
b9e0e8f	Merge branch 't/31399/mod_function_for_dynamicalsystem' into t/31464/add_the_function_is_prime_of_good_reduction
c8af081	Merge branch 't/31464/add_the_function_is_prime_of_good_reduction' into t/31872/added_function_all_possible_global_periods

[mkoeppe]

comment:3

Setting a new milestone for this ticket based on a cursory review.

[EnderWannabe]

comment:4

This seems like it extends existing functionality. There is already a possible periods function for the rationals, see possible_periods. This ticket seems to extend that functionality to function fields, so we should add to the existing function instead of creating a new one.

Further, what algorithm is this based on? You mention a paper by Hutz, which paper is it?

[bhutz]

comment:5

In dimension 1, this is not from my paper. As Alex said, this should be part of the possible_periods function rather than a new function. Similarly, the mod function it depends on should be part of change_ring.

Although since e can be unbounded in this case (see Silverman Arithmetic of Dynam. Sys. exercise 2.22), so some thought needs to be given here on what should be implemented. I'm less familiar with the function field set-up. Can you get around this unbounded e problem by using multiple primes? When the function field has base ring a finite field, don't all the residue fields have the same characteristic so that you can't get around this problem?

My concern is that no matter what the user passes in for e, the function could be missing valid periods.