Renaming rational_preperiodic_points() to all_preperiodic_points()

[EnderWannabe]

To be consistent with the new naming convention in ticket 28109, we rename rational_preperiodic_points() to all_preperiodic_points(). We also add a preperiod_points() method.

Component: dynamics

Keywords: SI2019, sd104

Author: Eric Zhu, Alex Galarraga, Bianca Thompson, Ben Hutz

Branch/Commit: b510b32

Reviewer: Jasmine Camero, Olivia Schwager, Anna Chlopecki, Simon Xu, Grayson Jorgenson, Juliano Levier-Gomes, Ben Hutz, Jamie Juul, Bella Tobin

Issue created by migration from https://trac.sagemath.org/ticket/28213

[EnderWannabe]

Branch: u/gh-EnderWannabe/28213

[EnderWannabe]

New commits:

e221285	started deprecation
0c5f507	finished deprecation

[EnderWannabe]

Commit: 0c5f507

[oliviaschwager]

Reviewer: Jasmine Camero, Olivia Schwager

[bhutz]

comment:5

I don't think this is quite ready yet. Don't we want a 'preperiodic_points()' function as well as an option to specify the ring like you did in #28109?

[sagetrac-git]

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

7a07a21	added ring parameter to all_preperiodic_points
7c2f54c	wrote perperiodic_points method
a54b88b	builds, but does not run

[sagetrac-git]

Changed commit from 0c5f507 to a54b88b

[sagetrac-git]

Changed commit from a54b88b to 2830a1d

[sagetrac-git]

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

2830a1d

working preperiodic_points

[sagetrac-git]

Changed commit from 2830a1d to d451af4

[sagetrac-git]

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

d451af4

added tests and fixed documentation

[annanc2]

comment:11

• This line L = [t for t in L if t != 0] is not needed: it should not affect the subscheme.
• X = PS.subscheme(L + list(dom.defining_polynomials())) - there are no examples where the domain is a proper subscheme of projective space. There should be an example illustrating when the domain is nontrivial.
• Provide more explanation for what m and n are relative to each other.
• The example below is pulled from the periodic_points function; it is a little slow as is. It would be nicer to find a faster version of this, but it does test the case where the domain is a nontrivial subscheme.

sage: R.<x> = QQ[]
sage: K.<u> = NumberField(x^2 - x + 3)
sage: P.<x,y,z> = ProjectiveSpace(K,2)
sage: X = P.subscheme(2*x-y)
sage: f = DynamicalSystem_projective([x^2-y^2, 2*(x^2-y^2), y^2-z^2], domain=X)
sage: f.preperiodic_points(2,2, R=QQbar)

[annanc2]

Changed reviewer from Jasmine Camero, Olivia Schwager to Jasmine Camero, Olivia Schwager, Anna Chlopecki, Simon Xu, Grayson Jorgenson, Juliano Levier-Gomes

[sagetrac-git]

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

0d06e77

added another example and cleaned up documentation

[sagetrac-git]

Changed commit from d451af4 to 0d06e77

[bhutz]

comment:15

Just one quick comment from a look through the branch.

In one function you use the keyword R, in the other the keyword ring. Those should be the same. If I recall correctly, you were using R for the similar periodic point functions, so I'd stick with that one.

[sagetrac-git]

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

67ae944

fixed keyword mismatch

[sagetrac-git]

Changed commit from 0d06e77 to 67ae944

[bhutz]

Changed branch from u/gh-EnderWannabe/28213 to u/bhutz/28213

[sagetrac-git]

Changed commit from 67ae944 to c427939

[sagetrac-git]

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

c427939

28213: minor changes from review

[bhutz]

Changed reviewer from Jasmine Camero, Olivia Schwager, Anna Chlopecki, Simon Xu, Grayson Jorgenson, Juliano Levier-Gomes to Jasmine Camero, Olivia Schwager, Anna Chlopecki, Simon Xu, Grayson Jorgenson, Juliano Levier-Gomes, Ben Hutz, Jamie Juul, Bella Tobin

[bhutz]

Changed keywords from SI2019 to SI2019, sd104

[bhutz]

comment:19

made some minor updates from the review, mostly adding some additional doc tests.

[bhutz]

comment:20

I have an example that takes much longer than it should. Looks like it is because in all_preperiodic_points. there is no way to pass in the algorithm parameter

R.<t> = PolynomialRing(QQ)
K.<v> = NumberField(t^3 + 16*t^2 - 10496*t + 94208)
PS.<x,y> = ProjectiveSpace(K,1)
f = DynamicalSystem([x^2-29/16*y^2,y^2])

with the 'lifting' algorithm it is fast, with the default it is very slow.

[sagetrac-git]

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

b510b32

28213: add algorithm parameters to preperiodic

[sagetrac-git]

Changed commit from c427939 to b510b32

[bhutz]

comment:22

added parameters to all_preperiodic_points to make the given example possible in a reasonable amount of time. It is too long to add as an example. I've also updated the example that uses the bounds.

[bhutz]

Changed author from Eric Zhu, Alex Galarraga, Bianca Thompson to Eric Zhu, Alex Galarraga, Bianca Thompson, Ben Hutz

[vbraun]

Changed branch from u/bhutz/28213 to b510b32