add level parameter to rational_preimages for projective points

[bhutz]

When working with preimage trees it is usefull to compute more than just the first preimages of a given point. The ticket is to add a parameter to rational_preimages() to specify how far back to find preimages. I.e. find all points Q with f^k(Q) =P for specified k.

Component: algebraic geometry

Author: Ben Hutz

Branch/Commit: 6377a27

Reviewer: Grayson Jorgenson, Rebecca Lauren Miller

Issue created by migration from https://trac.sagemath.org/ticket/20780

[bhutz]

Commit: e7db093

[bhutz]

Author: Ben Hutz

[bhutz]

New commits:

e7db093

20780: add level parameter to rational_preimages

[bhutz]

Branch: u/bhutz/t/20780

[sagetrac-gjorgenson]

Reviewer: Grayson Jorgenson

[sagetrac-gjorgenson]

comment:2

I think this looks good. The code makes sense and appears to work as intended. I just found some really minor things:

-algebraic_scheme.py

• line 2780 - change TypeError message to all lowercase
• Old issues present before this ticket that maybe could be addressed here:
• line 2680 - `False` to ``False``
• line 2711 - some spacing in ProjectiveSpace calls and in lists of defining polynomials

-projective_homset.py

• line 182 - the sorted() function takes any iterable and returns a list, so it shouldn't be necessary to convert rat_points to a list first

-projective_morphism.py

• line 3920 spacing around '>'
• lines 3790 - 3793, formatting issues: ``k``th and `k`th don't seem to render well, and perhaps
  `P` and `Q` should be replaced with ``P``, ``Q``.
• some ProjectiveSpace calls in examples of rational_preimages don't have any spacing in the arguments

[sagetrac-git]

Changed commit from e7db093 to 6377a27

[sagetrac-git]

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

6377a27

20780: minor fixes

[sagetrac-gjorgenson]

comment:4

Okay, this looks fine to me now.

[sagetrac-rlmiller]

comment:5

Looks good to me.

[sagetrac-rlmiller]

Changed reviewer from Grayson Jorgenson to Grayson Jorgenson, Rebecca Lauren Miller

[vbraun]

Changed branch from u/bhutz/t/20780 to 6377a27