Fix is_preperiodic function domain check

[pfili]

Currently, if we define a DynamicalSystem_projective without specifying the underlying domain (which is probably the most likely way the user will do this), the init function recreates the underlying projective space. As a result, any function that checks if the domain of a point "is" the domain of the map will fail, as is_preperiodic currently does:

sage: R.<X> = PolynomialRing(QQ)
sage: K.<a> = NumberField(X^2 + X - 1)
sage: P.<x,y> = ProjectiveSpace(K,1)
sage: f = DynamicalSystem_projective([x^2-2*y^2, y^2])
sage: Q = P.point([a,1])
sage: f.nth_iterate(Q,2) == Q
True
sage: Q.is_preperiodic(f)
Traceback (most recent call last):
...
TypeError: point must be in domain of map
sage: f.domain() is P
False
sage: f.domain() == P # It's basically the same but the space is not uniquely represented in memory
True

Instead, is_preperiodic should be using == to check that the domains are equivalent, rather than exactly the same under "is", and then things will work as expected. This fix changes that.

Depends on #23497

CC: @bhutz

Component: dynamics

Author: Paul Fili

Branch/Commit: 2a68ffb

Reviewer: Ben Hutz

Issue created by migration from https://trac.sagemath.org/ticket/23814

[pfili]

Dependencies: #23497

[pfili]

Branch: u/paulfili/preperiodic-fix

[pfili]

Last 10 new commits:

79378c3	Merge branch 8.1.beta3 into t/23497/arith_dyn
80ff2e6	23497: some fixes from review
fdf7265	23497: doc formatting INPUT/OUTPUT
cc50108	23497: use __classcall_private__
4bbdcde	Fixing things with __classcall_private__.
7408d79	Cleaning up the doc and improving the code.
d00cea2	23497: a couple minor fixes
300a3b1	Merge branch 8.1.beta4 into t/23497/arith_dyn-23497
bdbf658	Fixing typo in doctest.
9c3e7cf	Fix domain check for is_preperiodic from "is" to "=="

[pfili]

Commit: 9c3e7cf

[bhutz]

Changed branch from u/paulfili/preperiodic-fix to u/bhutz/preperiodic-fix

[bhutz]

Reviewer: Ben Hutz

[bhutz]

comment:5

Looks fine. Just fixed a minor typo.

---

New commits:

1f1a815

23814: minor typo fix

[bhutz]

Changed commit from 9c3e7cf to 1f1a815

[bhutz]

comment:6

merge conflict

[sagetrac-git]

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

2eecc68	Merge branch 8.1.beta5 into t/23497/arith_dyn-23497
2a68ffb	Merge branch 't/23497/arith_dyn-23497' into t/23814/preperiodic-fix

[sagetrac-git]

Changed commit from 1f1a815 to 2a68ffb

[bhutz]

comment:8

fixed

[vbraun]

Changed branch from u/bhutz/preperiodic-fix to 2a68ffb