Implement cluster algebras using the Parent-Element framework

[Etn40ff]

This module uses structural results from "Cluster algebras IV" to implement cluster algebras as a subobject of LaurentPolynomialRing_generic.

It provides a new class ClusterAlgebra, and two new auxiliary classes ClusterAlgebraSeed and ClusterAlgebraElement.

Depends on #22160

CC: @sagetrac-gmoose05 @sagetrac-drupel @stumpc5 mdpressland@bath.edu @tscrim @egunawan

Component: algebra

Keywords: cluster algebras, SageDays64.5, days79

Author: Dylan Rupel, Salvatore Stella

Branch/Commit: 389cdc9

Reviewer: Frédéric Chapoton

Issue created by migration from https://trac.sagemath.org/ticket/21254

[Etn40ff]

Commit: b76ba97

[Etn40ff]

Branch: public/ticket/21254

[Etn40ff]

Dependencies: #19538

[sagetrac-git]

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

e281061

Added warning to functions depending on _sd_iter

[sagetrac-git]

Changed commit from b76ba97 to e281061

[sagetrac-git]

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

2c64756

Spaaaaaace (again)

[sagetrac-git]

Changed commit from e281061 to 2c64756

[sagetrac-git]

Changed commit from 2c64756 to e272302

[sagetrac-git]

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

e272302

Catch only StopIteration

[sagetrac-git]

Changed commit from e272302 to 673926d

[sagetrac-git]

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

673926d

Added hash function to ClusterAlgebraSeed

[sagetrac-git]

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

31a51a1

Figured out how to continue seeds after a KeyboardInterrupt

[sagetrac-git]

Changed commit from 673926d to 31a51a1

[sagetrac-git]

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

13625a1

Rafactored all fuctions based on seeds()

[sagetrac-git]

Changed commit from 31a51a1 to 13625a1

[fchapoton]

comment:8

I have just launched my own patchbot on the ticket.

There are some missing empty lines, for example here

+    EXAMPLES::
+        sage: A = ClusterAlgebra(['B',2],principal_coefficients=True)

[sagetrac-git]

Changed commit from 13625a1 to 2e4ab20

[sagetrac-git]

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

bb66742	Better interrupt handling
2e4ab20	Fixed missing :

[sagetrac-git]

Changed commit from 2e4ab20 to 3dd81b4

[sagetrac-git]

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

3dd81b4

Fixed missing empty lines

[Etn40ff]

comment:11

There are some missing empty lines, for example here

I just fixed that; thank you for catching it. Is there any automatic way to check that the code adhere to all the conventions?
I only know of autopep8 but this does not test docstrings.
(By the way we have plenty of long lines so we do not really adhere to pep8
either.)

On a different topic: there has been a discussion on sage-devel on the best way
to implement the exploring iterator. The discussion migrated to #21312 where the
possibility to use RecursivelyEnumeratedSet has been explored. It turns out that
this can be done gaining a significant slowdown. I ended up writing the
current solution. A migration to RecursivelyEnumeratedSet might be considered
for a follow-up ticket. I am just writing this here for the record.

[sagetrac-git]

Changed commit from 3dd81b4 to 8f0480a

[sagetrac-git]

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

8f0480a

Missing digit in doctest

[sagetrac-git]

Changed commit from 8f0480a to 7400632

[sagetrac-git]

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

f441710

Removed blank line

[sagetrac-git]

Changed commit from a80a184 to f441710

[fchapoton]

comment:67

+Missing doctests in algebras/cluster_algebra.py: 74 / 75 = 98%

[sagetrac-git]

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

dbf42e6

Added missing doctest

[sagetrac-git]

Changed commit from f441710 to dbf42e6

[Etn40ff]

comment:69

Thank you for catching this Frédéric. I hope I added the test in the right place.

[fchapoton]

comment:70

Branch does no longer apply..

This has waited long enough..

If you rebase, I will run my bot, and give a positive review if some bot gives a green light and no other issue arise.

[sagetrac-git]

Changed commit from dbf42e6 to 06000a4

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. Last 10 new commits:

6c2d7a2	First attempt at using UniqueRepresentation, mutate_initial should now be broken
130de19	Second pass at using UniqueRepresentatio; still need to remove useless methods like __eq__
66e75cf	Removed useless methods and got the code to fail with UniqeRepresentation
bcac0e9	Implemented new mutate_initial; this is now consistent with the use of UniqueRepresentation
fdc90e8	Removed old mutate_initial; removed mutate_wrapper; refactored mutate
41560ee	Polish + removed MethodType
5a827a1	21254: add titles and authors to references LLZ2014 and NZ2012, remove duplicate FZ2007
3981299	21254: add cluster algebras to /algebras/catalog.py
94a5d1a	Revert 5341cbd219c650801030dd9df3dd49b34e3c6952
06000a4	Added missing doctest

[Etn40ff]

comment:72

Thank you Frédéric. I just rebased to the current develop and now it builds cleanly on my machine. Tests seems ok so far. I am starting my patchbot to run overnight.

[fchapoton]

comment:73

ok, let it be

[fchapoton]

Reviewer: Frédéric Chapoton

[vbraun]

comment:75

On 32-bit:

sage -t --long src/sage/algebras/cluster_algebra.py
1069**********************************************************************
1070File "src/sage/algebras/cluster_algebra.py", line 712, in sage.algebras.cluster_algebra.ClusterAlgebraSeed.__hash__
1071Failed example:
1072    hash(S)
1073Expected:
1074    6108559638409052534
1075Got:
1076    1755906422
1077**********************************************************************
10781 item had failures:
1079   1 of   4 in sage.algebras.cluster_algebra.ClusterAlgebraSeed.__hash__
1080    [402 tests, 1 failure, 11.03 s]
108

[Etn40ff]

comment:76

On 64-bit it works. Which is the correct way to doctest hash functions
independently of the architecture?

[tscrim]

comment:77

Copy and paste Volker's output with # 32-bit and # 64-bit. Although I prefer the softest that hash(x) == hash(x).

[sagetrac-git]

Changed commit from 06000a4 to 389cdc9

[sagetrac-git]

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

389cdc9

Fixed hash doctest

[Etn40ff]

comment:79

Done, thanks. I am setting this back to positive review because I do not have a 32-bit machine to test.

[vbraun]

Changed branch from public/ticket/21254 to 389cdc9