get rid of CartesianProduct

[videlec]

The features of sage.combinat.cartesian_product.CartesianProduct are now completely integrated into the category framework (see #18290). We remove all occurrences of CartesianProduct to either cartesian_product or itertools.product. We deprecate the CartesianProduct from sage.combinat.cartesian_product.

In order to support all features of the old class we also:

• move the __iter__ from EnumeratedSets.CartesianProducts.ParentMethods to Sets.CartesianProducts.ParentMethods
• allows cartesian_product to be called with list, tuple, set, frozenset
• make cartesian_product([]) works
• introduce a function some_tuples in sage.misc.misc that is intensively used in the testing framework (and incidentally speed up some doc test)
• refine the category of Set([1,2,3]) to be finite
• implement a (very naive) random_element for Set([1,2,3])
• implement a (naive) hash for EnumeratedSetFromIterator

see also : #15425, #19195
one that can be closed as duplicate: #14224, #19192

Depends on #17411

CC: @nthiery @nathanncohen

Component: combinatorics

Author: Vincent Delecroix

Branch/Commit: 6e27dde

Reviewer: Nicolas M. Thiéry

Issue created by migration from https://trac.sagemath.org/ticket/18411

[videlec]

Description changed:

--- 
+++ 
@@ -1,3 +1,3 @@
-The features of `sage.combinat.cartesian_product.CartesianProduct` are now completely integrated into the category framework. We just make `CartesianProduct` an alias for `sage.sets.cartesian_product.CartesianProduct` (with some tweak to support the behavior).
+The features of `sage.combinat.cartesian_product.CartesianProduct` are now completely integrated into the category framework (see #18290). We just make `CartesianProduct` an alias for `sage.sets.cartesian_product.CartesianProduct` (with some tweak to support the previous behavior which considered the cartesian product as a set of lists).
 
 `sage.combinat.cartesian_product.CartesianProduct` is deprecated.

[videlec]

Dependencies: #18290, #12955

[videlec]

Branch: public/18411

[sagetrac-git]

Commit: e703eb4

[sagetrac-git]

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

e703eb4

Trac 18411: remove occurrences of CartesianProduct

[sagetrac-git]

Changed commit from e703eb4 to 10df218

[sagetrac-git]

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

635279f	Trac 18411: a bounded_number_of_tuples function
1b60903	Trac 18411: remove occurrences of CartesianProduct
bec57ae	Trac 18411: cartesian_product works with tuple/list/set/frozenset
7dbb663	Trac 18411: move iteration of cartesian products to Sets
4fbb4ae	Trac 18411: refine category of Set(...)
10df218	Trac 18411: fix combinat tutorial

[videlec]

Author: Vincent Delecroix

[videlec]

Description changed:

--- 
+++ 
@@ -1,3 +1,5 @@
-The features of `sage.combinat.cartesian_product.CartesianProduct` are now completely integrated into the category framework (see #18290). We just make `CartesianProduct` an alias for `sage.sets.cartesian_product.CartesianProduct` (with some tweak to support the previous behavior which considered the cartesian product as a set of lists).
+The features of `sage.combinat.cartesian_product.CartesianProduct` are now completely integrated into the category framework (see #18290). We remove most occurrences of `CartesianProduct` to either `cartesian_product` or `itertools.product`.
 
-`sage.combinat.cartesian_product.CartesianProduct` is deprecated.
+follow up: #19192
+
+

[videlec]

Changed dependencies from #18290, #12955 to none