enhanced sets and cartesian products

[videlec]

We implement several missing features of sets, enumerated sets and their cartesian products.

We add methods is_empty and is_finite to all sets.

We implement most of the methods for cartesian products of sets and enumerated sets (cardinality, rank/unrank, iteration).

For example, all commands below were hanging

sage: C = cartesian_product([Permutations(7), Permutations(9)])
sage: C.cardinality()
1828915200
sage: C.unrank(143872745)
([1, 5, 3, 6, 2, 4, 7], [5, 3, 2, 4, 7, 8, 9, 6, 1])
sage: C.rank(_)
143872745
sage: C.random_element()   # random
([4, 2, 6, 7, 1, 3, 5], [4, 7, 2, 8, 6, 3, 9, 5, 1])

CC: @nathanncohen @nthiery

Component: categories

Keywords: cartesian_product

Author: Vincent Delecroix

Branch: 707bf1e

Reviewer: Nicolas M. Thiéry

Issue created by migration from https://trac.sagemath.org/ticket/18290

[videlec]

Description changed:

--- 
+++ 
@@ -1,4 +1,2 @@
-We implement three missing methods in `sage.sets.cartesian_product.CartesianProduct`:
-- `__hash__`
-- `is_finite`
-- `cardinality`
+We implement two missing methods in `sage.sets.cartesian_product.CartesianProduct`: `is_finite`
+and `cardinality`.

[videlec]

Branch: u/vdelecroix/18290

[videlec]

Commit: 7311911

[videlec]

New commits:

7311911

Trac 18290: cardinality/is_finite for cartesian products

[videlec]

Changed keywords from none to cartesian_product

[videlec]

Description changed:

--- 
+++ 
@@ -1,2 +1,14 @@
 We implement two missing methods in `sage.sets.cartesian_product.CartesianProduct`: `is_finite`
 and `cardinality`.
+
+For example, the following was hanging
+
+```
+sage: F = Permutations(10)
+sage: cartesian_product([ZZ, Set(), ZZ]).is_finite()
+True
+sage: cartesian_product([F, F]).is_finite()
+True
+sage: cartesian_product([F, F]).cardinality()
+13168189440000
+```

[nathanncohen]

comment:3

HMmmmmmmm O_o

I don't know enough about this code to be helpful, but computing the cardinality of those sets seems to be too much. Isn't there a 'is_empty' functio in those classes that you could use instead? And you probably should call is_empty before the is_finite. Deciding emptyness is probably easier than deciding if it is finite?... Or perhaps not, in some weird cases? ^^;;

[nathanncohen]

Description changed:

--- 
+++ 
@@ -1,14 +1,2 @@
 We implement two missing methods in `sage.sets.cartesian_product.CartesianProduct`: `is_finite`
 and `cardinality`.
-
-For example, the following was hanging
-
-```
-sage: F = Permutations(10)
-sage: cartesian_product([ZZ, Set(), ZZ]).is_finite()
-True
-sage: cartesian_product([F, F]).is_finite()
-True
-sage: cartesian_product([F, F]).cardinality()
-13168189440000
-```

[nathanncohen]

Description changed:

--- 
+++ 
@@ -1,2 +1,15 @@
 We implement two missing methods in `sage.sets.cartesian_product.CartesianProduct`: `is_finite`
 and `cardinality`.
+
+
+For example, the following was hanging
+
+```
+sage: F = Permutations(10)
+sage: cartesian_product([ZZ, Set(), ZZ]).is_finite()
+True
+sage: cartesian_product([F, F]).is_finite()
+True
+sage: cartesian_product([F, F]).cardinality()
+13168189440000
+```