Returns the combinatorial class of the Cartesian product of *iters.
EXAMPLES:
sage: cp = CartesianProduct([1,2], [3,4]); cp
Cartesian product of [1, 2], [3, 4]
sage: cp.list()
[[1, 3], [1, 4], [2, 3], [2, 4]]
Note that if you have a generator-type object that is returned by a function, then you should use IterableFunctionCall class defined in sage.combinat.misc.
sage: def a(n): yield 1*n; yield 2*n
sage: def b(): yield 'a'; yield 'b'
sage: CartesianProduct(a(3), b()).list()
[[3, 'a'], [3, 'b']]
sage: from sage.combinat.misc import IterableFunctionCall
sage: CartesianProduct(IterableFunctionCall(a, 3), IterableFunctionCall(b)).list()
[[3, 'a'], [3, 'b'], [6, 'a'], [6, 'b']]
See the documentation for IterableFunctionCall for more information.
EXAMPLES:
sage: cp = CartesianProduct([1,2],[3,4])
sage: [1,3] in cp
True
sage: [1,2] in cp
False
sage: [1, 3, 1] in cp
False
TESTS:
sage: import sage.combinat.cartesian_product as cartesian_product
sage: cp = cartesian_product.CartesianProduct_iters([1,2],[3,4]); cp
Cartesian product of [1, 2], [3, 4]
sage: loads(dumps(cp)) == cp
True
An iterator for the elements in the cartesian product of the iterables *iters.
From Recipe 19.9 in the Python Cookbook by Alex Martelli and David Ascher.
EXAMPLES:
sage: [e for e in CartesianProduct(range(3), range(3))]
[[0, 0], [0, 1], [0, 2], [1, 0], [1, 1], [1, 2], [2, 0], [2, 1], [2, 2]]
sage: [e for e in CartesianProduct('dog', 'cat')]
[['d', 'c'],
['d', 'a'],
['d', 't'],
['o', 'c'],
['o', 'a'],
['o', 't'],
['g', 'c'],
['g', 'a'],
['g', 't']]
EXAMPLES:
sage: CartesianProduct(range(2), range(3))
Cartesian product of [0, 1], [0, 1, 2]
Returns the number of elements in the cartesian product of everything in *iters.
EXAMPLES:
sage: CartesianProduct(range(2), range(3)).cardinality()
6
sage: CartesianProduct(range(2), xrange(3)).cardinality()
6
sage: CartesianProduct(range(2), xrange(3), xrange(4)).cardinality()
24
Returns
EXAMPLES:
sage: CartesianProduct(range(3), range(3)).list()
[[0, 0], [0, 1], [0, 2], [1, 0], [1, 1], [1, 2], [2, 0], [2, 1], [2, 2]]
sage: CartesianProduct('dog', 'cat').list()
[['d', 'c'],
['d', 'a'],
['d', 't'],
['o', 'c'],
['o', 'a'],
['o', 't'],
['g', 'c'],
['g', 'a'],
['g', 't']]
Returns a random element from the cartesian product of *iters.
EXAMPLES:
sage: CartesianProduct('dog', 'cat').random_element()
['d', 'a']