18.5 Cartesian Products

Module: sage.combinat.cartesian_product

Cartesian Products

Module-level Functions

CartesianProduct( )

Returns the combinatorial class of the cartesian product of *iters.

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(): yield 1; yield 2
sage: def b(): yield 'a'; yield 'b'
sage: CartesianProduct(a(), b()).list()
[[1, 'a'], [1, 'b']]
sage: from sage.combinat.misc import IterableFunctionCall
sage: CartesianProduct(IterableFunctionCall(a), IterableFunctionCall(b)).list()
[[1, 'a'], [1, 'b'], [2, 'a'], [2, 'b']]

Class: CartesianProduct_iters

class CartesianProduct_iters

CartesianProduct_iters( self)

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

Functions: count, $\,$ iterator, $\,$ list, $\,$ random_element

count( self)

Returns the number of elements in the cartesian product of everything in *iters.

sage: CartesianProduct(range(2), range(3)).count()
6
sage: CartesianProduct(range(2), xrange(3)).count()
6
sage: CartesianProduct(range(2), xrange(3), xrange(4)).count()
24

iterator( self)

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.

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']]

list( self)

Returns

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']]

random_element( self)

Returns a random element from the cartesian product of *iters.

sage: CartesianProduct('dog', 'cat').random_element()
['d', 'a']

Special Functions: __contains__, $\,$ __init__, $\,$ __repr__

__contains__( self, x)

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

__repr__( self)

sage: CartesianProduct(range(2), range(3))
Cartesian product of [0, 1], [0, 1, 2]

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