polynomials_on_simplices.set_theory module

Basic set theoretic calculations.

cartesian_product(s, t)

Compute the Cartesian product of two finite sets, \(S \times T\).

Parameters:

• s (set) – First set in the Cartesian product.
• t (set) – Second set in the Cartesian product.

Returns:

The Cartesian product of the two sets.

Return type:

set

>>> prod = cartesian_product({1, 2}, {1, 2})
>>> prod == {(1, 1), (1, 2), (2, 1), (2, 2)}
True

nfold_cartesian_product(s, n)

Compute the n-fold Cartesian product of a finite set, \(\underbrace{S \times S \times \ldots \times S}_{n \text{ times}}\).

Parameters:

• s – Set we take the n-fold Cartesian product of.
• n (int) – Number of times we take the Cartesian product.

Returns:

n-fold Cartesian product of the given set.

Return type:

set

>>> prod = nfold_cartesian_product({1, 2}, 3)
>>> prod == {(1, 1, 1), (1, 1, 2), (1, 2, 1), (1, 2, 2), (2, 1, 1), (2, 1, 2), (2, 2, 1), (2, 2, 2)}
True