Esempio n. 1
0
def intersecting_product(a, b):
    """
    Returns the intersecting product of given sequences.

    The indices of each argument, considered as bit strings, correspond to
    subsets of a finite set.

    The intersecting product of given sequences is the sequence which
    contains the sum of products of the elements of the given sequences
    grouped by the *bitwise-AND* of the corresponding indices.

    The sequence is automatically padded to the right with zeros, as the
    definition of subset based on bitmasks (indices) requires the size of
    sequence to be a power of 2.

    Parameters
    ==========

    a, b : iterables
        The sequences for which intersecting product is to be obtained.

    Examples
    ========

    >>> from sympy import symbols, S, I, intersecting_product
    >>> u, v, x, y, z = symbols('u v x y z')

    >>> intersecting_product([u, v], [x, y])
    [u*x + u*y + v*x, v*y]
    >>> intersecting_product([u, v, x], [y, z])
    [u*y + u*z + v*y + x*y + x*z, v*z, 0, 0]

    >>> intersecting_product([1, S(2)/3], [3, 4 + 5*I])
    [9 + 5*I, 8/3 + 10*I/3]
    >>> intersecting_product([1, 3, S(5)/7], [7, 8])
    [327/7, 24, 0, 0]

    References
    ==========

    .. [1] https://people.csail.mit.edu/rrw/presentations/subset-conv.pdf

    """

    if not a or not b:
        return []

    a, b = a[:], b[:]
    n = max(len(a), len(b))

    if n & (n - 1):  # not a power of 2
        n = 2**n.bit_length()

    # padding with zeros
    a += [S.Zero] * (n - len(a))
    b += [S.Zero] * (n - len(b))

    a, b = mobius_transform(a, subset=False), mobius_transform(b, subset=False)
    a = [expand_mul(x * y) for x, y in zip(a, b)]
    a = inverse_mobius_transform(a, subset=False)

    return a
Esempio n. 2
0
def intersecting_product(a, b):
    """
    Returns the intersecting product of given sequences.

    The indices of each argument, considered as bit strings, correspond to
    subsets of a finite set.

    The intersecting product of given sequences is the sequence which
    contains the sum of products of the elements of the given sequences
    grouped by the *bitwise-AND* of the corresponding indices.

    The sequence is automatically padded to the right with zeros, as the
    definition of subset based on bitmasks (indices) requires the size of
    sequence to be a power of 2.

    Parameters
    ==========

    a, b : iterables
        The sequences for which intersecting product is to be obtained.

    Examples
    ========

    >>> from sympy import symbols, S, I, intersecting_product
    >>> u, v, x, y, z = symbols('u v x y z')

    >>> intersecting_product([u, v], [x, y])
    [u*x + u*y + v*x, v*y]
    >>> intersecting_product([u, v, x], [y, z])
    [u*y + u*z + v*y + x*y + x*z, v*z, 0, 0]

    >>> intersecting_product([1, S(2)/3], [3, 4 + 5*I])
    [9 + 5*I, 8/3 + 10*I/3]
    >>> intersecting_product([1, 3, S(5)/7], [7, 8])
    [327/7, 24, 0, 0]

    References
    ==========

    .. [1] https://people.csail.mit.edu/rrw/presentations/subset-conv.pdf

    """

    if not a or not b:
        return []

    a, b = a[:], b[:]
    n = max(len(a), len(b))

    if n&(n - 1): # not a power of 2
        n = 2**n.bit_length()

    # padding with zeros
    a += [S.Zero]*(n - len(a))
    b += [S.Zero]*(n - len(b))

    a, b = mobius_transform(a, subset=False), mobius_transform(b, subset=False)
    a = [expand_mul(x*y) for x, y in zip(a, b)]
    a = inverse_mobius_transform(a, subset=False)

    return a