code: def covering_product(a, b):
      """
      Returns the covering product of given sequences.
  
      The indices of each argument, considered as bit strings, correspond to
      subsets of a finite set.
  
      The covering product of given sequences is a sequence which contains
      the sum of products of the elements of the given sequences grouped by
      the *bitwise-OR* 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 covering product is to be obtained.
  
      Examples
      ========
  
      >>> from sympy import symbols, S, I, covering_product
      >>> u, v, x, y, z = symbols('u v x y z')
  
      >>> covering_product([u, v], [x, y])
      [u*x, u*y + v*x + v*y]
      >>> covering_product([u, v, x], [y, z])
      [u*y, u*z + v*y + v*z, x*y, x*z]
  
      >>> covering_product([1, S(2)/3], [3, 4 + 5*I])
      [3, 26/3 + 25*I/3]
      >>> covering_product([1, 3, S(5)/7], [7, 8])
      [7, 53, 5, 40/7]
  
      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), mobius_transform(b)
      a = [expand_mul(x * y) for x, y in zip(a, b)]
      a = inverse_mobius_transform(a)
  
      return a
  
file_path: sympy/sympy/discrete/convolutions.py
imports: from sympy.core import S, sympify, Rational
  from sympy.core.function import expand_mul
  from sympy.discrete.transforms import fft, ifft, ntt, intt, fwht, ifwht, mobius_transform, inverse_mobius_transform
  from sympy.external.gmpy import MPZ, lcm
  from sympy.utilities.iterables import iterable
  from sympy.utilities.misc import as_int
label_desc: Use image node_id 6 for calling a global function with example usage: covering_product(a, b) and returns: a, list