def coordinatewise_product(L):
    """
    Returns the coordinatewise product of a list of vectors.

    INPUT:

    - ``L`` is a list of `n`-vectors or lists all of length `n` with a common
      parent. This returns the vector whose `i`-th coordinate is the product of
      the `i`-th coordinates of the vectors.

    EXAMPLES::

        sage: from sage.combinat.designs.incidence_structures import coordinatewise_product
        sage: L = [[1,2,3],[-1,-1,-1],[5,7,11]]
        sage: coordinatewise_product(L)
        [-5, -14, -33]
    """
    n = len(L[0])
    ans = [1]*n
    for x in L:
        ans = [ans[i]*x[i] for i in range(n)]
    return ans