# Revision history [back]

This is not immediately available in Sage, but you should be able to do it with a little work.

sage: R.<x1, x2, x3, x4> = GF(2)[]
sage: R
Multivariate Polynomial Ring in x1, x2, x3, x4 over Finite Field of size 2
sage: b = x1**2 * x3 * x4**3
sage: b.degrees()
(2, 0, 1, 3)

sage: a = Sq(3)
sage: x = a.coproduct_iterated(3)
sage: x
1 # 1 # 1 # Sq(3) + 1 # 1 # Sq(1) # Sq(2) + 1 # 1 # Sq(2) # Sq(1) + 1 # 1 # Sq(3) # 1 + 1 # Sq(1) # 1 # Sq(2) + 1 # Sq(1) # Sq(1) # Sq(1) + 1 # Sq(1) # Sq(2) # 1 + 1 # Sq(2) # 1 # Sq(1) + 1 # Sq(2) # Sq(1) # 1 + 1 # Sq(3) # 1 # 1 + Sq(1) # 1 # 1 # Sq(2) + Sq(1) # 1 # Sq(1) # Sq(1) + Sq(1) # 1 # Sq(2) # 1 + Sq(1) # Sq(1) # 1 # Sq(1) + Sq(1) # Sq(1) # Sq(1) # 1 + Sq(1) # Sq(2) # 1 # 1 + Sq(2) # 1 # 1 # Sq(1) + Sq(2) # 1 # Sq(1) # 1 + Sq(2) # Sq(1) # 1 # 1 + Sq(3) # 1 # 1 # 1
sage: x.support()
[((1,), (2,), (), ()),
((), (), (), (3,)),
((3,), (), (), ()),
((), (), (1,), (2,)),
((), (1,), (), (2,)),
((), (1,), (1,), (1,)),
((), (), (2,), (1,)),
((1,), (1,), (), (1,)),
((2,), (), (), (1,)),
((), (1,), (2,), ()),
((1,), (), (2,), ()),
((1,), (), (), (2,)),
((1,), (1,), (1,), ()),
((), (2,), (1,), ()),
((1,), (), (1,), (1,)),
((2,), (), (1,), ()),
((), (3,), (), ()),
((2,), (1,), (), ()),
((), (2,), (), (1,)),
((), (), (3,), ())]


Now you should sum over the entries in x.support() using the exponents listed in b.degrees(), with the appropriate binomial coefficients.