f calculates the number of 0-1 matrices with row sums A and column sums B.

axiom
f(A:List PI, B:List PI): FRAC INT == cap(reduce(*, [elementary i for i in A]),
reduce(*, [complete i for i in B]))

   Function declaration f : (List PositiveInteger,List PositiveInteger)
       -> Fraction Integer has been added to workspace.

For example, there are

axiom
f([2,2,2,2], [2,3,3])

Compiling function f with type (List PositiveInteger,List 
      PositiveInteger) -> Fraction Integer

(1)

0-1 matrices whose rows all sum up to two and whose first column has 2 entries equal to one, the others having 3 entries equal to one.