>>> d1 = BaseDyadic(a, b)
>>> 3 * d1
3*(a|b)
>>> type(_)
<class '__main__.DyadicMul'>
>>> d1 + c * BaseDyadic(m, n)
c*(m|n) + (a|b)
>>> type(_)
<class '__main__.DyadicAdd'>
>>> type(d1 + d1)
<class '__main__.DyadicMul'>
>>> d2 = 4 * BaseDyadic(a, b) + 5 * BaseDyadic(m, n)
>>> d2.expand()
4*(a|b) + 5*(m|n)
>>> type(_)
<class '__main__.DyadicAdd'>
>>> d2 * 0
0
>>> type(_)
<class 'sympy.core.numbers.Zero'>
>>> 3 * d2
12*(a|b) + 15*(m|n)
>>> d2.factor()

Traceback (most recent call last):
  File "<pyshell#126>", line 1, in <module>
    d2.factor()
  File "/home/sachin/dyadic.py", line 57, in factor
    raise TypeError("Factoring not supported for dyadics")
TypeError: Factoring not supported for dyadics
>>> d2 & V
4*(b.V)*a + 5*(n.V)*m
>>> d2 * d2

Traceback (most recent call last):
  File "<pyshell#128>", line 1, in <module>
    d2 * d2
  File "/home/sachin/pythlibs/sympy/core/decorators.py", line 115, in binary_op_wrapper
    return func(self, other)
  File "/home/sachin/dyadic.py", line 39, in __mul__
    return DyadicMul(self, other)
  File "/home/sachin/dyadic.py", line 147, in __new__
    raise ValueError("Cannot multiple two dyadics")
ValueError: Cannot multiple two dyadics
>>> d2 & d2
16*(b.a)*(a|b) + 20*(b.m)*(a|n) + 20*(n.a)*(m|b) + 25*(n.m)*(m|n)
>>> d3 = 5 * BaseDyadic(a, b)
>>> d3/5
(a|b)
>>> type(_)
<class '__main__.BaseDyadic'>