Let n be a positive integer and R be a primitive nth root of unity.
h = h_{k} x^{k}  (17) 
h_{k} = f_{i} g_{j}  (18) 
p = p_{k} x^{k}  (19) 
p_{k} = f_{i} g_{j}  (20) 

(21) 
f * g fg mod x^{n}1  (22) 
f = x^{3} + 1 and g = 2x^{3} + 3x^{2} + x + 1.  (23) 

(24) 
f * g = 3x^{3} + 4x + 2  (25) 
DFT_{}(f*g) = DFT_{}(f )DFT_{}(g)  (26) 
f * g = f g + q (x^{n}  1)  (27) 

(28) 
E_{} :  (29) 
R[x]/x^{n}  1 R^{n}  (30) 
If R is a field, then this a special case of the Chinese Remaindering Theorem where m_{i} = x  for i = 0^{ ... }n  1.