toom-cook algorithm matrix G

Question

For this toom-cook algorithm at https://arxiv.org/pdf/1803.10986v1.pdf#page=6 , how do I get the value 4/2 in the matrix G ?

Answer 1

We have

$$G = \begin{bmatrix} x_0^0 N^0 & x_0^1 N^0 & x_0^2 N^0 \\ x_1^0 N^1 & x_1^1 N^1 & x_1^2 N^1 \\ x_2^0 N^2 & x_2^1 N^2 & x_2^2 N^2 \\ x_3^0 N^3 & x_3^1 N^3 & x_3^2 N^3 \end{bmatrix} = \begin{bmatrix} (1)( -\dfrac{1}{6}) & (1)(-\dfrac{1}{6}) & (1)(-\dfrac{1}{6})\\ (1)(\dfrac{1}{2}) & (2)(\dfrac{1}{2}))& (4)(\dfrac{1}{2})) \\ (1)(-\dfrac{1}{2}) & (3)(-\dfrac{1}{2}) & (9)(-\dfrac{1}{2}) \\ (1)(\dfrac{1}{6}) & (4)(\dfrac{1}{6}) & (16)(\dfrac{1}{6}) \end{bmatrix}$$