A-16.3 Point-wise Multiplication

Once we have applied the forward FFT operation (§A-16.2) to polynomial $A(X)$ and $B(X)$ as ${\overrightarrow{y}}^{⟨a⟩}$ and ${\overrightarrow{y}}^{⟨b⟩}$, computing the point-value representation of $C(X)=A(X)\cdot B(X)$ can be done in $O(\log <!--\; FUNCTION\; APPLICATION\; -->n)$ by Hadamard product ${\overrightarrow{y}}^{⟨c⟩}={\overrightarrow{y}}^{⟨a⟩}\odot {\overrightarrow{y}}^{⟨b⟩}$ (as explained in §A-16.1).