前言

学多项式怎么能错过\(FWT\)呢，然而这真是个毒瘤的东西，蒟蒻就只会背公式了\(\%>\_<\%\)

或卷积

\[\begin{aligned}\\ tf(A) = (tf(A_0), tf(A_1) + tf(A_0))\\ utf(A) = (utf(A), utf(A_1) - utf(A_0))\\ \end{aligned}\]

与卷积

\[\begin{aligned}\\ tf(A) = (tf(A_0) + tf(A_1), tf(A_1))\\ utf(A) = (utf(A_0) - utf(A_1), utf(A_1))\\ \end{aligned}\]

异或卷积

\[\begin{aligned}\\ tf(A) = (tf(A_0) + tf(A_1), tf(A_0) - tf(A_1))\\ utf(A) = (\frac{utf(A_0) + utf(A_1)}{2}, \frac{utf(A_0) - utf(A_1)}{2})\\ \end{aligned}\]