Input:f,gEF[1,22,...,n of degree d Output:f g? equivalently: Input:fEF[1,22,...,n]of degree d Output:f≡0？ f(1,x2,.,xn)= ai,i2,,in riz...n i1,i2,,in之0 i1+i2++in≤dInput: of degree d Output: f ￾ g? f,g 2 F[x1, x2,...,xn] f(x1, x2,...,xn) = X i1,i2,...,in￾0 i1+i2+···+ind ai1,i2,...,in xi1 1 xi2 2 ··· xin n Input: of degree d Output: f ￾ 0? f 2 F[x1, x2,...,xn] equivalently: