 Given an arithmetic circuit that computes a polynomial in a field, determine whether the polynomial is equal to the zero polynomial (that is, the polynomial with no nonzero terms).In some cases, the specification of the arithmetic circuit is not given to the PIT solver, and the PIT solver can only input values into a "black box" that implements the circuit, and then analyze the output.Note that the solutions below assume that any operation (such as multiplication) in the given field takes constant time; further, all black-box algorithms below assume the size of the field is larger than the degree of the polynomial.