Write a computer program that computes Zechs log table for a primitive element in the finite field Fp(), where p is a prime. The

Write a computer program that computes Zech’s log table for a primitive element α in the finite field Fp(α), where p is a prime. The program should as an input take an irreducible polynomial f(x) ∈ Fp[x] such that one of its root α is a primitive root of Fp(α) (a check for that f(x) really has this property is not necessary to include in the program, but if you really feel for it then why not. . . ?). Demonstrate your program to compute Zech’s log table for the fields below (where the given polynomials are chosen to fulfill the requirements mentioned above). (a) F11(α) = F11[x]/(x^2 + 5x + 2) (b) F3(α) = F3[x]/(x^4 + 2x + 2) (c) F2(α) = F2[x]/(x^7 + x^4 + 1