Randpoly(n, x) mod p returns a polynomial of degree n in the variable x whose coefficients are selected at random from the integers mod p.

Randprime(n, x) mod p returns a random monic irreducible polynomial of degree  in the variable x over the integers mod p where p must be a prime integer.

The optional third argument alpha specifies a representation for the finite field .  The field extension alpha is specified by a RootOf a monic univariate polynomial of degree k which must be irreducible.

Thus Randprime(n, x, alpha) mod p creates a random monic irreducible polynomial of degree  in the variable x over .