Nextpoly(f, x) mod p returns the next polynomial from f in x in lexicographical order over the integers modulo p. Similarly, Prevpoly(f, x) mod p returns the previous polynomial from f in x in lexicographical order over the integers modulo p.

Nextprime(f, x) mod p returns the next irreducible polynomial from f in x in lexicographical order over the integers modulo p. Similarly, Prevprime(f, x) mod p returns the previous irreducible polynomial from f in x in lexicographical order over the integers modulo p.

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, Nextprime(f, x, alpha) mod p computes the next irreducible polynomial from f in lexicographical order over .