numOfIrreducible -- the number of irreducible polynomials

Synopsis

• Usage:

  numOfIrreducible(n,q)

• Inputs:

  • n, an integer, the degree of the polynomial
  • q, an integer, the number elements of the finite field, or
  • Q, a polynomial ring, the polynomial ring Q=QQ[q]
• Outputs:

  • an integer

Description

i1 : q=symbol q;Q=QQ[q]

o2 = Q

o2 : PolynomialRing

i3 : numOfIrreducible(6,Q)

     1 6   1 3   1 2   1
o3 = -q  - -q  - -q  + -q
     6     6     6     6

o3 : Q

i4 : numOfIrreducible(2,2)

o4 = 1