polynomialsWithFactor -- number of monic square-free polynomials of degree n with factor of degree degree k over F_q

Synopsis

• Usage:

  polynomialsWithFactor(n,k,Q)

• Inputs:

  • n, an integer, degree of the random polynomial
  • k, an integer, degree of the factor
  • Q, a polynomial ring, Q=QQ[q]
• Outputs:

  • a ring element, number of monic square-free polynomials of degree n with factor of degree degree k over F_q as function of q

Description

i1 : Q = QQ[q]

o1 = Q

o1 : PolynomialRing

i2 : polynomialsWithFactor(6,3,Q)

     29 6   11 5    5 4    5 3   13 2
o2 = --q  - --q  + --q  - --q  + --q
     80     16     16     16     40

o2 : Q