Number of irreducible polynomials

Computes the number of irreducible polynomials in a field of the desired degree.

Syntax

number_of_irreducible_polynomials(Integer, Field)
number_of_irreducible_polynomials(Integer, Integer)
number_of_irreducible_polynomials(Integer)

Description

Given an integer n and a field K, computes the number of irreducible polynomials over K of degree n.

abstract_algebra.number_of_irreducible_polynomials1.calc.png

Given two integers n and q, computes the number of irreducible polynomials over double-struckZq of degree n.

abstract_algebra.number_of_irreducible_polynomials2.calc.png

Given an integer n, computes the number of irreducible polynomials over double-struckZ2 of degree n.

abstract_algebra.number_of_irreducible_polynomials3.calc.png