number of monic irreducible univariate polynomials - Maple Help

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numtheory[mipolys] - number of monic irreducible univariate polynomials

Calling Sequence

mipolys(n, p, m)

Parameters

n

-

non-negative integer

p

-

prime integer (characteristic of a finite field)

m

-

(optional) positive integer

Description

• 

The mipolys function computes the number of monic irreducible univariate polynomials of degree n over the finite field Zmodp, if the parameter m is not specified.

• 

If m is specified, mipolys(n, p, m) computes the number of monic irreducible univariate polynomials of degree n over the Galois field GFpm.

• 

If m is not explicitly specified, m defaults to 1. In this context, the general mathematical definition of mipolys is

1nmobiusndpmd,forddivisorsn

Examples

withnumtheory:

mipolys3,5

40

(1)

mipolys1,2,4

16

(2)

seqmipolysn,p,n=1..4

p,12p212p,13p313p,14p414p2

(3)

mipolys3,p,4

13p1213p4

(4)

mipolys3,p,k

13pk313pk

(5)

See Also

GF, numtheory, numtheory[divisors], numtheory[mobius], seq


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