numtheory(deprecated)
mipolys
number of monic irreducible univariate polynomials
Calling Sequence
Parameters
Description
Examples
mipolys(n, p, m)
n
-
non-negative integer
p
prime integer (characteristic of a finite field)
m
(optional) positive integer
Important: The numtheory package has been deprecated. Use the superseding command NumberTheory[NumberOfIrreduciblePolynomials] instead.
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
1nsummobiusndpmd,ford∈divisorsn
withnumtheory:
mipolys3,5
40
mipolys1,2,4
16
seqmipolysn,p,n=1..4
p,12p2−12p,13p3−13p,14p4−14p2
mipolys3,p,4
13p12−13p4
mipolys3,p,k
pk33−pk3
See Also
GF
NumberTheory[NumberOfIrreduciblePolynomials]
numtheory(deprecated)[divisors]
numtheory(deprecated)[mobius]
seq
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