# PrimitivePolynomialQ

PrimitivePolynomialQ[poly,p]

tests whether poly is a primitive polynomial modulo a prime p.

# Details

• The polynomial poly must be univariate.

# Examples

open allclose all

## Basic Examples(2)

Test whether a polynomial is primitive modulo 13:

This polynomial can be factored modulo 2, and therefore it is not primitive:

## Scope(3)

Test for primitivity of a univariate polynomial modulo a prime:

Polynomials can be given in non-expanded form:

Coefficients of the polynomial do not have to be integers:

## Properties & Relations(4)

A polynomial must be irreducible in order to be primitive:

Irreducibility is a necessary but not-sufficient condition for a polynomial to be primitive:

A trinomial whose order is a Mersenne prime exponent is primitive modulo 2 if and only if it is irreducible:

Primitivity of a polynomial depends on the choice of prime:

Wolfram Research (2017), PrimitivePolynomialQ, Wolfram Language function, https://reference.wolfram.com/language/ref/PrimitivePolynomialQ.html.

#### Text

Wolfram Research (2017), PrimitivePolynomialQ, Wolfram Language function, https://reference.wolfram.com/language/ref/PrimitivePolynomialQ.html.

#### CMS

Wolfram Language. 2017. "PrimitivePolynomialQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PrimitivePolynomialQ.html.

#### APA

Wolfram Language. (2017). PrimitivePolynomialQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PrimitivePolynomialQ.html

#### BibTeX

@misc{reference.wolfram_2024_primitivepolynomialq, author="Wolfram Research", title="{PrimitivePolynomialQ}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/PrimitivePolynomialQ.html}", note=[Accessed: 05-August-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_primitivepolynomialq, organization={Wolfram Research}, title={PrimitivePolynomialQ}, year={2017}, url={https://reference.wolfram.com/language/ref/PrimitivePolynomialQ.html}, note=[Accessed: 05-August-2024 ]}