PrimitivePolynomialQ [poly,p]
tests whether poly is a primitive polynomial modulo a prime p.
PrimitivePolynomialQ
PrimitivePolynomialQ [poly,p]
tests whether poly is a primitive polynomial modulo a prime p.
Details
- The polynomial poly must be univariate.
Examples
open all close allBasic 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:
Related Guides
History
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_2025_primitivepolynomialq, author="Wolfram Research", title="{PrimitivePolynomialQ}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/PrimitivePolynomialQ.html}", note=[Accessed: 04-January-2026]}
BibLaTeX
@online{reference.wolfram_2025_primitivepolynomialq, organization={Wolfram Research}, title={PrimitivePolynomialQ}, year={2017}, url={https://reference.wolfram.com/language/ref/PrimitivePolynomialQ.html}, note=[Accessed: 04-January-2026]}