FactorSquareFree

FactorSquareFree[poly]

pulls out any multiple factors in a polynomial.

Details and Options

Examples

open allclose all

Basic Examples  (2)

Pull out multiple factors:

A complete factorization:

Scope  (10)

A univariate polynomial:

A multivariate polynomial:

A rational function:

A polynomial with complex coefficients:

Non-polynomial expressions:

FactorSquareFree threads over lists:

FactorSquareFree threads over equations and inequalities:

Square-free factorization of a polynomial over the integers modulo 3:

Square-free factorization of a polynomial over a finite field:

Compute the square-free factorization of a polynomial of degree :

Options  (4)

Extension  (2)

By default, algebraic number coefficients are treated as independent variables:

With Extension->Automatic, algebraic dependencies between coefficients are recognized:

Modulus  (1)

Pull out multiple factors over the integers modulo 2:

Trig  (1)

Pull out multiple factors in a trigonometric expression:

Properties & Relations  (4)

FactorSquareFree only pulls out multiple factors:

Factor gives a complete factorization:

Expand is effectively the inverse of FactorSquareFree:

FactorSquareFreeList gives a list of factors:

A univariate polynomial has multiple factors if and only if its Discriminant is zero:

Wolfram Research (1988), FactorSquareFree, Wolfram Language function, https://reference.wolfram.com/language/ref/FactorSquareFree.html (updated 2023).

Text

Wolfram Research (1988), FactorSquareFree, Wolfram Language function, https://reference.wolfram.com/language/ref/FactorSquareFree.html (updated 2023).

CMS

Wolfram Language. 1988. "FactorSquareFree." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2023. https://reference.wolfram.com/language/ref/FactorSquareFree.html.

APA

Wolfram Language. (1988). FactorSquareFree. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FactorSquareFree.html

BibTeX

@misc{reference.wolfram_2024_factorsquarefree, author="Wolfram Research", title="{FactorSquareFree}", year="2023", howpublished="\url{https://reference.wolfram.com/language/ref/FactorSquareFree.html}", note=[Accessed: 21-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_factorsquarefree, organization={Wolfram Research}, title={FactorSquareFree}, year={2023}, url={https://reference.wolfram.com/language/ref/FactorSquareFree.html}, note=[Accessed: 21-December-2024 ]}