SEARCH MATHEMATICA 8 DOCUMENTATION

THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.

SquareFreeQ

SquareFreeQ[expr]
gives True if expr is a square-free polynomial or number, and False otherwise.

SquareFreeQ[expr, vars]
gives True if expr is square-free with respect to the variables vars.

For integers and , SquareFreeQ[m+I n] automatically works over the Gaussian integers.

	GaussianIntegers	Automatic	whether to allow Gaussian integers
	Modulus	0	modulus for polynomial coefficients

12 has a factor 4, which is a square:

Integers:

Gaussian integers:

Univariate polynomials:

Multivariate polynomials:

Polynomials in specific variables:

Polynomials over a finite field:

This is square-free over the integers:

Square-free Gaussian integers:

Square-free polynomials over finite fields:

The central binomial coefficients Binomial[2n, n] are not square-free for n>4:

Square factors can be found using FactorSquareFreeList:

The polynomial p[x]/PolynomialGCD[p[x], p'[x]] is always square-free:

MoebiusMu is zero for non-square-free integers:

Pattern of square-free integers:

New in 6