Editing Polynomial ring (section)

====Square-free factorization====
{{main|Square-free polynomial}}

A polynomial with coefficients in a field or integral domain is ''square-free'' if it does not have a [[multiple root]] in the [[algebraically closed field]] containing its coefficients. In particular, a polynomial of degree {{mvar|n}} with real or complex coefficients is square-free if it has {{mvar|n}} distinct complex roots. Equivalently, a polynomial over a field is square-free if and only if the [[Polynomial greatest common divisor|greatest common divisor]] of the polynomial and its derivative is {{math|1}}.

A ''square-free factorization'' of a polynomial is an expression for that polynomial as a product of powers of [[pairwise relatively prime]] square-free factors. Over the real numbers (or any other field of [[characteristic 0]]), such a factorization can be computed efficiently by [[Yun's algorithm]]. Less efficient algorithms are known for [[Factorization_of_polynomials_over_finite_fields#Square-free_factorization|square-free factorization of polynomials over finite fields]].