Square-free criteria for polynomials using no derivatives
Emré Alkan, Anca Iuliana Bonciocat, Nicolae Ciprian Bonciocat, Alexandru Zaharescu · Proceedings of the American Mathematical Society · 2006
We provide some square-free criteria for primitive polynomials over unique factorization domains, which do not make use of derivatives or discriminants. Using some ideas of Ostrowski we establish nonvanishing conditions for determinants of matrices with polynomial entries and deduce square-free criteria for polynomials in several variables.