Dividing polynomials when you only know their values
Amirhossein Amiraslani · 2004
A recent paper by Amiraslani, Corless, Gonzalez-Vega and Shakoori studies polynomial algebra by values, without first converting to another basis such as the monomial basis. In this talk I expand on some details from that paper, namely the method we used to divide (multivariate and univariate) polynomials given only by values. This is a surprisingly valuable operation, and with it one can solve systems of polynomial equations without first constructing a Gröbner basis, or one can compute Gröbner bases if desired.