On factoring multi-variate polynomials over algebraically closed fields (abstract)
K. Yokoyama, Masayuki Noro, Taku Takeshima · 1990
For a problem how to find an extension field over which we can obtain an absolutely irreducible factor, Kaltofen gave an answer in 1983 and explicitly in 1985 by employing analytic argument for showing his answer, and Chistov and Grigor'ev also gave the same answer in 1983 by algebraic arguments. Here, we give an alternative proof for Kaltofen's answer in algebraic way, independently to Chistov and Grigor'ev, and by the benefit of new way, we also give several extensions of his answer and properties of absolutely irreducible factors. We also discuss usage of our results for actual computation of absolutely irreducible factors. Here we restrict ourselves to bi-variate polynomials with integer (or rational) coefficients. First we state Kaltofen's answer.