The Resultant, Episode 1: Inside the Episode

In Episode 1 of our miniseries, “The Resultant”, the characters were introduced: integral domain *R* with fraction field *K* and extension field *L*, and polynomials *E*(*x*) and *F*(*x*) in *R*[*x*], factoring completely in *L* as *a*(*x–u*_{1})···(*x–u _{m}*) and

*b*(

*x–v*

_{1})···(

*x–v*). (Repeated roots allowed.) We had our first formulas for the resultant:

_{n}