Loose entry formulas and the reduction of dixon determinant entries

Abstract

Recently there has been much effort in using the Dixon method toconstruct sparse resultants. In this thesis, we present new looseentry formulas for the Dixon matrix and introduce the concept ofexposed points for bidegree monomial supports. They combine toproduce important results: the rows and columns associated withexposed points have a very simple description, and rows andcolumns near exposed points can be greatly simplified. Theseresults provide useful information for the determination ofmaximal minors (numerators of the quotient sparse resultant) andexact information for the identification of extraneous factors(denominators of the quotient sparse resultant). In particular,for most corners with three exposed points, the thesis pinpointsthe rows or columns generating the expected extraneous factors.