**ABSTRACT: **"The
resultant is a useful mathematical tool for determining

the intersections of polynomial curves by reducing the curves into a

formula with roots at these intersections. In particular, they are

useful for eliminating variables in systems of equations. However,

the resultant is classically calculated using the determinant - a

computationally expensive operation. The goal of this presentation is

to explore various techniques for simplifying the computation of two

types of resultants: one for the case of two uni-variate polynomials,

the other for three bi-variate polynomials.
Specifically, this

presentation seeks to explore how the computations can be optimized

to reduce the number of operations in the the

O(n^3) to O(n^2) and the bi-variate case from O(m^4 n^4) to O(m^2

n^3), along with even further possible refinements."

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Related paper: fast-computation.pdf