119 citations · 224 across the 24 of their papers we have counts for
6 papers · 1 filter
Optimality of Curtiss Bound on Poincare Multiplier for Positive Univariate Polynomials
Hoon Hong, Brittany Riggs
Let be a monic univariate polynomial with non-zero constant term. We say that is positive if is positive over all . If all the coefficients of are non-ne…
Connectivity in Semi-Algebraic Sets I
Hoon Hong, James Rohal, Mohab Safey El Din +1
A semi-algebraic set is a subset of the real space defined by polynomial equations and inequalities having real coefficients and is a union of finitely many maximally connected com…
Degree-optimal moving frames for rational curves
Hoon Hong, Zachary Hough, Irina A. Kogan +1
A at a rational curve is a basis of vectors moving along the curve. When the rational curve is given parametrically by a row vector of u…
Number of common roots and resultant of two tropical univariate polynomials
Hoon Hong, J. Rafael Sendra
It is well known that for two univariate polynomials over complex number field the number of their common roots is equal to the order of their resultant. In this paper, we show tha…
Algorithm for computing -bases of univariate polynomials
Hoon Hong, Zachary Hough, Irina A. Kogan
We present a new algorithm for computing a -basis of the syzygy module of polynomials in one variable over an arbitrary field . The algorithm is conceptually dif…
On Lazard's Valuation and CAD Construction
Scott McCallum, Hoon Hong
In 1990 Lazard proposed an improved projection operation for cylindrical algebraic decomposition (CAD). For the proof he introduced a certain notion of valuation of a multivariate…