15 citations · 52 across the 35 of their papers we have counts for
22 papers · 1 filter
An Algorithm for Discriminating the Complete Multiplicities of a Parametric Univariate Polynomial
Simin Qin, Bican Xia, Jing Yang
In this paper, we tackle the parametric complete multiplicity problem for a univariate polynomial. Our approach to the parametric complete multiplicity problem has a significant di…
Isolating Bounded and Unbounded Real Roots of a Mixed Trigonometric-Polynomial
Rizeng Chen, Haokun Li, Bican Xia +2
Mixed trigonometric-polynomials (MTPs) are functions of the form with . In this paper, an algorithm ``isolating" all the real r…
Square-free Strong Triangular Decomposition of Zero-dimensional Polynomial Systems
Haokun Li, Bican Xia, Tianqi Zhao
Triangular decomposition with different properties has been used for various types of problem solving, e.g. geometry theorem proving, real solution isolation of zero-dimensional po…
Choosing the Variable Ordering for Cylindrical Algebraic Decomposition via Exploiting Chordal Structure
Haokun Li, Bican Xia, Huiying Zhang +1
Cylindrical algebraic decomposition (CAD) plays an important role in the field of real algebraic geometry and many other areas. As is well-known, the choice of variable ordering wh…
An Effective Framework for Constructing Exponent Lattice Basis of Nonzero Algebraic Numbers
Tao Zheng
Computing a basis for the exponent lattice of algebraic numbers is a basic problem in the field of computational number theory with applications to many other areas. The main cost…
Block SOS Decomposition
Haokun Li, Bican Xia
A widely used method for solving SOS (Sum Of Squares) decomposition problem is to reduce it to the problem of semi-definite programs (SDPs) which can be efficiently solved in theor…