5 papers
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…
Solving Satisfiability of Polynomial Formulas By Sample-Cell Projection
Haokun Li, Bican Xia
A new algorithm for deciding the satisfiability of polynomial formulas over the reals is proposed. The key point of the algorithm is a new projection operator, called sample-cell p…
A New Sparse SOS Decomposition Algorithm Based on Term Sparsity
Jie Wang, Haokun Li, Bican Xia
A new sparse SOS decomposition algorithm is proposed based on a new sparsity pattern, called cross sparsity patterns. The new sparsity pattern focuses on the sparsity of terms and…
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…