Real Solution Isolation with Multiplicity of Zero-Dimensional Triangular Systems (2009)
Zhang, Zhihai, Fang, Tian, Xia, Bican
Existing algorithms for isolating real solutions of zero-dimensional polynomial systems do not compute the multiplicities of the solutions. In this paper, we define in a natural way the multiplicity...
Termination of Linear Programs with Nonlinear Constraints (2009)
Tiwari proved that termination of linear programs (loops with linear loop conditions and updates) over the reals is decidable through Jordan forms and eigenvectors computation. Braverman proved that...
Computing Cylindrical Algebraic Decomposition via Triangular Decomposition (2009)
Chen, Changbo, Maza, Marc Moreno, Xia, Bican, Yang, Lu
Cylindrical algebraic decomposition is one of the most important tools for computing with semi-algebraic sets, while triangular decomposition is among the most important approaches for manipulating...
DISCOVERER: A tool for solving problems involving polynomial inequalities (2008)
Abstract discoverer, developed under Maple, is a package aiming at discovering and proving inequality-type theorems. It can discover new inequalities automatically, without requiring us to put...
Quantifier Elimination for Quartics (2008)
Abstract. Concerning quartics, two particular quantifier elimination (QE) problems of historical interests and practical values are studied. We solve the problems by the theory of complete...
Discovering non-linear ranking functions by solving semi-algebraic systems (2008)
Yinghua Chen, Bican Xia, Lu Yang, Naijun Zhan, Chaochen Zhou
Abstract. Differing from [6] this paper reduces non-linear ranking function discovering for polynomial programs to semi-algebraic system solving, and demonstrates how to apply the symbolic...
Yinghua Chen, Bican Xia, Lu Yang, Naijun Zhan
Abstract. This paper investigates how to apply the techniques on solving semi-algebraic systems to invariant generation of polynomial programs. By our approach, the generated invariants represented...
Algebraic Biology 2005 1 Algebraic Analysis of Stability for Some Biological Systems (2008)
This paper presents some results about the stability of certain biological systems, including the Cinquin–Demongeot model of multistable switch, self-assembling micelle systems, and the Cdc2cyclin...
Software Exhibition Abstracts (2007)
ISSAC 2007 organized sessions to exhibit software packages produced by academic developers. These sessions are intended to promote software development activities in all areas of symbolic...
Software Exhibition Abstracts (2007)
ISSAC 2007 organized sessions to exhibit software packages produced by academic developers. These sessions are intended to promote software development activities in all areas of symbolic...
Solution to the Generalized Champagne Problem on Simultaneous Stabilization of Linear Systems (2006)
Guan, Qiang, Wang, Long, Xia, Bican, Yang, Lu, Yu, Wensheng, Zeng, Zhenbing
The well-known "Generalized Champagne Problem" on simultaneous stabilization of linear systems is solved by using complex analysis \cite{A73,C78,G69,N52,R87} and Blondel's technique...
A Semi-Algebraic Approach for the Computation of Lyapunov Functions (2006)
She, Zhikun, Xia, Bican, Xiao, Rong
In this paper we deal with the problem of computing Lya punov functions for stability verification of differential sys tems. We concern on symbolic methods and start the dis cussion with a classical...
Solving parametric semi-algebraic systems (2005)
Let Q be the field of rational numbers and Q[u1,..., ud, x1,..., xs] the ring of polynomials in n indeterminates with coefficients in Q and d + s = n (0 ≤ d < n). The indeterminates are divided...
Real solution classifications of parametric semi-algebraic systems (2005)
Real solution classification of parametric polynomial systems is a crucial problem in real quantifier elimination which interests Volker Weispfenning and others. In this paper, we present a stepwise...
An algorithm for isolating the real solutions of semi-algebraic systems (2002)
We propose an algorithm for isolating the real solutions of semi-algebraic systems, which has been implemented as a Maple-program realzero. The performance of realzero in solving some examples from...
An explicit criterion to determine the number of roots of a polynomial on an interval (2000)
Abstract. In a recent article, a complete discrimination system was given for a polynomial with symbolic/literal coefficients. Such a system is a set of explicit expressions in terms of the...