Cylindrical algebraic decomposition I: the basic algorithm
SIAM Journal on Computing
Cylindrical algebraic decomposition II: an adjacency algorithm for the plane
SIAM Journal on Computing
An improved projection operation for cylindrical algebraic decomposition of three-dimensional space
Journal of Symbolic Computation
An adjacency algorithm for cylindrical algebraic decompositions of three-dimenslonal space
Journal of Symbolic Computation
On mechanical quantifier elimination for elementary algebra and geometry
Journal of Symbolic Computation
Quantifier elimination: Optimal solution for two classical examples
Journal of Symbolic Computation
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
An improvement of the projection operator in cylindrical algebraic decomposition
ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
Partial Cylindrical Algebraic Decomposition for quantifier elimination
Journal of Symbolic Computation
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
Quantifier elimination for real algebra—the cubic case
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
An efficient method for analyzing the topology of plane real algebraic curves
Selected papers presented at the international IMACS symposium on Symbolic computation, new trends and developments
Verification of Real-Time Systems using Linear Relation Analysis
Formal Methods in System Design - Special issue on computer aided verification (CAV 93)
Recent advances on determining the number of real roots of parametric polynomials
Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
Simple CAD construction and its applications
Journal of Symbolic Computation
Improved projection for cylindrical algebraic decomposition
Journal of Symbolic Computation
Automatic discovery of linear restraints among variables of a program
POPL '78 Proceedings of the 5th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Polyhedral Analysis for Synchronous Languages
SAS '99 Proceedings of the 6th International Symposium on Static Analysis
Abstract Interpretation Based Formal Methods and Future Challenges
Informatics - 10 Years Back. 10 Years Ahead.
Algorithmic Analysis of Nonlinear Hybrid Systems
Proceedings of the 7th International Conference on Computer Aided Verification
On using bi-equational constraints in CAD construction
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
The complete root classification of a parametric polynomial on an interval
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
| Hi-index | 0.00 |
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 discrimination systems and negative root discriminant sequences for polynomials that provide a method for real (positive/negative) and complex root classification for polynomials. The equivalent quantifier-free formulas are obtained mainly be hand and are simpler than those obtained automatically by previous methods or QE tools. Also, applications of the results to program verification and determination of positivity of symmetric polynomials are showed.