The complexity of linear problems in fields
Journal of Symbolic Computation
Real quantifier elimination is doubly exponential
Journal of Symbolic 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
Algebraic numbers: an example of dynamic evaluation
Journal of Symbolic Computation
Applying quantifier elimination to the Birkhoff interpolation problem
Journal of Symbolic 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
Simulation and optimization by quantifier elimination
Journal of Symbolic Computation - Special issue: applications of quantifier elimination
On projection in CAD-based quantifier elimination with equational constraint
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Solving systems of strict polynomial inequalities
Journal of Symbolic Computation
Improved projection for CAD's of R3
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
On propagation of equational constraints in CAD-based quantifier elimination
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Improved projection for cylindrical algebraic decomposition
Journal of Symbolic Computation
Global Optimization with Polynomials and the Problem of Moments
SIAM Journal on Optimization
Interval arithmetic in cylindrical algebraic decomposition
Journal of Symbolic Computation
About a New Method for Computing in Algebraic Number Fields
EUROCAL '85 Research Contributions from the European Conference on Computer Algebra-Volume 2
Algebraic Computation, Numerical Computation and Verified Inclusions
Proceedings of the International Symposium on Trends in Computer Algebra
Solution formula construction for truth invariant cad's
Solution formula construction for truth invariant cad's
QEPCAD B: a program for computing with semi-algebraic sets using CADs
ACM SIGSAM Bulletin
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Global Optimization of Polynomials Using Gradient Tentacles and Sums of Squares
SIAM Journal on Optimization
Computing the global optimum of a multivariate polynomial over the reals
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Proceedings of the 2009 conference on Symbolic numeric computation
Global optimization of polynomials using generalized critical values and sums of squares
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
Variant quantifier elimination
Journal of Symbolic Computation
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Hi-index | 5.23 |
With many applications in engineering and scientific fields, quantifier elimination (QE) has received increasing attention. Cylindrical algebraic decomposition (CAD) is used as a basis for a general QE algorithm. In this paper we present an effective symbolic-numeric cylindrical algebraic decomposition (SNCAD) algorithm for QE incorporating several new devices, which we call ''quick tests''. The simple quick tests are run beforehand to detect an unnecessary procedure that might be skipped without violating the correctness of results and they thus considerably reduce the computing time. The effectiveness of the SNCAD algorithm is examined in a number of experiments including practical engineering problems, which also reveal the quality of the implementation. Experimental results show that our implementation has significantly improved efficiency compared with our previous work.