Cylindrical algebraic decomposition II: an adjacency algorithm for the plane
SIAM Journal on Computing
The method of resultants for computing real solutions of polynomial systems
SIAM Journal on Numerical Analysis
Solving zero-dimensional algebraic systems
Journal of Symbolic Computation
Computing the isolated roots by matrix methods
Journal of Symbolic Computation - Special issue on symbolic numeric algebra for polynomials
On the theories of triangular sets
Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
Fast Multiple-Precision Evaluation of Elementary Functions
Journal of the ACM (JACM)
Fundamental problems of algorithmic algebra
Fundamental problems of algorithmic algebra
Interval arithmetic in cylindrical algebraic decomposition
Journal of Symbolic Computation
An algorithm for isolating the real solutions of semi-algebraic systems
Journal of Symbolic Computation
Efficient isolation of polynomial's real roots
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
Complete subdivision algorithms, I: intersection of Bezier curves
Proceedings of the twenty-second annual symposium on Computational geometry
Real solution isolation using interval arithmetic
Computers & Mathematics with Applications
Complete numerical isolation of real zeros in zero-dimensional triangular systems
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Determining the topology of real algebraic surfaces
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
A descartes algorithm for polynomials with bit-stream coefficients
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
Lower bounds for zero-dimensional projections
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Root isolation for bivariate polynomial systems with local generic position method
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Ambient Isotopic Meshing for Implicit Algebraic Surfaces with Singularities
CASC '09 Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing
Collision and intersection detection of two ruled surfaces using bracket method
Computer Aided Geometric Design
Univariate real root isolation in an extension field
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Complete subdivision algorithms, II: Isotopic meshing of singular algebraic curves
Journal of Symbolic Computation
Root isolation of zero-dimensional polynomial systems with linear univariate representation
Journal of Symbolic Computation
Homeomorphic approximation of the intersection curve of two rational surfaces
Computer Aided Geometric Design
Certified approximation of parametric space curves with cubic B-spline curves
Computer Aided Geometric Design
Local generic position for root isolation of zero-dimensional triangular polynomial systems
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
Univariate real root isolation in multiple extension fields
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
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We present a complete numerical algorithm for isolating all the real zeros of a zero-dimensional triangular polynomial system F"n@?Z[x"1...x"n]. Our system F"n is general, with no further assumptions. In particular, our algorithm successfully treats multiple zeros directly in such systems. A key idea is to introduce evaluation bounds and sleeve bounds. We also present a much more efficient algorithm for zero-dimensional triangular systems without multiple roots. We implemented our algorithms, and promising experimental results are shown.