The 40 “generic” positions of a parallel robot
ISSAC '93 Proceedings of the 1993 international symposium on Symbolic and algebraic computation
Efficient computation of zero-dimensional Gro¨bner bases by change of ordering
Journal of Symbolic Computation
A reordered Schur factorization method for zero-dimensional polynomial systems with multiple roots
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Computing the isolated roots by matrix methods
Journal of Symbolic Computation - Special issue on symbolic numeric algebra for polynomials
Matrices in elimination theory
Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
Solving projective complete intersection faster
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
A Gröbner free alternative for polynomial system solving
Journal of Complexity
Numerical Polynomial Algebra
Solving Polynomial Equations: Foundations, Algorithms, and Applications (Algorithms and Computation in Mathematics)
Approximate radical of ideals with clusters of roots
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
On probabilistic analysis of randomization in hybrid symbolic-numeric algorithms
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Border bases of positive dimensional polynomial ideals
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Computing the multiplicity structure from geometric involutive form
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Stable normal forms for polynomial system solving
Theoretical Computer Science
Stable border bases for ideals of points
Journal of Symbolic Computation
A prolongation-projection algorithm for computing the finite real variety of an ideal
Theoretical Computer Science
On the topology of planar algebraic curves
Proceedings of the twenty-fifth annual symposium on Computational geometry
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Moments and sums of squares for polynomial optimization and related problems
Journal of Global Optimization
Artificial discontinuities of single-parametric Gröbner bases
Journal of Symbolic Computation
Border basis detection is NP-complete
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Flat families by strongly stable ideals and a generalization of Gröbner bases
Journal of Symbolic Computation
Maximum Block Improvement and Polynomial Optimization
SIAM Journal on Optimization
Complexity of Gröbner basis detection and border basis detection
Theoretical Computer Science
Moment matrices, border bases and real radical computation
Journal of Symbolic Computation
Border basis representation of a general quotient algebra
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Selecting lengths of floats for the computation of approximate Gröbner bases
Journal of Symbolic Computation
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This paper describes a new method for computing the normal form of a polynomial modulo a zero-dimensional ideal I. We give a detailed description of the algorithm, a proof of its correctness, and finally experimentations on classical benchmark polynomial systems. The method that we propose can be thought as an extension of both the Gröbner basis method and the Macaulay construction. We have weaken the monomial ordering requirement for bases computations, which allows us to construct new type of representations for the quotient algebra. This approach yields more freedom in the linear algebra steps involved, which allows us to take into account numerical criteria while performing the symbolic steps. This is a new feature for a symbolic algorithm, which has a huge impact on the practical efficiency.