Solving zero-dimensional algebraic systems
Journal of Symbolic Computation
Representation for the radical of a finitely generated differential ideal
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Modern computer algebra
On the theories of triangular sets
Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
The differential ideal [P]: M∞
Journal of Symbolic Computation - Special issue on differential algebra and differential equations
Deformation techniques for efficient polynomial equation solving
Journal of Complexity
A Gröbner free alternative for polynomial system solving
Journal of Complexity
When Polynomial Equation Systems Can Be "Solved" Fast?
AAECC-11 Proceedings of the 11th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
On the Invariants of the Quotients of the Jacobian of a Curve of Genus 2
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Computation with polynomial systems
Computation with polynomial systems
Complexity results for triangular sets
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
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We study the representation of the solutions of a polynomial system by triangular sets, and concentrate on the positive-dimensional case. We reduce to dimension zero by placing the free variables in the base-field, so the solutions can be represented by triangular sets with coefficients in a rational function field. First, we give bounds on the degree of these coefficients; then we show how to apply lifting techniques in this context, and point out the role played by the evaluation properties of the input system. Our algorithms are implemented in Magma; we present two applications.