
Solving Polynomial Systems Efficiently and Accurately
We consider the problem of finding the isolated common roots of a set of...
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Computing in quotients of rings of integers
We develop algorithms to turn quotients of rings of rings of integers in...
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Truncated Normal Forms for Solving Polynomial Systems: Generalized and Efficient Algorithms
We consider the problem of finding the isolated common roots of a set of...
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A Stabilized Normal Form Algorithm for Generic Systems of Polynomial Equations
We propose a numerical linear algebra based method to find the multiplic...
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BOSPHORUS: Bridging ANF and CNF Solvers
Algebraic Normal Form (ANF) and Conjunctive Normal Form (CNF) are common...
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Toric Eigenvalue Methods for Solving Sparse Polynomial Systems
We consider the problem of computing homogeneous coordinates of points i...
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Normal and Triangular Determinantal Representations of Multivariate Polynomials
In this paper we give a new and simple algorithm to put any multivariate...
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Solving Polynomial System Efficiently and Accurately
We consider the problem of finding the isolated common roots of a set of polynomial functions defining a zerodimensional ideal I in a ring R of polynomials over C. Normal form algorithms provide an algebraic approach to solve this problem. We use new characterizations of normal forms and describe accurate and efficient constructions that allow us to compute the algebra structure of R/I, and hence the solutions of I. We show how the resulting algorithms give accurate results in double precision arithmetic and compare with normal form algorithms using Groebner bases and homotopy solvers.
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