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Solving Systems of Polynomial Equations
 AMERICAN MATHEMATICAL SOCIETY, CBMS REGIONAL CONFERENCES SERIES, NO 97
, 2002
"... One of the most classical problems of mathematics is to solve systems of polynomial equations in several unknowns. Today, polynomial models are ubiquitous and widely applied across the sciences. They arise in robotics, coding theory, optimization, mathematical biology, computer vision, game theory, ..."
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Cited by 223 (13 self)
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One of the most classical problems of mathematics is to solve systems of polynomial equations in several unknowns. Today, polynomial models are ubiquitous and widely applied across the sciences. They arise in robotics, coding theory, optimization, mathematical biology, computer vision, game theory
The Hardness of Polynomial Equation Solving
, 2003
"... Elimination theory is at the origin of algebraic geometry in the 19th century and deals with algorithmic solving of multivariate polynomial equation systems over the complex numbers, or, more generally, over an arbitrary algebraically closed field. In this paper we investigate the intrinsic seq ..."
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Cited by 26 (14 self)
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Elimination theory is at the origin of algebraic geometry in the 19th century and deals with algorithmic solving of multivariate polynomial equation systems over the complex numbers, or, more generally, over an arbitrary algebraically closed field. In this paper we investigate the intrinsic
Inductive databases of polynomial equations
 In Proceedings of the Second International Workshop on Knowledge Discovery in Inductive Databases (at ECML/PKDD2003
, 2003
"... Abstract. Inductive databases (IDBs) contain both data and patterns. Here we consider IDBs where patterns are polynomial equations. We present a constraintbased approach to answering inductive queries in this domain. The approach is based on heuristic search through the space of polynomial equation ..."
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Cited by 1 (1 self)
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Abstract. Inductive databases (IDBs) contain both data and patterns. Here we consider IDBs where patterns are polynomial equations. We present a constraintbased approach to answering inductive queries in this domain. The approach is based on heuristic search through the space of polynomial
Solving Monotone Polynomial Equations
"... Abstract We survey some recent results on iterative methods for approximating the least solution of a system of monotone fixedpoint polynomial equations. 1 ..."
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Cited by 1 (1 self)
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Abstract We survey some recent results on iterative methods for approximating the least solution of a system of monotone fixedpoint polynomial equations. 1
Singular Points of Polynomial Equations By
, 2002
"... In this paper we study an important class of polynomial equations known as Schubert cycles. They are the result of equating to zero the minors of certain matrices. We provide an algorithm to compute these equations and identify their singular points. ..."
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In this paper we study an important class of polynomial equations known as Schubert cycles. They are the result of equating to zero the minors of certain matrices. We provide an algorithm to compute these equations and identify their singular points.
Polynomial Equation in Radicals
 KYUNGPOOK MATH. J. 48(2008), 545551
, 2008
"... Necessary and sufficient conditions for a radical class ρ of rings to satisfy the polynomial equation ρ(R[x]) = (ρ(R))[x] have been investigated. The interrelationship of polynomial equation, Amitsur property and polynomial extensibility is given. It has been shown that complete analogy of R.E. P ..."
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Necessary and sufficient conditions for a radical class ρ of rings to satisfy the polynomial equation ρ(R[x]) = (ρ(R))[x] have been investigated. The interrelationship of polynomial equation, Amitsur property and polynomial extensibility is given. It has been shown that complete analogy of R
Solving systems of polynomial equations
 COMPUTER GRAPHICS AND APPLICATIONS 14, IEEE
, 1994
"... Current geometric and solid modeling systems use semialgebraic sets for defining the boundaries of solid objects, curves and surfaces, geometric constraints with mating relationship in a mechanical assembly, physical contacts between objects, collision detection. It turns out that performing many o ..."
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Cited by 41 (8 self)
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of the geometric operations on the solid boundaries or interacting with geometric constraints is reduced to nding common solutions of the polynomial equations. Current algorithms in the literature based on symbolic, numeric and geometric methods su er from robustness, accuracy or efficiency problems or are limited
CORRESPONDENCES WITH SPLIT POLYNOMIAL EQUATIONS
"... Abstract. We introduce endomorphisms of special jacobians and show that they satisfy polynomial equations with all integer roots which we compute. The eigenabelian varieties for these endomorphisms are generalizations of PrymTyurin varieties and naturally contain special curves representing cohomo ..."
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Cited by 3 (3 self)
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Abstract. We introduce endomorphisms of special jacobians and show that they satisfy polynomial equations with all integer roots which we compute. The eigenabelian varieties for these endomorphisms are generalizations of PrymTyurin varieties and naturally contain special curves representing
Solving Polynomial Equations
, 1994
"... This paper is divided into two parts. The first part traces (in details providing proofs and examples) the history of the solutions of polynomial equations(of the first, second, third, and fourth degree) by radicals from Babylonian times (2000 B.C.) through 20th century. Also it is shown that there ..."
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This paper is divided into two parts. The first part traces (in details providing proofs and examples) the history of the solutions of polynomial equations(of the first, second, third, and fourth degree) by radicals from Babylonian times (2000 B.C.) through 20th century. Also it is shown
Regression for sets of polynomial equations
 JMLR Workshop and Conference Proceedings
"... We propose a method called ideal regression for approximating an arbitrary system of polynomial equations by a system of a particular type. Using techniques from approximate computational algebraic geometry, we show how we can solve ideal regression directly without resorting to numerical optimizati ..."
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Cited by 2 (0 self)
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We propose a method called ideal regression for approximating an arbitrary system of polynomial equations by a system of a particular type. Using techniques from approximate computational algebraic geometry, we show how we can solve ideal regression directly without resorting to numerical
Results 1  10
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