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Implicitization of Rational Curves
A new technique for finding the implicit equation of a rational curve is investigated. It is based on efficient computation of the Bézout resultant...
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Cayley-Dixon Resultant Matrices of Multi-univariate Composed Polynomials
The behavior of the Cayley-Dixon resultant construction and the structure of Dixon matrices are analyzed for composed polynomial systems constructed...
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Resultant-Based Methods for Plane Curves Intersection Problems
We present an algorithm for solving polynomial equations, which uses generalized eigenvalues and eigenvectors of resultant matrices. We give special...
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Exacus: Efficient and Exact Algorithms for Curves and Surfaces
We present the first release of the Exacus C++ libraries. We aim for systematic support of non-linear geometry in software libraries. Our goals are...
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Formal Power Series and Loose Entry Formulas for the Dixon Matrix
Formal power series are used to derive four entry formulas for the Dixon matrix. These entry formulas have uniform and simple summation bounds for...
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The Offset to an Algebraic Curve and an Application to Conics
Curve offsets are important objects in computer-aided design. We study the algebraic properties of the offset to an algebraic curve, thus obtaining a...
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7. Computing All Integral Roots of the Resultant
In this chapter, we discuss modular algorithms for the following problem. Given two bivariate polynomials f, g ∈ ℤ[x, y], compute all integral roots...
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Various New Expressions for Subresultants and Their Applications
This article is devoted to presenting new expressions for Subresultant Polynomials, written in terms of some minors of matrices different from the...
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Algebraic Methods for Computing Smallest Enclosing and Circumscribing Cylinders of Simplices
We provide an algebraic framework to compute smallest enclosing and smallest circumscribing cylinders of simplices in Euclidean space
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Fast Arithmetic on Jacobians of Picard Curves
In this paper we present a fast addition algorithm in the Jacobian of a Picard curve over a finite field...
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Comparing Real Algebraic Numbers of Small Degree
We study polynomials of degree up to 4 over the rationals or a computable real subfield. Our motivation comes from the need to evaluate predicates in...
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Computing Parametric Geometric Resolutions
Given a polynomial system of n equations in n unknowns that depends on some parameters, we define the notion of parametric geometric resolution as a...
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Cryptanalysis of Unbalanced RSA with Small CRT-Exponent
We present lattice-based attacks on RSA with prime factors p and q of unbalanced size. In our scenario, the factor q is smaller than N...
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On the Time–Space Complexity of Geometric Elimination Procedures
In [25] and [22] a new algorithmic concept was introduced for the symbolic solution of a zero dimensional complete intersection polynomial equation...
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Subresultants Revisited
The Euclidean Algorithm was first documented by Euclid (320–275 BC). Knuth (1981), p. 318, writes: “We might call it the granddaddy of all...
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Cryptanalysis of the RSA Schemes with Short Secret Exponent from Asiacrypt ’99
At Asiacrypt’ 99, Sun, Yang and Laih proposed three RSA variants with short secret exponent that resisted all known attacks, including the recent...
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Computer Algebra Methods for Studying and Computing Molecular Conformations
A relatively new branch of computational biology has been emerging as an effort to supplement traditional techniques of large scale search in drug...
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Probabilistic Algorithms for Geometric Elimination
We develop probabilistic algorithms that solve problems of geometric elimination theory using small memory resources. These algorithms are obtained...
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Number of Solutions for Motion and Structure from Multiple Frame Correspondence
Much of the dynamic computer vision literature deals with the determination of motion and structure by observing two frames captured at two instants...
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When polynomial equation systems can be “solved” fast?
We present a new method for solving symbolically zero-dimensional polynomial equation systems in the affine and toric case. The main feature of our...