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On the History of Multivariate Polynomial Interpolation
 Computation of Curves and Surfaces
, 2000
"... Multivariate polynomial interpolation is a basic and fundamental subject in Approximation Theory and Numerical Analysis, which has received and continues receiving not deep but constant attention. In this short survey we review its development in the first 75 years of this century, including a p ..."
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Cited by 38 (6 self)
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Multivariate polynomial interpolation is a basic and fundamental subject in Approximation Theory and Numerical Analysis, which has received and continues receiving not deep but constant attention. In this short survey we review its development in the first 75 years of this century, including a
Approximate GCD of multivariate polynomials
 Proc.ASCM 2000, World Scientific Press
, 2000
"... We describe algorithms for computing the greatest common divisor of two multivariate polynomials with inexactly known coefficients. We focus on extending standard exact EZGCD algorithm to an efficient and stable algorithm in approximate case. Various issues related to the implementation of the algo ..."
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Cited by 9 (4 self)
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We describe algorithms for computing the greatest common divisor of two multivariate polynomials with inexactly known coefficients. We focus on extending standard exact EZGCD algorithm to an efficient and stable algorithm in approximate case. Various issues related to the implementation
Multivariate polynomials in R
"... In this short article I introduce the multipol package, which provides some functionality for handling multivariate polynomials; the package is discussed here from a programming perspective. An example from the field of enumerative combinatorics is presented. This vignette is based on Hankin (2008). ..."
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In this short article I introduce the multipol package, which provides some functionality for handling multivariate polynomials; the package is discussed here from a programming perspective. An example from the field of enumerative combinatorics is presented. This vignette is based on Hankin (2008).
Approximate GCD of Multivariate. Polynomials
"... Problem. Given two multivariate polynomials with inexact coefficients, how to produce a ‘satisfactory ’ GCD for a given error tolerance $\epsilon$? $F $ $= $ $C(x_{1}, \ldots, x_{n})\overline{F}(x_{1}, \ldots, x_{n})+\mathrm{O}(\epsilon(x_{1}, \ldots, x_{n}))$ ..."
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Problem. Given two multivariate polynomials with inexact coefficients, how to produce a ‘satisfactory ’ GCD for a given error tolerance $\epsilon$? $F $ $= $ $C(x_{1}, \ldots, x_{n})\overline{F}(x_{1}, \ldots, x_{n})+\mathrm{O}(\epsilon(x_{1}, \ldots, x_{n}))$
MULTIVARIATE POLYNOMIALS IN SAGE
 SÉMINAIRE LOTHARINGIEN DE COMBINATOIRE 66 (2011), ARTICLE B66Z
, 2011
"... We have developed a patch implementing multivariate polynomials seen as a multibase algebra. The patch is to be released into the software Sage and can already be found within the SageCombinat distribution. One can use our patch to define a polynomial in a set of indexed variables and expand it i ..."
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Cited by 1 (0 self)
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We have developed a patch implementing multivariate polynomials seen as a multibase algebra. The patch is to be released into the software Sage and can already be found within the SageCombinat distribution. One can use our patch to define a polynomial in a set of indexed variables and expand
mpoly: Multivariate Polynomials in R
"... The mpoly package is a general purpose collection of tools for symbolic computing with multivariate polynomials in R. In addition to basic arithmetic, mpoly can take derivatives of polynomials, compute Gröbner bases of collections of polynomials, and convert polynomials into a functional form to be ..."
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The mpoly package is a general purpose collection of tools for symbolic computing with multivariate polynomials in R. In addition to basic arithmetic, mpoly can take derivatives of polynomials, compute Gröbner bases of collections of polynomials, and convert polynomials into a functional form
WORKING WITH MULTIVARIATE POLYNOMIALS IN MAPLE
, 2005
"... We comment on the implementation of various algorithms in multivariate polynomial theory. Specifically, we describe a modular computation of triangular sets and possible applications. Next we discuss an implementation of the F4 algorithm for computing Gröbner bases. We also give examples of how to ..."
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We comment on the implementation of various algorithms in multivariate polynomial theory. Specifically, we describe a modular computation of triangular sets and possible applications. Next we discuss an implementation of the F4 algorithm for computing Gröbner bases. We also give examples of how
Multivariate polynomials for hashing
 In Inscrypt, Lecture Notes in Computer Science
, 2007
"... Abstract. We propose the idea of building a secure hash using quadratic or higher degree multivariate polynomials over a finite field as the compression function. We analyze some security properties and potential feasibility, where the compression functions are randomly chosen highdegree polynomials ..."
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Cited by 4 (1 self)
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Abstract. We propose the idea of building a secure hash using quadratic or higher degree multivariate polynomials over a finite field as the compression function. We analyze some security properties and potential feasibility, where the compression functions are randomly chosen highdegree
Executable multivariate polynomials
, 2013
"... We define multivariate polynomials over arbitrary (ordered) semirings in combination with (executable) operations like addition, multiplication, and substitution. We also define (weak) monotonicity of polynomials and comparison of polynomials where we provide standard estimations like absolute posit ..."
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Cited by 1 (1 self)
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We define multivariate polynomials over arbitrary (ordered) semirings in combination with (executable) operations like addition, multiplication, and substitution. We also define (weak) monotonicity of polynomials and comparison of polynomials where we provide standard estimations like absolute
Pseudozeros Of Multivariate Polynomials
 Math. Comp
, 2000
"... . The pseudozero set of a system f of polynomials in n complex variables is the subset of C n which is the union of the zero  sets of all polynomial systems g that are near to f in a suitable sense. This concept is made precise and general properties of pseudozero sets are established. In partic ..."
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Cited by 6 (0 self)
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ideas are proposed for solving multivariate polynomials. 1. Introduction 1.1. Summary. The pseudozero set of a general polynomial in a single variable was investigated in [18]. Our purpose here is to extend some ideas from that work to systems of polynomials in several variables, with special attention
Results 1  10
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