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Gröbner Bases and Primary Decomposition of Polynomial Ideals
TLDR
We present an algorithm to compute the primary decomposition of any ideal in a polynomialring over a factorially closed algorithmic principal ideal domain R. We show how basic ideal theoretic operations can be performed using Grobner bases and we exploit these constructions to inductively reduce the problem to zero dimensional ideals. Expand
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The singular value decomposition for polynomial systems
TLDR
This paper introduces singular value decomposition (SVD) algorithms for some standard polynomial computations, in the case where the coecients are inexact or imperfectly known. Expand
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Algebraic factoring and rational function integration
TLDR
This paper presents a new, simple, and efficient algorithm for factoring polynomials in several variables over an algebraic number field. Expand
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Computing with polynomials given by black boxes for their evaluations: greatest common divisors, factorization, separation of numerators and denominators
TLDR
Algorithms are developed that adopt a novel implicit representation for multivariate polynomials and rational functions with rational coefficients, that of black boxes for their evaluation. Expand
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Computing with Polynomials Given By Black Boxes for Their Evaluations: Greatest Common Divisors, Factorization, Separation of Numerators and Denominators
TLDR
Algorithms are developed that adopt a novel implicit representation for multivariate polynomials and rational functions with rational coefficients, that of black boxes for their evaluation. Expand
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Integration of algebraic functions
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A reordered Schur factorization method for zero-dimensional polynomial systems with multiple roots
TLDR
The technique of solving systems of multivariate polynomial equations via rigenproblems has become a topic of active research (with applications in computer-aided design and untrul theory, for example) at least since the papers [2, 6, 9]. Expand
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GCD's and Factoring Multivariate Polynominals Using Gröbner Bases
TLDR
This paper shows how Grobner basis computations can be used to compute multivariate gcds, perform Hensel lifting, and reduce multivariate factorization to univariate. Expand
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Decomposition of Algebras
TLDR
We solve this problem by reducing it to the problem of finding a decomposition of finite communtative Q-algebras as a direct product of local Q- algebnas over finite field. Expand
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Integral closure of Noetherian rings
TLDR
We show that for the common case of affine domains, i.e. domains which are finitely generated over fields, we can use an effective localization in order to perform most of the computation in one dimensional rings where it can be done with linear algebra. Expand
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