Implicitization of rational hypersurfaces via linear syzygies: A practical overview

We unveil in concrete terms the general machinery of the syzygy-based algorithms for the implicitization of rational surfaces in terms of the monomials in the polynomials defining the parametrization, following and expanding our joint article with M. Dohm. These algebraic techniques, based on the th...

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Detalles Bibliográficos
Autor principal: Dickenstein, Alicia Marcela
Publicado: 2016
Materias:
Implicitization
Matrix representation
Rational surface
Sparse polynomial
Syzygy
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_07477171_v74_n_p493_Botbol
http://hdl.handle.net/20.500.12110/paper_07477171_v74_n_p493_Botbol
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_07477171_v74_n_p493_Botbol
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spelling paper:paper_07477171_v74_n_p493_Botbol2023-06-08T15:45:12Z Implicitization of rational hypersurfaces via linear syzygies: A practical overview Dickenstein, Alicia Marcela Implicitization Matrix representation Rational surface Sparse polynomial Syzygy We unveil in concrete terms the general machinery of the syzygy-based algorithms for the implicitization of rational surfaces in terms of the monomials in the polynomials defining the parametrization, following and expanding our joint article with M. Dohm. These algebraic techniques, based on the theory of approximation complexes due to J. Herzog, A. Simis and W. Vasconcelos, were introduced for the implicitization problem by J.-P. Jouanolou, L. Busé, and M. Chardin. Their work was inspired by the practical method of moving curves, proposed by T. Sederberg and F. Chen, translated into the language of syzygies by D. Cox. Our aim is to express the theoretical results and resulting algorithms into very concrete terms, avoiding the use of the advanced homological commutative algebraic tools which are needed for their proofs. © 2015 Elsevier Ltd. Fil:Dickenstein, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2016 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_07477171_v74_n_p493_Botbol http://hdl.handle.net/20.500.12110/paper_07477171_v74_n_p493_Botbol
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Implicitization
Matrix representation
Rational surface
Sparse polynomial
Syzygy
spellingShingle Implicitization
Matrix representation
Rational surface
Sparse polynomial
Syzygy
Dickenstein, Alicia Marcela
Implicitization of rational hypersurfaces via linear syzygies: A practical overview
topic_facet Implicitization
Matrix representation
Rational surface
Sparse polynomial
Syzygy
description We unveil in concrete terms the general machinery of the syzygy-based algorithms for the implicitization of rational surfaces in terms of the monomials in the polynomials defining the parametrization, following and expanding our joint article with M. Dohm. These algebraic techniques, based on the theory of approximation complexes due to J. Herzog, A. Simis and W. Vasconcelos, were introduced for the implicitization problem by J.-P. Jouanolou, L. Busé, and M. Chardin. Their work was inspired by the practical method of moving curves, proposed by T. Sederberg and F. Chen, translated into the language of syzygies by D. Cox. Our aim is to express the theoretical results and resulting algorithms into very concrete terms, avoiding the use of the advanced homological commutative algebraic tools which are needed for their proofs. © 2015 Elsevier Ltd.
author Dickenstein, Alicia Marcela
author_facet Dickenstein, Alicia Marcela
author_sort Dickenstein, Alicia Marcela
title Implicitization of rational hypersurfaces via linear syzygies: A practical overview
title_short Implicitization of rational hypersurfaces via linear syzygies: A practical overview
title_full Implicitization of rational hypersurfaces via linear syzygies: A practical overview
title_fullStr Implicitization of rational hypersurfaces via linear syzygies: A practical overview
title_full_unstemmed Implicitization of rational hypersurfaces via linear syzygies: A practical overview
title_sort implicitization of rational hypersurfaces via linear syzygies: a practical overview
publishDate 2016
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_07477171_v74_n_p493_Botbol
http://hdl.handle.net/20.500.12110/paper_07477171_v74_n_p493_Botbol
work_keys_str_mv AT dickensteinaliciamarcela implicitizationofrationalhypersurfacesvialinearsyzygiesapracticaloverview
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