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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Autores principales: Botbol, N., Dickenstein, A.
Formato: JOUR
Materias:
Implicitization
Matrix representation
Rational surface
Sparse polynomial
Syzygy
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_07477171_v74_n_p493_Botbol
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_07477171_v74_n_p493_Botbol
record_format dspace
spelling todo:paper_07477171_v74_n_p493_Botbol2023-10-03T15:39:00Z Implicitization of rational hypersurfaces via linear syzygies: A practical overview Botbol, N. Dickenstein, A. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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
Botbol, N.
Dickenstein, A.
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.
format JOUR
author Botbol, N.
Dickenstein, A.
author_facet Botbol, N.
Dickenstein, A.
author_sort Botbol, N.
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
url http://hdl.handle.net/20.500.12110/paper_07477171_v74_n_p493_Botbol
work_keys_str_mv AT botboln implicitizationofrationalhypersurfacesvialinearsyzygiesapracticaloverview
AT dickensteina implicitizationofrationalhypersurfacesvialinearsyzygiesapracticaloverview
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