Effective computation of singularities of parametric affine curves
type: Item
instance of: scholarly article
title: Effective computation of singularities of parametric affine curves
zbMATH Open document ID: 1052.14072
DOI: 10.1016/S0022-4049(02)00017-8
author: Hyungju Park
published in: Journal of Pure and Applied Algebra
publication date: 2002-08-22T00:00:00Z
review text: Given a parametric affine curve \(\phi:C\to {\mathbb A}^n_K\), defined by polynomials \(f_1(t),\dots,f_n(t)\), the author introduces a new method for determining if the parametrization is birational or an immersion. The proof is based on the observation that \(\phi\) is birational (respectively, an immersion) when the locus of the polynomials: \[ g_i(t,s)={{f_i(t)-f_i(s)}\over {(t-s)}} \] is finite (respectively, empty). With respect to previously known methods, this one has the advantage of using Gröbner basis computations with just two variables.
Mathematics Subject Classification ID: 14Q05
Mathematics Subject Classification ID: 13P10
Mathematics Subject Classification ID: 14E05
zbMATH DE Number: 1787484
zbMATH Keywords: parametric curves
zbMATH Keywords: Gröbner basis
zbMATH Keywords: birational parametrization
reviewed by: Luca Chiantini
describes a project that uses: SINGULAR
MaRDI profile type: Publication
cites work: Q3491708
cites work: Q4097032
cites work: Q4305609
cites work: A rational function decomposition algorithm by near-separated polynomials
cites work: The 𝐷-resultant, singularities and the degree of unfaithfulness
cites work: Q3156433
cites work: $D$-resultant for rational functions
cites work: Using Gröbner bases to determine algebra membership, split surjective algebra homomorphisms determine birational equivalence
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description: scientific article; zbMATH DE number 1787484