Evaluating and Differentiating a Polynomial Using a Pseudo-witness Set

Polynomials which arise via elimination can be difficult to compute explicitly. By using a pseudo-witness set, we develop an algorithm to explicitly compute the restriction of a polynomial to a given line. The resulting polynomial can then be used to evaluate the original polynomial and directional...

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Detalles Bibliográficos
Autores principales: Hauenstein, Jonathan D., Regan, Margaret H.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7340945/
http://dx.doi.org/10.1007/978-3-030-52200-1_6
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author Hauenstein, Jonathan D.
Regan, Margaret H.
author_facet Hauenstein, Jonathan D.
Regan, Margaret H.
author_sort Hauenstein, Jonathan D.
collection PubMed
description Polynomials which arise via elimination can be difficult to compute explicitly. By using a pseudo-witness set, we develop an algorithm to explicitly compute the restriction of a polynomial to a given line. The resulting polynomial can then be used to evaluate the original polynomial and directional derivatives along the line at any point on the given line. Several examples are used to demonstrate this new algorithm including examples of computing the critical points of the discriminant locus for parameterized polynomial systems.
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spelling pubmed-73409452020-07-08 Evaluating and Differentiating a Polynomial Using a Pseudo-witness Set Hauenstein, Jonathan D. Regan, Margaret H. Mathematical Software – ICMS 2020 Article Polynomials which arise via elimination can be difficult to compute explicitly. By using a pseudo-witness set, we develop an algorithm to explicitly compute the restriction of a polynomial to a given line. The resulting polynomial can then be used to evaluate the original polynomial and directional derivatives along the line at any point on the given line. Several examples are used to demonstrate this new algorithm including examples of computing the critical points of the discriminant locus for parameterized polynomial systems. 2020-06-06 /pmc/articles/PMC7340945/ http://dx.doi.org/10.1007/978-3-030-52200-1_6 Text en © Springer Nature Switzerland AG 2020 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Article
Hauenstein, Jonathan D.
Regan, Margaret H.
Evaluating and Differentiating a Polynomial Using a Pseudo-witness Set
title Evaluating and Differentiating a Polynomial Using a Pseudo-witness Set
title_full Evaluating and Differentiating a Polynomial Using a Pseudo-witness Set
title_fullStr Evaluating and Differentiating a Polynomial Using a Pseudo-witness Set
title_full_unstemmed Evaluating and Differentiating a Polynomial Using a Pseudo-witness Set
title_short Evaluating and Differentiating a Polynomial Using a Pseudo-witness Set
title_sort evaluating and differentiating a polynomial using a pseudo-witness set
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7340945/
http://dx.doi.org/10.1007/978-3-030-52200-1_6
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