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Titlebook: Rational Algebraic Curves; A Computer Algebra A J. Rafael Sendra,Franz Winkler,Sonia Pérez-Díaz Textbook 2008 Springer-Verlag Berlin Heidel

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发表于 2025-3-21 16:18:18 | 显示全部楼层 |阅读模式
书目名称Rational Algebraic Curves
副标题A Computer Algebra A
编辑J. Rafael Sendra,Franz Winkler,Sonia Pérez-Díaz
视频video
概述Nice and easy introduction to topic for students.Includes supplementary material:
丛书名称Algorithms and Computation in Mathematics
图书封面Titlebook: Rational Algebraic Curves; A Computer Algebra A J. Rafael Sendra,Franz Winkler,Sonia Pérez-Díaz Textbook 2008 Springer-Verlag Berlin Heidel
描述Algebraic curves and surfaces are an old topic of geometric and algebraic investigation. They have found applications for instance in ancient and m- ern architectural designs, in number theoretic problems, in models of b- logical shapes, in error-correcting codes, and in cryptographic algorithms. Recently they have gained additional practical importance as central objects in computer-aided geometric design. Modern airplanes, cars, and household appliances would be unthinkable without the computational manipulation of algebraic curves and surfaces. Algebraic curves and surfaces combine fas- nating mathematical beauty with challenging computational complexity and wide spread practical applicability. In this book we treat only algebraic curves, although many of the results and methods can be and in fact have been generalized to surfaces. Being the solution loci of algebraic, i. e. , polynomial, equations in two variables, plane algebraiccurvesarewellsuited forbeing investigatedwith symboliccomputer algebra methods. This is exactly the approach we take in our book. We apply algorithms from computer algebra to the analysis, and manipulation of al- braic curves. To a large extent this am
出版日期Textbook 2008
关键词algebra; algebraic curves; computer; computer algebra; geometric computation; geometry; rational parametri
版次1
doihttps://doi.org/10.1007/978-3-540-73725-4
isbn_softcover978-3-642-09291-6
isbn_ebook978-3-540-73725-4Series ISSN 1431-1550
issn_series 1431-1550
copyrightSpringer-Verlag Berlin Heidelberg 2008
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发表于 2025-3-21 22:14:27 | 显示全部楼层
Plane Algebraic Curves,ction 2.4 is devoted to the study of linear systems of curves. We will see in the following chapters that this notion is crucial for solving the problem of parametrizing a rational curve. The chapter ends with Sect. 2.5 where we show how to locally parametrize a curve around a point of the curve by means of Puiseux series.
发表于 2025-3-22 00:35:45 | 显示全部楼层
Rational Reparametrization,n Section 6.2, and normality of parametrizations in Section 6.3. There are other criteria that might be considered. For instance, as we did in Chap. 5, one may ask for the algebraic optimality of the parametrization. For this case we refer to [ARS97], [ARS99], [ARS04], [RSV04], [SeV01], [SeV02].
发表于 2025-3-22 07:53:12 | 显示全部楼层
The Genus of a Curve, divisors on C and their associated linear spaces.We do not want to repeat this classical development here (for further details see for instance [Ful89] or [Wal50]), but we give a kind of road map for getting to the definition of the genus and from there to a method for computing it.
发表于 2025-3-22 09:54:45 | 显示全部楼层
Textbook 2008rn architectural designs, in number theoretic problems, in models of b- logical shapes, in error-correcting codes, and in cryptographic algorithms. Recently they have gained additional practical importance as central objects in computer-aided geometric design. Modern airplanes, cars, and household a
发表于 2025-3-22 14:02:04 | 显示全部楼层
发表于 2025-3-22 20:07:43 | 显示全部楼层
Plane Algebraic Curves,he general working environment of the book. This chapter consists of five sections. In Sect. 2.1, we present the basic notions on curves distinguishing between affine and projective curves. Section 2.2 is devoted to polynomial and rational functions. The material of this section is presented for the
发表于 2025-3-22 22:24:48 | 显示全部楼层
The Genus of a Curve,aic curves in general). In fact, only curves of genus 0 can be rationally parametrized. So in the process of parametrization we will first compute the genus of the curve .. This will involve an analysis of the singularities of ., and we will determine the genus as the deficiency between a bound on t
发表于 2025-3-23 01:55:38 | 显示全部楼层
Rational Parametrization,type of curves and we show how to algorithmically parametrize a rational curve. The chapter consists of three conceptual blocks. The first one (Sect. 4.1) is devoted to the notion of rational parametrization of a curve, and to the study of the class of rational curves, i.e., curves having a rational
发表于 2025-3-23 07:12:03 | 显示全部楼层
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