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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Rational Parametrization,n, in Sect. 4.4 the inversion problem for proper parametrizations is studied, and in Sect. 4.5 the implicitization question is addressed. The third block of the chapter (Sects. 4.6–4.8) deals with the problem of algorithmically deciding whether a given curve is rational, and in the affirmative case,

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Algebraically Optimal Parametrization,ssible field extension of the ground field. After introducing the notion of the field of parametrization in Section 5.1 and describing the Legendre method for finding rational points on conics in Section 5.2, we present in Section 5.3 an algebraically optimal parametrization of algebraic curves.

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Real Curves,ining real normal parametrizations; i.e., real parametrizations .(.) covering the whole curve and not just a dense subset of it, with real values of the parameter .. The material in this part of the chapter follows the ideas in [Sen02].

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Textbook 2008ial, 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

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ther chapters show that they are active and dynamic members of soil floras that interact widely with other soil inhabitants, with roles in nitrogen fixation, denitrification, and soil remediation.978-3-642-27067-3978-3-642-19577-8Series ISSN 1613-3382 Series E-ISSN 2196-4831

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ther chapters show that they are active and dynamic members of soil floras that interact widely with other soil inhabitants, with roles in nitrogen fixation, denitrification, and soil remediation.978-3-642-27067-3978-3-642-19577-8Series ISSN 1613-3382 Series E-ISSN 2196-4831

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ther chapters show that they are active and dynamic members of soil floras that interact widely with other soil inhabitants, with roles in nitrogen fixation, denitrification, and soil remediation.978-3-642-27067-3978-3-642-19577-8Series ISSN 1613-3382 Series E-ISSN 2196-4831