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2015 | OriginalPaper | Buchkapitel

1. Geometry, Algebra, and Algorithms

verfasst von : David A. Cox, John Little, Donal O’Shea

Erschienen in: Ideals, Varieties, and Algorithms

Verlag: Springer International Publishing

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Abstract

This chapter will introduce some of the basic themes of the book. The geometry we are interested in concerns affine varieties, which are curves and surfaces (and higher dimensional objects) defined by polynomial equations. To understand affine varieties, we will need some algebra, and in particular, we will need to study ideals in the polynomial ring k[x1, …, xn]. Finally, we will discuss polynomials in one variable to illustrate the role played by algorithms.

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Nächstes Kapitel Gröbner Bases
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Metadaten
Titel
Geometry, Algebra, and Algorithms
verfasst von
David A. Cox
John Little
Donal O’Shea
Copyright-Jahr
2015
Verlag
Springer International Publishing
Buch
Ideals, Varieties, and Algorithms

Print ISBN: 978-3-319-16720-6

Electronic ISBN: 978-3-319-16721-3

Copyright-Jahr: 2015

DOI
https://doi.org/10.1007/978-3-319-16721-3_1