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ISBN: 9780387946801

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Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (Undergraduate Texts in Mathematics) - Cox, David, Little, John, OSHEA, DONAL
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Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (Undergraduate Texts in Mathematics) - copertina rigida, flessible

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Springer, Gebundene Ausgabe, Auflage: 2nd ed. 1997. Corr. 3rd printing, 551 Seiten, Publiziert: 1996-11-14T00:00:01Z, Produktgruppe: Buch, 0.96 kg, Verkaufsrang: 4185357, Geometrie, Natur… Altro …

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Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (Undergraduate Texts in Mathematics) - copertina rigida, flessible

1996

ISBN: 0387946802

[EAN: 9780387946801], Gebraucht, sehr guter Zustand, [SC: 0.0], [PU: Springer], / MATHEMATICAL FOUNDATIONS MATHEMATICS LOGIC HC MATHEMATIK GRUNDLAGEN, 551 Seiten; 9780387946801.3 Sprache:… Altro …

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Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (Undergraduate Texts in Mathematics) - copertina rigida, flessible

2006, ISBN: 0387946802

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Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (Undergraduate Texts in Mathematics) - Cox, David; Little, John; O'Shea, Donal
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Cox, David; Little, John; O'Shea, Donal:
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (Undergraduate Texts in Mathematics) - copertina rigida, flessible

2006, ISBN: 0387946802

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Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (Undergraduate Texts in Mathematics)
Autore:
Titolo:
ISBN:

9780387946801


Algebraic Geometry is the study of systems of polynomial equations in one or more variables, asking such questions as: Does the system have finitely many solutions, and if so how can one find them? And if there are infinitely many solutions, how can they be described and manipulated? The solutions of a system of polynomial equations form a geometric object called a variety; the corresponding algebraic object is an ideal. There is a close relationship between ideals and varieties which reveals the intimate link between algebra and geometry. Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory. The algorithms to answer questions such as those posed above are an important part of algebraic geometry. This book bases its discussion of algorithms on a generalization of the division algorithm for polynomials in one variable that was only discovered in the 1960's. Although the algorithmic roots of algebraic geometry are old, the computational aspects were neglected earlier in this century. This has changed in recent years, and new algorithms, coupled with the power of fast computers, have let to some interesting applications, for example in robotics and in geometric theorem proving. In preparing a new edition of Ideals, Varieties and Algorithms the authors present an improved proof of the Buchberger Criterion as well as a proof of Bezout's Theorem. Appendix C contains a new section on Axiom and an update about Maple , Mathematica and REDUCE. TOC:Geometry, Algebra, and Algorithms.- Groebner Bases.- Elimination Theory.- The Algebra-Geometry Dictionary.- Polynomial and Rational Functions on a Variety.- Robotics and Automatic Geometric Theorem Proving.- Invariant Theory of Finite Groups.- Projective Algebraic Geometry.- The Dimension of a Variety.- Some Concepts from Algebra.- Pseudocode.- Computer Algebra Systems.- Independent Projects.

Informazioni dettagliate del libro - Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (Undergraduate Texts in Mathematics)


EAN (ISBN-13): 9780387946801
ISBN (ISBN-10): 0387946802
Copertina rigida
Copertina flessibile
Anno di pubblicazione: 2006
Editore: Springer

Libro nella banca dati dal 2007-06-05T12:28:46+02:00 (Rome)
Pagina di dettaglio ultima modifica in 2024-03-22T19:27:44+01:00 (Rome)
ISBN/EAN: 9780387946801

ISBN - Stili di scrittura alternativi:
0-387-94680-2, 978-0-387-94680-1
Stili di scrittura alternativi e concetti di ricerca simili:
Autore del libro : cox little, donal shea, david little, john cox
Titolo del libro: algebraic geometry, introduction geometry, undergraduate algebra, computational algebra, introduction commutative algebra, introduction algorithms, ideals varieties and algorithms, ideal, introduction algorithm, undergraduate text, little, john cox, david cox

Dati dell'editore

Autore: David Cox; John Little; DONAL OSHEA
Titolo: Undergraduate Texts in Mathematics; Ideals, Varieties, and Algorithms - An Introduction to Computational Algebraic Geometry and Commutative Algebra
Editore: Springer; Springer US
538 Pagine
Anno di pubblicazione: 2006-02-24
New York; NY; US
Peso: 0,952 kg
Lingua: Inglese
85,59 € (DE)
87,99 € (AT)
106,60 CHF (CH)
Not available, publisher indicates OP

BB; Book; Hardcover, Softcover / Mathematik/Grundlagen; Mathematische Grundlagen; Verstehen; Dimension; algebraic geometry; Grad; proof; A; Mathematical Logic and Foundations; Mathematics and Statistics; Mathematik: Logik; BB; BC; EA; BB

1. Geometry, Algebra, and Algorithms.- 2. Groebner Bases.- 3. Elimination Theory.- 4. The Algebra-Geometry Dictionary.- 5. Polynomial and Rational Functions on a Variety.- 6. Robotics and Automatic Geometric Theorem Proving.- 7. Invariant Theory of Finite Groups.- 8. Projective Algebraic Geometry.- 9. The Dimension of a Variety.- Appendix A. Some Concepts from Algebra.- §1 Fields and Rings.- §2. Groups.- §3. Determinants.- Appendix B. Pseudocode.- §1. Inputs, Outputs, Variables, and Constants.- §2. Assignment Statements.- §3. Looping Structures.- §4. Branching Structures.- Appendix C. Computer Algebra Systems.- §1. AXIOM.- §2. Maple.- §3. Mathematica.- §4. REDUCE.- §5. Other Systems.- Appendix D. Independent Projects.- §1. General Comments.- §2. Suggested Projects.- References.
Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory. In preparing a new edition of "Ideals, Varieties and Algorithms" the authors present an improved proof of the Buchberger Criterion as well as a proof of Bezout's Theorem. Appendix C contains a new section on Axiom and an update about Maple, Mathematica and REDUCE.

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