Record Nr.

UNINA9910480269303321

Autore

Cox David

Titolo

Ideals, Varieties, and Algorithms [[electronic resource] ] : An Introduction to Computational Algebraic Geometry and Commutative Algebra / / by David Cox, John Little, DONAL OSHEA

Pubbl/distr/stampa


New York, NY : , : Springer New York : , : Imprint : Springer, , 1997

ISBN

1-4757-2693-7

Edizione

[2nd ed. 1997.]

Descrizione fisica

1 online resource (XIII, 538 p. 44 illus.)

Collana

Undergraduate Texts in Mathematics, , 0172-6056

Disciplina

511.3

Soggetti

Mathematical logic

Mathematical Logic and Foundations

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Bibliographic Level Mode of Issuance: Monograph

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

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.

Sommario/riassunto

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.

Record Nr.

UNINA9910459662103321

Autore

Martinez-Diaz Leonardo <1976->

Titolo

Globalizing in hard times [[electronic resource] ] : the politics of banking-sector opening in the emerging world / / Leonardo Martinez-Diaz

Pubbl/distr/stampa


Ithaca, : Cornell University Press, 2009

ISBN

0-8014-5984-2

Descrizione fisica

1 online resource (253 p.)

Collana

Cornell studies in political economy

Disciplina

332.109172/4

Soggetti

Banks and banking, Foreign - Developing countries

Banks and banking, International - Developing countries

Banks and banking - Deregulation - Developing countries

Financial crises - Developing countries

Globalization - Economic aspects - Developing countries

Electronic books.