Descripción del título
Algorithms in real algebrai...
The algorithmic problems of real algebraic geometry such as real root counting, deciding the existence of solutions of systems of polynomial equations and inequalities, finding global maxima or deciding whether two points belong in the same connected component of a semi-algebraic set appear frequently in many areas of science and engineering. In this first-ever graduate textbook on the algorithmic aspects of real algebraic geometry, the main ideas and techniques presented form a coherent and rich body of knowledge, linked to many areas of mathematics and computing. Mathematicians already aware of real algebraic geometry will find relevant information about the algorithmic aspects, and researchers in computer science and engineering will find the required mathematical background. Being self-contained the book is accessible to graduate students and even, for invaluable parts of it, to undergraduate students. This revised second edition contains several recent results, notably on discriminants of symmetric matrices, real root isolation, global optimization, quantitative results on semi-algebraic sets and the first single exponential algorithm computing their first Betti number. An index of notation has also been added
Monografía
monografia Rebiun25190201 https://catalogo.rebiun.org/rebiun/record/Rebiun25190201 m o d cr cn||||||||| 081017s2006 gw a ob 001 0 eng d 225367883 288297052 317881331 607281090 613677015 646746996 739131573 756424376 880103584 922961124 957339054 1035661050 1044594123 1056381800 1086930801 1097262947 1102297344 1110949284 1111042813 1112542066 9783540330998 3540330992 9783540330981 3540330984 9783540009733 3540009736 3540009736 10.1007/3-540-33099-2. doi AU@ 000042135414 DEBSZ 449600513 DKDLA 820120-katalog:000662658 HEBIS 192071408 NLGGC 384205178 NZ1 12054275 978-3-540-33098-1 Springer http://www.springerlink.com GW5XE eng pn GW5XE AU@ HEBIS W2U NUI DAY E7B UBC OCLCQ OCLCO OCLCQ A7U OCLCQ OCLCF DKDLA COO SLY YDXCP IDEBK OCLCQ EBLCP DEBSZ OCLCQ Z5A LIP OCLCQ UAB ESU OCLCQ VT2 STF OCLCQ CEF U3W OCLCQ WYU ICG YOU CNTRU AUD OCLCQ ZHM DCT ERF OCLCQ INARC UKAHL QA lcco PBMW. bicssc MAT012010. bisacsh 516.3/5 22 31.51 bcl O187-37 clc Basu, Saugata 1968-) Algorithms in real algebraic geometry Saugata Basu, Richard Pollack, Marie-Françoise Roy 2nd ed Berlin New York Springer 2006 Berlin New York Berlin New York Springer 1 online resource (ix, 662 pages) illustrations 1 online resource (ix, 662 pages) Text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Algorithms and computation in mathematics 1431-1550 v. 10 Includes bibliographical references (pages 587-593)-and indexes Introduction -- 1 Algebraically Closed Fields -- 2 Real Closed Fields -- 3 Semi-Algebraic Sets -- 4 Algebra -- 5 Decomposition of Semi-Algebraic Sets -- 6 Elements of Topology -- 7 Quantitative Semi-Algebraic Geometry -- 8 Complexity of Basic Algorithms -- 9 Cauchy Index and Applications -- 10 Real Roots -- 11 Cylindrical Decomposition Algorithm -- 12 Polynomial System Solving -- 13 Existential Theory of the Reals -- 14 Quantifier Elimination -- 15 Computing Roadmaps and Connected Components of Algebraic Sets -- 16 Computing Roadmaps and Connected Components of Semi-Algebraic Sets -- References -- Index of Notation -- Index The algorithmic problems of real algebraic geometry such as real root counting, deciding the existence of solutions of systems of polynomial equations and inequalities, finding global maxima or deciding whether two points belong in the same connected component of a semi-algebraic set appear frequently in many areas of science and engineering. In this first-ever graduate textbook on the algorithmic aspects of real algebraic geometry, the main ideas and techniques presented form a coherent and rich body of knowledge, linked to many areas of mathematics and computing. Mathematicians already aware of real algebraic geometry will find relevant information about the algorithmic aspects, and researchers in computer science and engineering will find the required mathematical background. Being self-contained the book is accessible to graduate students and even, for invaluable parts of it, to undergraduate students. This revised second edition contains several recent results, notably on discriminants of symmetric matrices, real root isolation, global optimization, quantitative results on semi-algebraic sets and the first single exponential algorithm computing their first Betti number. An index of notation has also been added Geometry, Algebraic- Data processing Algorithms Algorithms. Algebraïsche meetkunde. Geometria algébrica real. Algoritmos Geometry, Algebraic- Data processing. Algorithms. Geometry, Algebraic- Data processing. Algebraïsche meetkunde. Geometria algébrica real. Algoritmos Electronic books Pollack, Richard Roy, M.-F. Marie-Françoise) Print version Basu, Saugata, 1968-. Algorithms in real algebraic geometry. 2nd ed. Berlin ; New York : Springer, 2006 3540330984 9783540330981 (DLC) 2006927110 (OCoLC)70573945 Algorithms and computation in mathematics v. 10. 1431-1550