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# Current Textbooks in Algorithmic Algebra Xv

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Mathematics document containing theorems and formulas.

Excerpt
Excerpt: Syzygies; Bounds In Polynomial Ideal Theory; Some Bounds In Polynomial Ideal Theory; The Hilbert?Serre Theorem; Homogeneous Sets; Cone Decomposition; Exact Decomposition Of Nf(I ); Exact Decomposition Of Ideals; Bounding The Macaulay Constants; Term-Rewriting Systems; A Quadratic Counter; Uniqueness Property; Lower Bounds; and Appendix A: Properties Of S0.

CONTENTS Preface xiii Current Textbooks in Algorithmic Algebra xv 0 Introduction 1 0.1 FUNDAMENTAL PROBLEM OF ALGEBRA 2 0.2 FUNDAMENTAL PROBLEM OF CLASSICAL ALGEBRAIC GEOMETRY 4 0.3 FUNDAMENTAL PROBLEM OF IDEAL THEORY 6 0.4 REPRESENTATION ANDSIZE 9 0.5 COMPUTATIONAL MODELS 10 0.6 ASYMPTOTIC NOTATIONS 13 0.7 COMPLEXITY OF MULTIPLICATION 15 0.8 ON BIT VERSUS ALGEBRAIC COMPLEXITY 18 0.9 MISCELLANY 20 0.10 COMPUTER ALGEBRA SYSTEMS 26 1 Arithmetic 27 1.1 THE DISCRETE FOURIER TRANSFORM 28 1.2 POLYNOMIAL MULTIPLICATION 32 1.3 MODULAR FAST FOURIER TRANSFORM 34 1.4 FAST INTEGER MULTIPLICATION 37 1.5 MATRIX MULTIPLICATION 41 2 The Greatest Common Denominator 43 2.1 UNIQUE FACTORIZATION DOMAIN 44 2.2 EUCLID?S ALGORITHM 47 2.3 EUCLIDEAN RING 50 2.4 THE HALF-GREATESTCOMMONDENOMINATOR PROBLEM 54 2.5 PROPERTIES OF THE NORM 5712.8 SYZYGIES 393 13 Bounds in Polynomial Ideal Theory 398 13.1 SOME BOUNDS IN POLYNOMIAL IDEAL THEORY 399 13.2 THE HILBERT?SERRE THEOREM 401 13.3 HOMOGENEOUS SETS 407 13.4 CONE DECOMPOSITION 412 13.5 EXACT DECOMPOSITION OF NF(I ) 416 13.6 EXACT DECOMPOSITION OF IDEALS 423 13.7 BOUNDING THE MACAULAY CONSTANTS 424 13.8 TERM-REWRITING SYSTEMS 428 13.9 A QUADRATIC COUNTER 432 13.10 UNIQUENESS PROPERTY 436 13.11 LOWER BOUNDS 438 APPENDIX A: Properties of S0 442

Book Id: WPLBN0000662522
Format Type: PDF eBook
File Size: 41.01 KB
Reproduction Date: 2005
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Title: Current Textbooks in Algorithmic Algebra Xv
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