| 000 | 00940pamuu2200277 a 4500 | |
| 001 | 000045361234 | |
| 005 | 20070612153944 | |
| 008 | 930513s1993 nyua b 001 0 eng | |
| 010 | ▼a 93014094 | |
| 020 | ▼a 0387940901 (New York : acid-free paper) | |
| 020 | ▼a 3540940901 (Berlin : acid-free paper) | |
| 020 | ▼a 9780387940908 | |
| 035 | ▼a (KERIS)BIB000001759440 | |
| 040 | ▼a 247020 ▼c 247020 ▼d 211009 | |
| 050 | 0 0 | ▼a QA155.7.E4 ▼b M57 1993 |
| 082 | 0 0 | ▼a 512/.00285 ▼2 22 |
| 090 | ▼a 512.00285 ▼b M678a | |
| 100 | 1 | ▼a Mishra, Bhubaneswar , ▼d 1958-. |
| 245 | 1 0 | ▼a Algorithmic algebra / ▼c Bhubaneswar Mishra. |
| 260 | ▼a New York : ▼b Springer-Verlag , ▼c c1993. | |
| 300 | ▼a xii, 416 p. : ▼b ill. ; ▼c 24 cm. | |
| 440 | 0 | ▼a Texts and monographs in computer science |
| 504 | ▼a Includes bibliographical references (p. 391-407) and index. | |
| 650 | 0 | ▼a Algebra ▼x Data processing. |
| 945 | ▼a KINS |
Holdings Information
| No. | Location | Call Number | Accession No. | Availability | Due Date | Make a Reservation | Service |
|---|---|---|---|---|---|---|---|
| No. 1 | Location Science & Engineering Library/Sci-Info(Stacks2)/ | Call Number 512.00285 M678a | Accession No. 121147394 | Availability Available | Due Date | Make a Reservation | Service |
Contents information
Table of Contents
1 Introduction.- 1.1 Prologue: Algebra and Algorithms.- 1.2 Motivations.- 1.2.1 Constructive Algebra.- 1.2.2 Algorithmic and Computational Algebra.- 1.2.3 Symbolic Computation.- 1.2.4 Applications.- 1.3 Algorithmic Notations.- 1.3.1 Data Structures.- 1.3.2 Control Structures.- 1.4 Epilogue.- Bibliographic Notes.- 2 Algebraic Preliminaries.- 2.1 Introduction to Rings and Ideals.- 2.1.1 Rings and Ideals.- 2.1.2 Homomorphism, Contraction and Extension.- 2.1.3 Ideal Operations.- 2.2 Polynomial Rings.- 2.2.1 Dickson's Lemma.- 2.2.2 Admissible Orderings on Power Products.- 2.3 Grobner Bases.- 2.3.1 Grobner Bases in K[x1, x2,...,xn].- 2.3.2 Hilbert's Basis Theorem.- 2.3.3 Finite Grobner Bases.- 2.4 Modules and Syzygies.- 2.5 S-Polynomials.- Problems.- Solutions to Selected Problems.- Bibliographic Notes.- 3 Computational Ideal Theory.- 3.1 Introduction.- 3.2 Strongly Computable Ring.- 3.2.1 Example: Computable Field.- 3.2.2 Example: Ring of Integers.- 3.3 Head Reductions and Grobner Bases.- 3.3.1 Algorithm to Compute Head Reduction.- 3.3.2 Algorithm to Compute Grobner Bases.- 3.4 Detachability Computation.- 3.4.1 Expressing with the Grobner Basis.- 3.4.2 Detachability.- 3.5 Syzygy Computation.- 3.5.1 Syzygy of a Grobner Basis: Special Case.- 3.5.2 Syzygy of a Set: General Case.- 3.6 Hilbert's Basis Theorem: Revisited.- 3.7 Applications of Grobner Bases Algorithms.- 3.7.1 Membership.- 3.7.2 Congruence, Subideal and Ideal Equality.- 3.7.3 Sum and Product.- 3.7.4 Intersection.- 3.7.5 Quotient.- Problems.- Solutions to Selected Problems.- Bibliographic Notes.- 4 Solving Systems of Polynomial Equations.- 4.1 Introduction.- 4.2 Triangular Set.- 4.3 Some Algebraic Geometry.- 4.3.1 Dimension of an Ideal.- 4.3.2 Solvability: Hilbert's Nullstellensatz.- 4.3.3 Finite Solvability.- 4.4 Finding the Zeros.- Problems.- Solutions to Selected Problems.- Bibliographic Notes.- 5 Characteristic Sets.- 5.1 Introduction.- 5.2 Pseudodivision and Successive Pseudodivision.- 5.3 Characteristic Sets.- 5.4 Properties of Characteristic Sets.- 5.5 Wu-Ritt Process.- 5.6 Computation.- 5.7 Geometric Theorem Proving.- Problems.- Solutions to Selected Problems.- Bibliographic Notes.- 6 An Algebraic Interlude.- 6.1 Introduction.- 6.2 Unique Factorization Domain.- 6.3 Principal Ideal Domain.- 6.4 Euclidean Domain.- 6.5 Gauss Lemma.- 6.6 Strongly Computable Euclidean Domains.- Problems.- Solutions to Selected Problems.- Bibliographic Notes.- 7 Resultants and Subresultants.- 7.1 Introduction.- 7.2 Resultants.- 7.3 Homomorphisms and Resultants.- 7.3.1 Evaluation Homomorphism.- 7.4 Repeated Factors in Polynomials and Discriminants.- 7.5 Determinant Polynomial.- 7.5.1 Pseudodivision: Revisited.- 7.5.2 Homomorphism and Pseudoremainder.- 7.6 Polynomial Remainder Sequences.- 7.7 Subresultants.- 7.7.1 Subresultants and Common Divisors.- 7.8 Homomorphisms and Subresultants.- 7.9 Subresultant Chain.- 7.10 Subresultant Chain Theorem.- 7.10.1 Habicht's Theorem.- 7.10.2 Evaluation Homomorphisms.- 7.10.3 Subresultant Chain Theorem.- Problems.- Solutions to Selected Problems.- Bibliographic Notes.- 8 Real Algebra.- 8.1 Introduction.- 8.2 Real Closed Fields.- 8.3 Bounds on the Roots.- 8.4 Sturm's Theorem.- 8.5 Real Algebraic Numbers.- 8.5.1 Real Algebraic Number Field.- 8.5.2 Root Separation, Thorn's Lemma and Representation.- 8.6 Real Geometry.- 8.6.1 Real Algebraic Sets.- 8.6.2 Delineability.- 8.6.3 Tarski-Seidenberg Theorem.- 8.6.4 Representation and Decomposition of Semialgebraic Sets.- 8.6.5 Cylindrical Algebraic Decomposition.- 8.6.6 Tarski Geometry.- Problems.- Solutions to Selected Problems.- Bibliographic Notes.- Appendix A: Matrix Algebra.- A.1 Matrices.- A.2 Determinant.- A.3 Linear Equations.
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