Some tapas of computer algebra
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| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1999
|
| Schriftenreihe: | Algorithms and computation in mathematics
4 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 245 | 1 | 0 | |a Some tapas of computer algebra |c Arjeh M. Cohen ... (ed.) |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1999 | |
| 300 | |a XIV, 352 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Algorithms and computation in mathematics |v 4 | |
| 650 | 7 | |a Calcul formel |2 ram | |
| 650 | 7 | |a Computerwiskunde |2 gtt | |
| 650 | 7 | |a algèbre Lie |2 inriac | |
| 650 | 7 | |a algèbre polynomiale |2 inriac | |
| 650 | 7 | |a algèbre quaternion |2 inriac | |
| 650 | 7 | |a base Gröbner |2 inriac | |
| 650 | 7 | |a calcul formel |2 inriac | |
| 650 | 7 | |a cinématique robot |2 inriac | |
| 650 | 7 | |a code Golay |2 inriac | |
| 650 | 7 | |a décodage |2 inriac | |
| 650 | 7 | |a démonstration théorème |2 inriac | |
| 650 | 7 | |a factorisation polynôme |2 inriac | |
| 650 | 7 | |a groupe Mathieu |2 inriac | |
| 650 | 7 | |a groupe fini |2 inriac | |
| 650 | 7 | |a interpolation |2 inriac | |
| 650 | 7 | |a programmation en nombres entiers |2 inriac | |
| 650 | 7 | |a théorie codage |2 inriac | |
| 650 | 7 | |a treillis |2 inriac | |
| 650 | 7 | |a équation différentielle |2 inriac | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Algebra |x Data processing | |
| 650 | 0 | 7 | |a Computeralgebra |0 (DE-588)4010449-7 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4143413-4 |a Aufsatzsammlung |2 gnd-content | |
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| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Cohen, Arjeh M. |d 1949- |e Sonstige |0 (DE-588)121202119 |4 oth | |
| 830 | 0 | |a Algorithms and computation in mathematics |v 4 |w (DE-604)BV011131286 |9 4 | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-008334785 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 DAT 702f 2001 A 11545 |
|---|---|
| DE-BY-TUM_katkey | 1024730 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040020274704 |
| _version_ | 1820800267755454465 |
| adam_text | Contents
Chapter 1. Grobner Bases, an Introduction
Arjeh M. Cohen 1
1. Introduction 1
2. Monomials 4
3. The Buchberger Algorithm 7
4. Standard Monomials 15
5. Solving Polynomial Equations 17
6. Effectiveness of Polynomial Rings 23
Chapter 2. Symbolic Recipes for Polynomial
System Solving
Laureano Gonzalez Vega, Fabrice Rouillier,
and Marie Franc_oise Roy 34
1. Introduction 34
2. General Systems of Equations 35
2.1 Algebraic Preliminaries 35
2.2 First Recipes for Polynomial System Solving 40
3. Linear Algebra, Traces, and Polynomial Systems 46
3.1 Eigenvalues and Polynomial Systems 46
3.2 Counting Solutions and Removing Multiplicities 48
3.3 Rational Univariate Representation 51
4. As Many Equations as Variables 58
4.1 Generalities on Complete Intersection Polynomial Systems .... 58
4.2 Recipes for Polynomial System Solving When the Number
of Equations Equals the Number of Unknowns 60
5. Grobner Bases and Numerical Approximations 61
Chapter 3. Lattice Reduction
Frits Beukers 66
1. Introduction 66
2. Lattices 66
3. Lattice Reduction in Dimension 2 68
4. Lattice Reduction in Any Dimension 70
5. Implementations of the LLL Algorithm 73
6. Small Linear Forms 75
VIII Contents
Chapter 4. Factorisation of Polynomials
Frits Beukers 78
1. Introduction 78
2. Berlekamp s Algorithm 78
3. Additional Algorithms 81
4. Polynomials with Integer Coefficients 82
5. Factorisation of Polynomials with Integer Coefficients, 1 84
6. Factorisation of Polynomials with Integer Coefficients, II 86
7. Factorisation in .K f.X ], K Algebraic Number Field 88
Chapter 5. Computations in Associative and Lie Algebras
Gabor Ivanyos and Lajos Ronyai 91
1. Introduction 91
2. Basic Definitions and Structure Theorems 91
3. Computing the Radical 97
4. Applications to Lie Algebras 105
5. Finding the Simple Components of Semisimple Algebras 108
6. Zero Divisors in Finite Algebras 112
Chapter 6. Symbolic Recipes for Real Solutions
Laureano Gonzalez Vega, Fabrice Rouillier, Marie Frangoise Roy,
and Guadalupe Trujillo 121
1. Introduction 121
2. Real Root Counting: The Univariate Case 122
2.1 Computing the Number of Real Roots 123
2.2 Sylvester Sequence 124
2.3 Sylvester Habicht Sequence 128
2.4 Some Recipes for Counting Real Roots 133
3. Real Root Counting: The Multivariate Case 134
4. The Sign Determination Scheme 139
5. Real Algebraic Numbers and Thom Codes 142
6. Quantifier Elimination 145
7. Appendix: Properties of the Polynomials in the Sylvester Habicht
Sequence 149
7.1 Definition and the Structure Theorem 150
7.2 Proof of the Structure Theorem 154
7.3 Sylvester Habicht Sequences and Cauchy Index 161
Chapter 7. Grobner Bases and Integer Programming
Gunter M. Ziegler 168
1. Introduction 168
2. What is Integer Programming? 168
3. A Buchberger Algorithm for Integer Programming 169
Contents IX
4. A Geometric Buchberger Algorithm 175
5. A Variant of the Buchberger Algorithm 177
6. Exercises 180
Chapter 8. Working with Finite Groups
Hans Cuypers, Leonard H. Soicher, and Hans Sterk 184
1. Introduction 184
2. Permutation Groups 185
2.1 The Setting 185
2.2 Computing Orbits and Stabilizers 187
2.3 Computing Bases and Strong Generating Sets 192
2.4 Generators for Some Subgroups 194
3. Coset Enumeration 197
3.1 Introduction 197
3.2 Todd Coxeter Coset Enumeration 197
Chapter 9. Symbolic Analysis of Differential Equations
Marius van der Put 208
1. Introduction 208
2. The Equation y = f with / G C(x) 208
2.1 The Algorithm 210
3. The Equation y = fy with / € C{x)* 212
4. Rational Solutions of an Equation of Order n 213
5. Some Differential Galois Theory 216
5.1 Picard Vessiot Theory 218
6. Order Two Equations Over C(x) 222
7. The Local Differential Galois Group 225
8. The Equation y = ry with r E C[x], r ^ 0 229
9. The Equation y = ry with r G C[x.x~x] 231
Chapter 10. Grobner Bases for Codes
Mario de Boer and Ruud Pellikaan 237
1. Introduction 237
2. Basic Facts from Coding Theory 237
2.1 Hamming Distance 238
2.2 Linear Codes 238
2.3 Weight Distribution 239
2.4 Automorphisms and Isoinetries of Codes 239
3. Determining the Minimum Distance 240
3.1 Exhaustive Search 240
3.2 Linear Algebra 241
3.3 Finite Geometry 242
3.4 Arrangements of Hyperplanes 243
3.5 Algebra 245
X Contents
4. Cyclic Codes 247
4.1 The Mattson Solomon Polynomial , 248
4.2 Codewords of Minimal Weight 250
5. Codes from Varieties 251
5.1 Order and Weight Functions 252
5.2 A Bound on the Minimum Distance 254
Chapter 11. Grobner Bases for Decoding
Mario de Boer and Ruud Pellikaan 260
1. Introduction 260
2. Decoding 260
3. Decoding Cyclic Codes with Grobner Bases 262
3.1 One Step Decoding of Cyclic Codes 265
4. The Key Equation 267
4.1 The Algorithms of Euclid and Sugiyama 269
4.2 The Algorithm of Berlekamp Massey 270
5. Grobner Bases and Arbitrary Linear Codes 271
Project 1. Automatic Geometry Theorem Proving
Tomas Recio, Hans Sterk, and M. Pilar Velez 276
1. Introduction 276
2. Approaches to Automatic Geometry Theorem Proving 277
3. Algebraic Geometry Formulation 277
4. Searching for Conditions 282
5. Searching for Extra Hypotheses 291
Project 2. The Birkhoff Interpolation Problem
Maria Jose Gonzalez Lopez and Laureano Gonzalez Vega 297
1. Introduction 297
2. Poised Matrices 297
3. Examples 301
4. Conclusions 303
Project 3. The Inverse Kinematics Problem in Robotics
Maria Jose Gonzalez Lopez and Laureano Gonzalez Vega 305
1. Introduction 305
2. The ROMIN Manipulator 305
3. The Elbow Manipulator 307
Project 4. Quaternion Algebras
Gabor Ivanyos and Lajos Ronyai 311
1. Introduction 311
2. Four Dimensional Simple Algebras 311
3. Quaternion Algebras and Quadratic Forms 312
Contents XI
Project 5. Explorations with the Icosahedral Group
Arjeh M. Cohen, Hans Cuypcrs, Remko Riebeek 315
1. Introduction 315
2. Three Dimensional Representations for W(H j) 31G
3. Coset Enumeration 318
4. The Permutation Representation of W on the Coscts of 7 318
Project 6. The Small Mathieu Groups
Hans Cuypers, Leonard H. Soicher, and Hans Sterk 323
1. Introduction 323
2. The Affine Plane of Order 3 324
3. A 3 (10,4,1) Design and the Mathieu Group Mw 326
4. The Groups Mu and M12 328
5. Two 2 Transitive Subgroups of M12 329
6. Graphs Which Are Locally the Incidence Graph of the Biplane .... 332
Project 7: The Golay Codes
Mario de Boer and Ruud Pellikaan 338
1. Introduction 338
2. Minimal Weight Codewords of Gu 338
3. Decoding of G23 with Grobner Bases 341
4. One Step Decoding of G2j 343
5. The Key Equation for G23 344
6. Exercises 346
Index 349
|
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| genre | (DE-588)4143413-4 Aufsatzsammlung gnd-content |
| genre_facet | Aufsatzsammlung |
| id | DE-604.BV012292114 |
| illustrated | Illustrated |
| indexdate | 2024-12-23T15:00:00Z |
| institution | BVB |
| isbn | 3540634800 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008334785 |
| oclc_num | 40359459 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-739 DE-20 DE-703 DE-824 DE-92 DE-1051 DE-634 DE-83 DE-11 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-739 DE-20 DE-703 DE-824 DE-92 DE-1051 DE-634 DE-83 DE-11 DE-188 |
| physical | XIV, 352 S. graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Springer |
| record_format | marc |
| series | Algorithms and computation in mathematics |
| series2 | Algorithms and computation in mathematics |
| spellingShingle | Some tapas of computer algebra Algorithms and computation in mathematics Calcul formel ram Computerwiskunde gtt algèbre Lie inriac algèbre polynomiale inriac algèbre quaternion inriac base Gröbner inriac calcul formel inriac cinématique robot inriac code Golay inriac décodage inriac démonstration théorème inriac factorisation polynôme inriac groupe Mathieu inriac groupe fini inriac interpolation inriac programmation en nombres entiers inriac théorie codage inriac treillis inriac équation différentielle inriac Datenverarbeitung Algebra Data processing Computeralgebra (DE-588)4010449-7 gnd |
| subject_GND | (DE-588)4010449-7 (DE-588)4143413-4 |
| title | Some tapas of computer algebra |
| title_auth | Some tapas of computer algebra |
| title_exact_search | Some tapas of computer algebra |
| title_full | Some tapas of computer algebra Arjeh M. Cohen ... (ed.) |
| title_fullStr | Some tapas of computer algebra Arjeh M. Cohen ... (ed.) |
| title_full_unstemmed | Some tapas of computer algebra Arjeh M. Cohen ... (ed.) |
| title_short | Some tapas of computer algebra |
| title_sort | some tapas of computer algebra |
| topic | Calcul formel ram Computerwiskunde gtt algèbre Lie inriac algèbre polynomiale inriac algèbre quaternion inriac base Gröbner inriac calcul formel inriac cinématique robot inriac code Golay inriac décodage inriac démonstration théorème inriac factorisation polynôme inriac groupe Mathieu inriac groupe fini inriac interpolation inriac programmation en nombres entiers inriac théorie codage inriac treillis inriac équation différentielle inriac Datenverarbeitung Algebra Data processing Computeralgebra (DE-588)4010449-7 gnd |
| topic_facet | Calcul formel Computerwiskunde algèbre Lie algèbre polynomiale algèbre quaternion base Gröbner calcul formel cinématique robot code Golay décodage démonstration théorème factorisation polynôme groupe Mathieu groupe fini interpolation programmation en nombres entiers théorie codage treillis équation différentielle Datenverarbeitung Algebra Data processing Computeralgebra Aufsatzsammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008334785&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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