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Cohen A.M., Cuypers H., Sterk H. — Some tapas of computer algebra
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Название: Some tapas of computer algebraАвторы: Cohen A.M., Cuypers H., Sterk H.Аннотация: This book arose from a series of courses on computer algebra which were given at Eindhoven Technical University. Its chapters present a variety of topics in computer algebra at an accessible (upper undergraduate/graduate) level with a view towards recent developments. For those wanting to acquaint themselves somewhat further with the material, the book also contains seven 'projects', which could serve as practical sessions related to one or more chapters.
Язык: Рубрика: Computer science /Компьютерная алгебра /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1999Количество страниц: 352Добавлена в каталог: 15.11.2005Операции: Положить на полку |
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(lattice) basis 67 (regular) d-couple 150 -t 186 action 100 185 Additive group 221 Algebra 91 Algebraic subgroup 219 Algorithm, Arimoto — Peterson — Gorenstein — Zierler 268 Algorithm, Berlekam — Massey 270 Algorithm, Berlekamp 78 Algorithm, Brouwer 241 Algorithm, Buchberger 1 10 Algorithm, Cantor — Zassenhaus 81 Algorithm, decoding cyclic codes 264 Algorithm, Euclid 68 269 Algorithm, extended Euclidean 15 Algorithm, ExtendedGroebnerBasis 28 Algorithm, ExtendedReduce 23 Algorithm, factorisation 84 86 Algorithm, FGLM 45 Algorithm, Gram — Schmidt 70 Algorithm, GroebnerBasis 10 Algorithm, GroebnerVectorSyzygies 26 Algorithm, Hensel 85 Algorithm, Kovacic 208 224 Algorithm, LLL 66 74 Algorithm, membership 192 Algorithm, minimum distance 241 Algorithm, normal closure 196 Algorithm, orbits 194 Algorithm, Reduce 7 Algorithm, Risch 209 Algorithm, Schreier — Sims 192 193 Algorithm, stabilizer 191 Algorithm, StronglyReduce 8 Algorithm, Sugiyama 269 Algorithm, Syzygies 28 Algorithm, Todd Cooieter 197 Base 192 Bases 2 BCH bound 248 Bezout relation 152 Bezoutian 59 Binomial ideal 175 Birkhoff Interpolation Problem 298 Bounded distance decoder 261 Cauchy index 123 Central 91 Centre 91 Code 237 Coincidence 201 Collapse 201 Commutative algebra 91 Complete intersection polynomial systems 58 Composition series 100 Condition, irrelevant 283 Condition, nontrivial 283 Condition, relevant 283 Condition, trivial 283 Condition, true nondegeneracy 289 consecutive 158 Content 82 Coset enumeration 197 Coset enumeration, Todd — Coxeter 197 Coset table 198 Coxeter group 315 Cyclic code 247 Decoder 260 Defective 151 Defining set 247 Defining set, complete 247 Degree 185 dependent variables 278 Derived series 106 Descending central series 106 Determinant 67 Differential field 217 Differential Galois group 219 DIMENSION 287 Distinct degree factorisation 81 Dorroh extension 97 Dual code 238 Dualizing 58 Effective 1 2 Equality standard form 169 Equivalent 239 321 Error-locator ideal 272 F-algorithm 96 Factor algebra 92 Factor module 100 Factorisation 78 Factorisation, distinct degree 81 feasible 168 169 Field of constants 217 Field of formal Laurent series 216 Galois correspondence 218 Galois group 218 Gaussian remainder 154 Gaussian remainder sequence 154 GENERATED 2 Generator polynomial 247 Generators 187 GENERIC 168 Generically false 291 Generically true 289 Geometrically independent variables 287 Geometrically true 279 Geometrically true under the condition 282 Golay codes 338 Graded lex order 41 Graded reverse lex order 41 Gram-matrix 67 Gram-Schmidt coefficients 70 Groebner basis 10 Groebner basis of a lattice 175 Groebner basis, reduced 13 Group algebra 92 Group permutation 185 H-trace bilinear form 48 Hadamard’s inequality 70 Hamming code 239 Hamming distance 238 Hensel lift 84 Hermite quadratic form 48 Homogeneous 216 Homomorphism 92 Hypotheses ideal 279 Hypotheses variety 279 Hypotheses+condition variety 282 Icosahedral group 223 315 icosahedron 315 Ideal 2 92 Ideal generated by a subset 35 Ideal of nondegeneracy conditions 283 Idempotent 92 Imprimitive 223 Incidence matrix 298 Independent modulo the ideal 287 Independent variables 278 Inequality standard form with upper bounds 177 Inhomogeneous 216 Integer programming 169 Integral vector 169 Irreducible 100 317 Jacobian 59 Jacobson radical 92 Katsura3 55 Key equation 269 Las Vegas algorithms 96 Lattice 67 175 Lattice ideal 175 Leading coefficient 7 Leading monomial 7 Leading term 7 Least common multiple 9 Left ideal 92 Lemma of Gauss 82 Lexicographic order 5 40 Lexicographic total degree order 5 Lie algebra 105 Lie algebra, factor algebra 106 Lie algebra, homomorphism 106 Lie algebra, ideal 106 Lie algebra, nilpotent 106 Lie algebra, solvable 106 Lie algebra, subalgebra 106 Linear code 238 Linear Lie algebras 106 Linear programming problem 168 Liouvillian 220 LLL 66 LLL-reduced 71 Local differential Galois group 225 Local ring 46 Locally a given graph 332 Locator polynomial 249 MacWilliams identity 239 Mathieu group 327 328 Matrix of syndromes 255 Matrix representation 100 Mattson — Solomon polynomial 248 Minimal Groebner basis 13 Minimal polynomial 312 Minimum distance 238 Minimum distance decoder 261 Module 92 Module isomorphism 100 Monic 14 35 Multiplicative group 221 Multiplicity 46 100 123 Newton sum 51 Newton’s formula 52 Nilpotent 92 Nilpotent ideal 93 Nilradical 106 Noetherian 2 Non-optimal 171 Nondegeneracy condition 283 Norm 113 normal 298 Normal form 16 41 Not generically true 289 Octahedral group 223 Optimal 168 Orbit 186 Orbital 318 Order 216 226 Order function 252 Partial base 193 Partial strong generating set 193 Permutation group 185 Permutation representation 185 Picard — Vessiot field 219 Picard — Vessiot theory 219 Poise-indicator 299 Poised 298 Polar multiplicity 123 Polya Condition 299 Polyhedron 168 Polytope 168 Primary factors 78 primitive 82 Principal 36 Projective system 242 Quotient in the signed Euclidean division 125 Quotient ring 4 Radical 38 106 Rank 67 Rational univariate representation 53 Reduced 8 Reduced form 8 Reduced Groebner basis 13 Reduced Groebner basis of a lattice 175 Reduction order 5 Reed — Muller codes 256 Reed — Solomon codes 256 Regular 46 164 Regular couple 150 Regular representation 92 Relator 197 Relator table 198 Remainder 8 Representation, linear 316 Representation, permutation 185 Resultant 209 Riccati equation 224 Right ideal 92 S-polynomial 9 Schreier elements 190 Schreier generators 190 Schreier tree 188 Second symmetric power 230 Semisimple 93 Separating 39 Sequence of principal Sylvester — Habicht coefficients 151 Sifting 193 Signature 134 Signed Euclidean transition matrix 125 Signed remainder sequence 124 SIMPLE 92 100 Solution 169 Solutions 35 Specialization 131 Specialization problems 126 specialized 126 Splitting element 111 Splitting field 218 Square-free decomposition 210 Stabilizer 186 Stabilizer chain 192 Standard 15 Strong generating set 192 Strongly nilpotent 92 Strongly reduced 9 Structure constants 95 Sturm Query 134 Sturm sequence 124 Sturm — Habicht sequence 130 Subalgebra 91 Subgroup table 198 Submodule 100 Support 238 Sylvester matrix 150 Sylvester sequence 124 Sylvester — Habicht sequence 151 Sylvester — Habicht transition matrix 158 Symmetric group 185 Syzygies 24 Terms 3 Test set 169 171 177 Tetrahedral group 223 Thesis variety 279 Thorn code 142 Total degree 5 35 Total degree order 5 Trace form 134 Trace matrix 50 147 Transitive 186 Under the staircase 40 Unimodular 125
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