Cohen A.M., Cuypers H., Sterk H. — Some tapas of computer algebra :: Электронная библиотека попечительского совета мехмата МГУ

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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 algebra

Авторы: 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.
The contributions focus on topics like Gröbner bases, real algebraic geometry, Lie algebras, factorisation of polynomials, integer programming, permutation groups, differential equations, coding theory, automatic theorem proving, and polyhedral geometry.
This book is a must-read for everybody interested in computer algebra.

Язык:

Рубрика: Computer science/Компьютерная алгебра/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 352

Добавлена в каталог: 15.11.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

(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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