Becker T., Weispfenning V. — Groebner bases and commutative algebra :: Электронная библиотека попечительского совета мехмата МГУ

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Becker T., Weispfenning V. — Groebner bases and commutative algebra

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Название: Groebner bases and commutative algebra

Авторы: Becker T., Weispfenning V.

Аннотация:

The centerpiece of Grobner basis theory is the Buchberger algorithm, the importance of which is explained, as it spans mathematical theory and computational applications. This comprehensive treatment is useful as a text and as a reference for mathematicians and computer scientists and requires no prerequisites other than the mathematical maturity of an advanced undergraduate. Strong emphasis is placed on algorithms and their verification, with no sacrifices in mathematical rigor.

Язык:

Рубрика: Математика/Алгебра/Вычислительная алгебра/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1993

Количество страниц: 574

Добавлена в каталог: 12.03.2005

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

Предметный указатель

Least element      159
Length, ideal chain      323
Length, reduction chain      175
Lexicographical order on $\mathbb{N}^n$       168
Lexicographical term order      190
Lifting of syzygies      252
LINDEP      127
linear combination      121
Linear equation      250
Linear equation, homogeneous      244
Linear equations, homogeneous      489
Linear equations, inhomogeneous      489
Linear equations, system of      489
Linear hull      135
Linear map      120
Linear order      151
Linear quasi-order      151
Linearly dependent set      121
Linearly independent set      121
Linearly independent set, maximal      123
LL-reduction      499
LMINTERM      431
Local confluence      175
localization      55
Loop invariant      10
Lowest form      498
Lowest term      496
Map inclusion      7
Map, bijective      7
Map, injective      6
Map, linear      120
Map, one-to-one      6
Map, onto      6
Map, surjective      6
Maximal algebraically independent set      303
Maximal element      155
Maximal ideal      47
Maximal linearly independent set      123
Maximal strongly independent set      448
Membership test, ideal      86 215
Membership test, radical      268
Membership test, subring      269
Min-class      158
Minimal element      155
Minimal finite basis      161
Module of syzygies      136 244
Monadic primary ideal      358
Monic polynomial      71 194
Monoid      62
Monoid of terms      70
Monoid ring      64
Monoid, Abelian      62
Monoid, commutative      62
Monoid, computable      178
Monoid, ordered      167
Monomial      64 191
Monomials of a polynomial      71
Multivariate polynomial      64
Narrow quasi-order      160
Natural partial order on $\mathbb{N}^n$       189
Neutral element      16 62
Newman's lemma      176
Noetherian (ring)      87
Noetherian Induction      157
Noetherian relation      156
Noetherian ring      144
Normal form      175 196
Normal position      371
Normal strategy      225
NORMPOS      379
NORMPR/MDEC      373
Nullstellensatz, Hilbert      312
Nullstellensatz, weak      280
One-to-one      6
Onto      6
Operation, binary      15
Order      151
Order, admissible      167
Order, decidable      179
Order, inverse lexicographical      168
Order, lexicographical      168
Order, linear      151
Order, partial      151
Order, partial, associated with quasi-order      154
Order, partial, Koenig      165
Order, partial, natural on $\mathbb{N}^n$       189
Order, partial, strict      155
Order, quasi-      150
Order, quasi-, Dickson      160
Order, quasi-, linear      151
Order, quasi-, narrow      160
Order, well-quasi-      160
Ordered monoid      167
Ordered set      162
Partial order      151
Partial order, associated with quasi-order      154
Partial order, Koenig      165
Partial order, natural on $\mathbb{N}^n$       189
Partial order, strict      155
Partially ordered set      162
Partition      152
Perfect field      311
Permutation      7
PID      41
PID, computable      460
Polynomial      64
Polynomial reduction      195
Polynomial ring      64 77
Polynomial ring, multivariate      64
Polynomial ring, univariate      64
Polynomial, $\Gamma$ -homogeneous      466
Polynomial, constant      69
Polynomial, irreducible      88
Polynomial, minimal      294
Polynomial, monic      71 194
Polynomial, multivariate      64
Polynomial, primitive      93
Polynomial, separable      309
Polynomial, symmetric      502
Polynomial, symmetric, elementary      502
Polynomial, univariate      64
Power set      15
PREDEC      338
Primality test      382
Primary component      362
Primary component, embedded      363
Primary component, isolated      363
Primary decomposition      362
Primary ideal      351
Primary ideal, monadic      358
PRIMDEC      395
Prime      4 88
Prime (ring element)      87
Prime basis      315
Prime factor decomposition      91
Prime field      50
Prime ideal      47
Prime number      4 88
Prime ring      50
Primitive element      293
Primitive element, theorem on the      386
Primitive part      93
Primitive polynomial      93
Principal ideal      26
Principal ideal domain      41
Principal ideal ring      41
Product of relations      150
Projection      53
Proper      258
Proper ideal      25

Quasi-order      150
Quasi-order, Dickson      160
Quasi-order, linear      151
Quasi-order, narrow      160
Quasi-ordered set      162
Quotient      79
Quotient (ideal)      264
Quotient field      55
R-module      134
R-module, finitely generated      135
R-module, free      134
R-module, noetherian      135
Radical      393
Radical ideal      147
Radical membership test      268
RADICALMEMTEST      268
RANGE      5
Rank      134
Rational function field      94
REALZEROES      414
Recursion principle      9
REDGROEBNER      216
REDPOL      198
REDTERMS      423
Reduced (set of polynomials)      203
Reduced Groebner basis      208
Reduced terms      272
Reducible ideal      358
Reduction      203
Reduction polynomial      195
Reduction relation      174
Reduction relation, adequate      178
Reduction relation, confluent      175
Reduction relation, decidable      178
Reduction relation, locally confluent      175
Reduction, $\sigma$ -      504
Reduction, D-      453
Reduction, E-      463
Reduction, LL-      499
Reductum      194
Reflexive relation      150
Reflexive-transitive closure      155
Relation      149
Relation, antisymmetric      150
Relation, binary      149
Relation, connex      150
Relation, inverse      150
Relation, irreflexive      150
Relation, noetherian      156
Relation, reflexive      150
Relation, strictly antisymmetric      150
Relation, symmetric      150
Relation, transitive      150
Relation, well-founded      156
Relatively prime      38 43
Remainder      79
Representative      27
Residue class      27
Residue class ring      31
Restriction of a map      5
Ring      19 20
Ring of quotients      55
Ring with unity      19
Ring, boolean      283
Ring, commutative      19
Ring, computable      78 178
Ring, Noetherian      87 144
Ring, principal ideal      41
S-polynomial      211 457
scalar      119
Scalar multiplication      119 134
Second isomorphism theorem      36
Separable polynomial      309
Set of isolating intervals      408
Simple extension (field)      293
Squarefree      100
Squarefree decomposition      100
Squarefree part      100
SQUEEZE      412
stairs      424
Standard basis      496
Standard representation      218 454
Steinitz exchange theorem      132
STRCONST      438
Strict part of a relation      155
Strictly antisymmetric relation      150
Strictly ascending chain      155
Strictly descending chain      155
Strong dimension      443
Strongly independent set      443
Strongly independent set, maximal      448
Structure constants      434
Structure constants, combined      438
Sturm sequence      401
Sturm's theorem      407
STURMSEQ      405
Subfield      23
Subgroup      18
Submodule      135
Subring      22
Subring membership test      269
SUBRINGMEMTEST      270
subspace      120
Substitution homomorphism      75
Support      63
Surjective      6
Symmetric closure      154
Symmetric difference      17
Symmetric function      502
Symmetric polynomial      502
Symmetric polynomial, elementary      502
Symmetric relation      150
System of linear equations      489
System of unique representatives      152
Syzygies      136
Syzygies, (first) module of      136 244
Syzygies, lifting of      252
t-representation      219
Tangent cone      498
Term      70 188
Term order      189
Term order, $\Gamma$ -compatible      466
Term order, inverse lexicographical      190
Term order, lexicographical      190
Term order, total degree      191
Term, descending      502
Term, lowest      496
Terms of a polynomial      71
Theorem on the primitive element      386
Top-reduction      196
Total degree      70 71
Total degree order      191
Transcendence base      304
Transcendence degree      304
Transcendental element      293
Transcendental extension (field)      293
Transitive closure      154
Transitive relation      150
Translation lemma      200
Trivial ideal      25
UFD      90
UFD, computable      111
Unique factorization domain      90
Unique factorization domain, computable      111
Unique representatives      152
UNIT      20
Unity      19
Univariate exponent      345
Univaxiate polynomial      64
UNIVPOL      427

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