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Mishra B. — Algorithmic algebra
Mishra B. — Algorithmic algebra



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Название: Algorithmic algebra

Автор: Mishra B.

Аннотация:

Four main topics are covered: Gr<:;o>bner bases, characteristic sets, resultants and semialgebraic sets. The text is written for theoretical computer science students who would like to do research or understand the algorithmic underpinning of various commercial symbolic computations systems such as Mathematica, Maple, or Axiom. The book is self-contained, and focuses on very basic material. Problems with selected solutions are included.


Язык: en

Рубрика: Математика/Алгебра/Вычислительная алгебра/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1993

Количество страниц: 416

Добавлена в каталог: 12.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\lambda$-calculus      4
AAAS, American Association for the Advancement of Science      21
AAECC, Applicable Algebra in Engineering, Communication and Computer Science      21
Abelian group, congruence      26
Abelian group, residue class      26
ACM SIGSAM, Association for Computing Machinery, Special Interest Group on Symbolic and Algebraic Manipulation      21
ACS, American Chemical Society      21
Addition algorithm for algebraic numbers      332
AdditiveInverse algorithm for algebraic numbers      331
Adjoint      386
Admissible ordering      39 69
Admissible ordering, examples      40
Admissible ordering, lexicographic      40
Admissible ordering, total lexicographic      42
Admissible ordering, total reverse lexicographic      42
ALDES      8
Algebraic cell decomposition      225
Algebraic element      316
Algebraic integer      298 316
Algebraic number      298 316
Algebraic number, degree      319
Algebraic number, minimal polynomial      319
Algebraic number, polynomial      319
Algebraic set      139—140
Algebraic set, product      141
Algebraic set, properties      140—141
Algebraically closed field      138
Algol      13
ALPAK      8
ALTRAN      8
AMS, American Mathematical Society      21
Analytical engine      3
AND-OR tree      359
APS, American Physical Society      21
Ascending chain      173
Ascending set      173
Ascending set, ordering      174
Ascending set, type      173—174
assignment statement      15
Associate      201
Axiom      8 9
Back substitution      134
Bezout, identity      226
Bezout, inequality      182
Bezout, method of elimination      296
Boolean      14
Bound variables      354
CAD algorithm      351
Calculus ratiocanator      3
CAMAL      8 9
Cantorian/Weirstrassian view      5
Cell complex      352
Cellular decomposition      337
Characteristic set      20 167—168 174
Characteristic set, algorithm      181 186
Characteristic set, complexity      197
Characteristic set, extended      168 178
Characteristic set, general upper bound      183
Characteristic set, geometric properties      176
Characteristic set, geometric theorem proving      186
Characteristic set, irreducible      197—198
Characteristic set, zero-dimensional upper bound      182
Characteristica generalis      3
Chinese remainder theorem      223
class      172
Class, degree      172
Coding theory      10
Coherence      6
Colactor      386
Collin's theorem      352
COLOSSUS      3
Combinatorial algorithms      4
Computable field      73
Computable ring      72
Computational geometry      4 297—298 334
Computational number theory      4 10
Computer vision      10 297
Computer vision, generalized cones      10
Computer-aided design (CAD)      10 298
Computer-aided design, blending surfaces      10
Computer-aided design, smoothing surfaces      10
Computer-aided manufacturing (CAM)      10 297
Conditional and      15
Conditional or      15
Configuration space      10
Configuration space, forbidden points      11
Configuration space, free points      11
Congruence      26
Connected component      336
Connectivity      298
Connectivity graph      354
Connectivity, path connected      336
Connectivity, semialgebraically connected      336
Connectivity, semialgebraically path connected      336
Content      205
Coprime      205
Coset      25
Cyclic submodule      52
Cylindrical algebraic decomposition, CAD      298 337 348 359
Data structures      7
Decomposition      298
DEDUCE      3
Delineability      339
dependent variables      141
Deque      14
DETACH algorithm      92
Detachability      71—72 87—92 213
Detachability, correctness      92
Detachability, detachable ring      72
Detachabilityin Euclidean domain      213
Determinant      386
Determinant polynomial      241—242
Dickson's lemma      36—37 69
Differentiation      239
DIMENSION      186
Discriminant      225 240
divisors      199
Divisors, common      200
Divisors, maximal common      200
Divisors, proper      201
EDVAC      3
Effective Hilbert's Nullstellensatz      166
Eliminant      225
Elimination ideal      136—137
Elimination theory      2 20 225
ENIAC      3
Entsheidungsproblem      3
Euclid's Algorithm      213 226
Euclidean Domain      199 208
Euclidean polynomial remainder sequence, EPRS      248
Euler's method of elimination      296
Extended characteristic set      168 178—179
Extended characteristic set, geometric properties      180
Extended-Euclid algorithm      214
Extension field      29
Factor      199
Factor, proper factor      201
Factorization      200 223
Field      14 29
Field of fractions      30 197
Field of residue classes rood p, $\mathbb{Z}_p$      29
Field, algebraically closed      138
Field, characteristic      29
Field, examples      29
Field, extension field      29
Field, multiplicative group of the field      29
Field, prime field      29
Field, quotient field      30
Field, residue classes rood p, $\mathbb{Z}_p$      29
Field, subfield      29
Filtration      69
FindZeros algorithm      150
Finite solvability      145 149 190
FiniteSolvability algorithm      149
First module of syzygies      54
for-loop statement      17
FORMAC      8
Formal derivative      311
Formal power series ring      70
Formally real field      297 300
Fourier sequence      320 325
Free module      52 69
Free variables      35
Full quotient ring      30
Full ring of fractions      30
Fundamental theorem of algebra      302
G-bases      70
Gap theorem      186;
Gauss lemma      211—212
Gaussian elimination      133
Gaussian polynomial      320
Generalized pseudoremainder      171 175
Generic point      197
Generically true      187
Geometric decomposition      198
Geometric theorem proving      10 198 297
Geometry statement      187
Geometry statement, degeneracies      187
Geometry statement, elementary      187
Greatest common divisor, GCD      17—18 36 204
Greatest common divisor, polynomials      226
Groebner algorithm      85
Groebner algorithm, modified      88 90
Groebner basis      20 23 44 69 79 84—85
Groebner basis, algorithm      80 85
Groebner basis, applications      71 103—108
Groebner basis, complexity      131—132
GroebnerP algorithm      84
groups      14 24 69
Groups, Abelian      24
Groups, coset      25
Groups, examples      24
Groups, left coset      25
Groups, product of subsets      25
Groups, quotient      26
Groups, right coset      25
Groups, subgroup      25
Groups, symmetric      24
H-bases      70
Habicht's theorem      274—275
Head coefficient      43 205
Head monomial      43
Head monomial ideal      44
Head monomial, examples      43
Head monomial, head coefficient      43 205
Head monomial, head term      43
Head reducible      80
Head reduct      80
Head reduction      71 80
HeadReduction algorithm      83
HeadReduction algorithm, modified      88—90
Hensel's lemma      223
Hilbert Basissatz      69
Hilbert's basis theorem      6 23 48 69 71
Hilbert's basis theorem, stronger form      102—103
Hilbert's Nullstellensatz      13 134 142—143 182 226
Hilbert's program      3
Homomorphism      31
Homomorphism, image      31
Homomorphism, kernel      31
Homomorphism, module      50
Ideal      23 28 69 139
Ideal basis      23 28
Ideal congruence      71
Ideal congruence problem      103
Ideal contraction      32
Ideal dimension      141
Ideal equality      71
Ideal equality problem      103—104
Ideal extension      33
Ideal intersection      103 105
Ideal map      139
Ideal membership      71
Ideal membership problem      87 103 178
Ideal membership problem, prime ideal      178 197
Ideal membership problem, using characteristic sets      178
Ideal operations      33 103—107
Ideal power      33
Ideal principal      28
Ideal product      33 71 103—104
Ideal quotient      34 103 106—107
Ideal sum      33 103—104
Ideal, annihilator      34
Ideal, codimension      141
Ideal, comaximal      34
Ideal, coprime      34
Ideal, generated by      28
Ideal, Groebner basis      23
Ideal, Hilbert's basis theorem      23
Ideal, ideal operations      33
Ideal, improper      28
Ideal, intersection      33
Ideal, modular law      34
Ideal, monomial ideal      37
Ideal, proper      28
Ideal, properties of ideal operations      34
Ideal, radical      34
Ideal, subideal      28
Ideal, system of generators      28
Ideal, zero-dimensional      145
IEEE, The Institute of Electrical and Electronics Engineers      21
if-then-else statement      16
Indecomposable element      200
Independent variables      141
Indeterminate      35
Initial polynomial      173
Integral domain      29
Integral element      316
Intersection of ideals      71
interval      14 299
Interval representation      327
Interval, closed      299
Interval, half-open      299
Interval, open      299
IntervalToOrder conversion algorithm for algebraic numbers      330—331
Isolating interval      324
ISSAC, International Symposium on Symbolic and Algebraic Compntation      21
Jacobian conjecture      196
Journal of Symbolic Computation, JSC      21
Kapur's ALGORITHM      192
Laplace expansion formula      386
Least common multiple, LCM      36 204
Leibnitz wheel      3
Lexicographic ordering      40 136
Lexicographic ordering, generalization      137 142
Lingua characteristica      3
Lisp      4
Loop statement, until      16
Loop statement, while      16
Macdonald — Morris conjecture      9
Macsyma      8 9
Maple      9
Mathematica      9
MATHLAB-68      8 9
Matrix      385
Matrix addition      385
Matrix determinant      386
Matrix multiplication      385
Matrix of a polynomial      242
Matrix, adjoint      386
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