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| Mishra B. — Algorithmic algebra |
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| Предметный указатель |
 -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,  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, 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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