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| Bykov V., Kytmanov A., Lazman M. — Elimination methods in polynomial computer algebra |
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| Предметный указатель |
Analytic calculation 173
Analytic polyhedron 21
Basis of Groebner 187
Basis of Groebner, reducing 188
Bernoulli numbers 11
Complete sum of residues 35
Complex chemical reaction 99
Complex line 35
Computer algebra 173
Computer algebra, basic problems 179
Computer algebra, methods and algorithms 184
Corollary, Aizenberg 40
Corollary, Bolotov 87
Corollary, Kytmanov 35
Corollary, Yuzhakov 35
Cycle characteristic 146
Derivative, formal 2
Derivative, logarithmic 3
Derivative, logarithmic, multidimensional 64
Discriminant 28
Elimination of unknowns 24
Equation, Cauchy — Riemann 2
Equation, Cauchy — Riemann, multidimensional 21
Equation, chemical kinetics 99
Equation, chemical kinetics, stationary case 99
Expansion, Laurent 3
Expansion, Taylor 1
Form, Hankel 13
Form, meromorphic differential 17
Form, quadratic 11
Formula, Euler — Maclaurin 96
Formula, logarithmic derivative of resultant 64
Formula, Newton recursion for meromorphic function 10
Formula, Newton recursion for polynomial 6
Formula, Newton recursion for system of algebraic equation 78 85
Formula, tranformation of local residue 19
Formula, tranformation of local residue, generalized 31
Formula, Waring, for meromorphic function 10
Formula, Waring, for polynomial 8
Function, holomorphic 1
Function, holomorphic, multidimensional 17
Function, rational 1
Function, rational, multidimensional 17
Higher homogeneous part of polynomial 36
Homogeneous coordinates 60
Ideal, polynomial 187
Index, Cauchy 14
Index, Poincare 93
Infinite plane 35
intermediate 99
Jacobian 18
Maple procedure for resultant of an algebraic system 208
Maple procedure for resultant of two polynomial 193
Mappings holomorphic 17
Mappings holomorphic, nonsingular 21
Mass conservation law 100
Mathematical kinetics 99
Mechanism of chemical reaction, many-route 162
Mechanism of chemical reaction, single-route 137
Mechanism of chemical reaction, three stage 154
Mechanism of chemical reaction, three stage, of oxidation 104
Mechanism of chemical reaction, three stage, on catalyst 127
Mechanism of chemical reaction, two stage nonlinear 153
Mechanism of chemical reaction, two-route 166
Method of elimination, classical 29
Method of elimination, modified 42
Method of elimination, modified, with parameter 48
Monomial, multidimensional 36 116
Multiplicity of a root (zero) of holomorphic function 3
Multiplicity of a root (zero) of holomorphic mapping 21
Neighborhood 17
Orientation of a boundary 1
Orientation of a cycle 17
Permanent 61
Plurality of steady states 195
Polyhedron of chemical reaction 100
Polynomial 1
Polynomial, homogeneous 35
| Polynomial, kinetic 137
Polynomial, Laurent 38
Polynomial, multidimensional 17
Power series 1
Power series, multidimensional 16
Power sum 6
Power sum, multidimensional 77
Pseudopower sum 77
Rate of chemical reaction 100
REDUCE procedure for Groebner basis 199
REDUCE procedure for resultant 217
Residue, global 35 63
Residue, local 2
Residue, local, of Grothendieck 17
Residue, logarithmic 2
Residue, logarithmic, multidimensional 21
Resultant 24
Resultant of a polynomial with respect to a system 48
Resultant of Sylvester 24
Root of a system of equations 36
Root of a system of equations on infinite plane 36
Root, positive 133
Scheme of transformation 99
Scheme of transformation without interactions 156
Scheme of transformation, linear 152
Scheme of transformation, short 101
Scheme of transformation, short, parallel 101
Scheme of transformation, short, sequential 116
Series, Sturm 15
Series, Sturm, generalized 15
Series, Taylor 4
Sign change 12
Simplex of chemical reaction 100
Skeleton 21
Space, projective 35
Space, theory of functions 60
Stage of chemical reaction 99
Steady stage (s.s.) 99
Stoichiometric coefficients 99
Substance 100
System of algebraic equations 36
System of algebraic equations, nondegenerate 36
System of computer algebra 175
System of computer algebra, Maple 175
System of computer algebra, REDUCE 175
System of resultants 29
Theorem on logarithmic residue 4
Theorem, Aizenberg — Bolotov — Tsikh 89 90
Theorem, Aizenberg — Kytmanov 78 80
Theorem, Aizenberg — Tsikh 40
Theorem, Bezout 39
Theorem, Budan — Fourier 16
Theorem, Cacciopoli — Martinelli — Sorani 22
Theorem, Cauchy 2
Theorem, Cauchy — Poincare 21
Theorem, Descartes 16
Theorem, Dubovitskii 183
Theorem, Hermite 12
Theorem, Hilbert (Nullstellensats) 37
Theorem, Jacobi 11
Theorem, Kytmanov 31 38 64 71 75 85 91 95 152
Theorem, Kytmanov — Mkrtchyan 85 87
Theorem, Macaulay 37
Theorem, Rouche 5
Theorem, Rouche, multidimensional 23
Theorem, Sturm 15
Theorem, Sylvester 24
Theorem, Tarkanov 93
Theorem, Tarski — Seidenberg 181
Theorem, Tsikh 61 62
Theorem, Yuzhakov 23 52 58
Total degree 16
Vector of balance 16
Zero of holomorphic function 3
Zero of holomorphic mapping 17
Zero, real, of a polynomial 11
Zero, real, of holomorphic mappings 89
Zero, simple 3
Zero, simple, of holomorphic mappings 21
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