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| Gatermann K. — Computer Algebra Methods for Equivariant Dynamical Systems |
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| Предметный указатель |
Algebraic extension 29
Algebraic group 68 108
Algebraic relations 53
Algorithm, Buchberger 10
Algorithm, completeness 53
Algorithm, equivariants 64 70 84 85
Algorithm, FGLM 31
Algorithm, invariants 57 68 81
Algorithm, torus invariants 69
Bergman 13
Bifurcation subgroup 97
Bipartite graph 33
Bipartite graph, matching 34
Buchberger algorithm 10 24 27 39 40 61
Buchberger criteria 11
Canonical basis 58
Cartan decomposition 62
Cartan subalgebra 63
Center manifold reduction 98
Characteristic sets 43
CoCoa 13
Cohen — Macaulay module 84
Cohen — Macaulay ring 76 79 117
Compact Lie group 48
Conjugate group 96
Contact equivalent 98
Cyclo hexane 22 111
Depth 75
DIMENSION 6 43
Division algorithm 6 11 66
Elimination 110
Elimination ideal 44
Equivariant 49
Equivariant branching lemma 97 100
Equivariants 110
Exact solution 106
Face 6
Facet 6
Fixed point space 96
Flow-invariant 123
Fractal walk 32
Function, generating 17
Fundamental equivariants 49
Fundamental invariants 49
Gap 98
GB 13
Graded 3
Graded algebra 49
Graded lexicographical ordering 2
Grading 13
Grading, Kronecker 15
Grading, natural 3
Grading, weighted 3
grevlex 2
grlex 2
Groebner basis 5 108
Groebner basis, comprehensive 13
Groebner basis, detection 31 32 36
Groebner basis, minimal 7
Groebner basis, non-commutative 13
Groebner basis, reduced 7
Groebner basis, truncated 15 16
Groebner walk 31
Group orbit 106
H-basis 9
Haar measure 51
Hamiltonian 69 121
Head term 5
Hilbert basis 49 105 114
Hilbert mapping 106
Hilbert polynomial 19
Hilbert series 19 81 122
Hilbert — Poincare series 17 21 39 60
Hironaka decomposition 80 100
Homogeneous 3
Homogeneous system of parameters 74
Hopf bifurcation, secondary 99
Hopf bifurcation, symmetric 99
Ideal of definition 74
Ideal, elimination 44
Initial ideal 5
integral 74 118
Invar 82
Invariant ideal 107
Invariant ring 49 81
Isotropy group 96
Isotropy subgroup 116
Isotropy subgroup lattice 97
Kantororich trick 83
Kantorovich trick 119
| Kronecker grading 15
Krull dimension 74 75
Leading term 5
lexicographical ordering 2
Liapunov Schmidt reduction 98
Lie algebra 56
Lie group 56
Local ring 74
M-regular 75
m-sequence 75
Macau lay 13 22
Macaulay basis 9
Magma 13
Matrix term order 6
Minimal Groebner basis 7
Mode interaction 66
Module, graded 13
Molien series 50
Natural grading 3
Newton poly tope 6
Noether normalization 43 45 75 77 86 117
Noetherian 2 11
Normal form 6 45
Normal, outer 6
Nullcone 67 107 119
Orbit 96
Orbit space reduction 105 114
Orbit type 96
Ordering 2
Ordering, elimination 44
Ordering, graded lexicographical 2
Ordering, graded reverse lex 2
Ordering, lexicographical 2
Parameters 45 74 77
Polynomial, invariant 48
Polynomial, sparse 36
Primary invariant 79
Primary invariants 100
Quotient ring 7 55
Reduce 28
Reduced Groebner basis 7
Reductive group 81
Relevant subgroups 97
Residues 52
Resonance 69 121
Resultant 43
Reynolds operator 55
Reynolds projection 108
Reynolds, equivariant 61
Root spaces 62
S-polynomial 10 11
S-polynomial, homogeneous 16
Sagbi basis 58
Secondary invariants 79 100
Semi-algebraic set 115
Sequence, regular 75
Series, Hilbert — Poincare 17
Series, Molien 50
singular 82
Standard basis 132
Standard monomials 7
Stanley decomposition 90 93 124
State polytope 31
Strata 115 116
Stratification 115 116
Stratification, natural 115
Stratification, secondary 115
Sugar selection strategy 11
Support 6
Symcon 97
Symmetric systems 109 111
Symmetry adapted coordinates 125
Syzygy 10
Tangent cone 132
Taylor — Couette 125
Tdeg 2
Term order 2
Term order, matrix 6
Theorem (Bierstone) 115
Theorem (Poenaru) 100
Theorem (Schwarz) 100
Torus 69
Unfolding parameter 98
Walk, Fractal 32
Walk, Groebner 31
Weight space 63
Weight system 18
Weighted degree 3
Weights 3
Weyl group 51
Weyl integral formula 50
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