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Gatermann K. — Computer Algebra Methods for Equivariant Dynamical Systems
Gatermann K. — Computer Algebra Methods for Equivariant Dynamical Systems



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Название: Computer Algebra Methods for Equivariant Dynamical Systems

Автор: Gatermann K.

Аннотация:

This book starts with an overview of the research of Gröbner bases which have many applications in various areas of mathematics since they are a general tool for the investigation of polynomial systems.
The next chapter describes algorithms in invariant theory including many examples and time tables. These techniques are applied in the chapters on symmetric bifurcation theory and equivariant dynamics.
This combination of different areas of mathematics will be interesting to researchers in computational algebra and/or dynamics.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 154

Добавлена в каталог: 18.11.2009

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