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| Glenn O.E. — A Treatise on the Theory of Invariants |
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| Предметный указатель |
Absolute covariants 2 42
Algebraically complete systems see “fundamental systems”
Anharmonic ratio 3
Annihilators: binary 25
Annihilators: ternary 189
Anti-seminvariants 176 179
Apolarity 51 173
Arithmetical invariants 12 32 48 157
Aronhold's polar operators 46
Associated forms 158
Bezout's resultant 168
Bilinear invariants 51
Boolean concomitants of a linear form 156
Boolean concomitants of a quadratic 157
Canonical forms: binary cubic 108
Canonical forms: binary quartic 111
Canonical forms: binary sextic 112
Canonical forms: ternary cubic 111
Class of ternary form 230
Classes in modular theory 204
Co variant curves 171
Cogrediency 20
Combinants 162
Complete system: absolutely 129
Complete system: relatively 130
Conic, system of 224
Contragrediency 212
Contravariants 228
conversion operators 70
Convolution 93 220
coordinates 15
Covariants: definition 23
Covariants: systems 144—161
Covariants: universal 32
Cubic, binary: canonical form 108
Cubic, binary: fundamental system 68 100 141
Cubic, binary: syzygy 107 110 161
Cubic, ternary: canonical form 111
Cubic, ternary: fundamental system 225
Cubic, ternary: semi-discrimiuants 193
Degree 20
Determinant, symbolical 55 170
Differential equation, satisfied by combinants 163; see “also annihilators”
Differential invariant 9
Diophantine equations 116
Discriminant 4 31
Eliminant 30
End coefficients 179
Euler's theorem 44
Existence theorem 40
Factors of forms 69 191
Fermat's theorem 14 21
Finiteness: algebraical concomitants 66
Finiteness: formal-modular concomitants 204
Finiteness: modular concomitants 204
Formal modular concomitants 12 157
Fundamental systems 144 161 204 223 225
Geometry of point ranges 78
Gordan's proof of Hilbert's theorem 112
Gordan's series 83
Gordan's Theorem 128
Grade of binary concomitant 123
Grade of ternary concomitant 220
Group of transformations 18
Group, the induced group 19
Harmonically conjugate 6
Hermite's reciprocity theorem 76
Hesse's canonical form 111
Hessians 28
Hilbert's theorem 112
Identities, fundamental: binary 66
Identities, fundamental: ternary 218
INDEX 34
Induced group 19
Inflexion points 171
Intermediate concomitants 47
Invariant area 1
| Invariants: formal modular 157 204
Invariants: fundamental systems 144—161
Invariants: modular 203
Involution 78
Irreducible systems see “fundamental systems”
Isobarism 35
Jacobians 27
Jordan's lemma 119
Line equation of conic 223
Line equation of cubic 229
Line equation of form of order m 230
Linear transformations 15
Linearly independent seminvariants 178 205
Mixed concomitants 228
Modular: concomitants 203
Modular: forms 203
Modular: transformation 12
Operators see “annihilators”
Operators, Aronhold 46
operators, conversion 70
Parametric representation 169
Partitions 238
Polars 42
Projective properties 78
Quadratic 65
Quadric 225
Quartic 89
Quaternary form 33
Quintic 147
Range of points 78
Rational curves 169
Reciprocity, Hermite's law 76
Reduction 64 83
Representation, typical 159
Resultants 29 166 168
Resultants in Aronhold's symbols 151
Robert's theorem 179
Roots, concomitants in terms of 69
Semi-discriminants 193
Seminvariants: algebraic 175
Seminvariants: modular 205
Sextic, canonical form of 112
Simultaneous concomitants 23
Skew concomitants 39
Standard method of transvection: binary 57
Standard method of transvection: ternary 219
Stroh's series 89
Symbolical theory: binary 53
Symbolical theory: ternary 209
Symmetric funtions: binary 69
Symmetric funtions: ternary 191
Symmetry 39
Syzygies: algebraic 104
Syzygies: modular 208
Tables: I. Concomitants of binary cubic 68
Tables: II. Concomitants of binary quartic 89
Tables: III. System of quadratic and cubic 147
Tables: IV. System of quintic 150
Tables: V. Semi-discriminants of ternary cubic 200
Tables: VI. Modular system of quadratic 204
Tables: VII. System of ternary cubic 225
Ternary quantics: fundamental systems 223 225
Ternary quantics: symbolical theory 209
Ternary quantics: transvection 219
Transformations, non-linear 9; see “linear transformations”
Transformed form: binary 16
Transformed form: ternary 187
Translation principle: Clebsch's 228
Translation principle: Meyer's 169
Transvectants, binary: definition 51
Transvectants, binary: theorems on 92
Transvectants, ternary: definition 209 219
Transvectants, ternary: theorems on 220
Types 48
Typical representation 159
Uniqueness of canonical reduction 109 112
Universal covariants 32 212
Weight 34
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