|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Grace J.H., Young A. — The Algebra of Invariants |
|
|
|
| Предметный указатель |
Alexeleff 367 368
Algebraically complete system for binary forms 150
Algebraically complete system for ternary forms 265
Anharmonic ratio see “Cross-ratio”
Apolarity of binary forms, application to canonical forms 229
Apolarity of binary forms, defined 213
Apolarity of binary forms, forms of different orders 225
Apolarity of binary forms, the cubic apolar to three given cubics 220
Apolarity of binary forms, the forms of order n apolar to a given m-ic ( ) 228
Apolarity of binary forms, the n linearly independent forms of order m apolar to a binary m-ic () 226
Apolarity of binary forms, the n linearly independent forms of order n apolar to a binary n-ic 214
Apolarity of binary forms, there are s linearly independent forms of order n apolar to n-s+1 given binary n-ics 220
Apolarity of ternary forms of curves in general 303
Apolarity of ternary forms of two conies 299
Apolarity of ternary forms, conics apolar to fundamental conic 308 310
Apolarity of ternary forms, cubics which possess an apolar conic 312
Apolarity of ternary forms, curves which possess an apolar conic 304
Apolarity of ternary forms, quartics which possess an apolar conic 313
Argand diagram, interpretation of invariant properties of binary forms by means of the 208
Aronhold 70 84 357
Aronhold operator is invariantive 31 32
Associated forms 148 157
Ausdehnungslehre 279
Baker 298
bezout 318
Brianchon 280
Canonical forms 233 234 235
Canonical forms for quintic 231
Canonical forms for sextic 231 232
Capelli 359 360
Catalecticant of binary forms of even order 232
Catalecticant of ternarv quartic 318
Cayley 3 84 131 365
Chemico-algebraic theory 366 367 368
Ciamberlini 274
Circle, director 302
Circle, self-conjugate 302
class 255
Clebsch 31 132 138 147 150 157 255 265 271 274 326
Clifford 288
Cogredient, sets of variables, forms with 40 60 61
Cogredient, transformation defined 36
Combinants 314—318
Complete systems 85 109
Complete systems, completeness of system derived from two 111 113 114
Complete systems, relatively 109 110
Complex variable 208—212
Concomitant, mixed 255
Conic, apolar see “Apolarity of ternary forms”
Conic, binary quadratic and geometry of 235—240
Conic, polar 251 256
Conic, ternary quadratics and geometry of two 288—294
Conjugate lines 300 302
Conjugate points 300
Contragredience of point and line coordinates in ternary forms 255
Contragredience, defined 36
Contragredience, fundamental property of 37
Contravariant 255 256
Convolution, defined 40 41
Coordinates, line 255 361
Copied forms 80 81 82
Covariants of binary forms with several sets of variables 40
Covariants of binary forms, defined 8
Covariants of binary forms, symbolical expression of 16 17 18
Covariants of degree four 71—74 76 77
Covariants of degree three 62—71
Covariants of ternary forms, symbolical expression of 250
Cross ratio of the roots of a quartic 204—206
Cross ratio of the roots of two quadratics 192 193
Cross ratio, cross ratios of roots of a quantic and the invariants 189—191
Cross ratio, defined 186
Cubic, binary, associated forms for 157
Cubic, binary, cubic apolar to three given cubics 220 221
Cubic, binary, geometry of 193 194
Cubic, binary, geometry on Argand diagram of 211 212
Cubic, binary, irreducible system for one 89—91 122
Cubic, binary, irreducible system for quadratic and 164 165
Cubic, binary, irreducible system of types of 323—325
Cubic, binary, pencil of cubics  194—197
Cubic, binary, pencil of cubics having a given Jacobian 241 242
Cubic, binary, range formed by three points and one of their Hessian points is equian-harmonic 196 211
Cubic, binary, rational plane cubic curve represented by 221—224
Cubic, binary, Syzygy for 96
Cubic, binary, transvectants of 96 97 194
Cubic, binary, twisted cubic curve and binary cubics 240—242
Cubic, ternary, canonical form for 312 313
Cubic, ternary, has three linearly independent apolar conies 304
Cyclically projective range 196
Darboux 306
Degree defined for binary forms 9
Degree defined for ternary forms 255
Determinant formed by coefficients of n+1 binary n-ics is a reducible invariant if n is odd 350
Determinant formed by coefficients of n+1 binary n-ics is an irreducible invariant if n=4 350
Differential equation whose coefficients are polynomials can be reduced to a relation between transvectants 873
Diophantine equations 102—106
Discriminant of binary cubic 194
Discriminant of binary forms 191
Discriminant of binary quadratic 86
Discriminant of binary quartic 199
Discriminant, tangential equation of curve found from the 266 267
Double points 223 224
Duality, principle of 256 257 267
Elliott 61 150 157 366
Equianharmonic range formed by cubic and one of its Hessian points 196 211
Faltung 40
Forsyth 264 265
Franklin 131
Fundamental theorem for binary forms 25—27 31—35
Fundamental theorem for ternary forms 258—264
Generating function 330
Gordan 61 67 68 85 128 131 132 138 150 169 274 294 326 860 367 868
Gordan's proof of Hilbert's lemma 178—182
Gordan's series, coefficients of 53—55
Gordan's series, deductions from 55—57
Gordan's series, existence proved 45 46
Gordan's series, inversion of 59 60
Gordan's Theorem 101 118—121
Grace 326 378
Grade of covariants of degree four 77
Grade of covariants of degree three 66 67
Grade, classification by 119—121
Grade, defined 62
Grassmann 279
Groups, continuous 6 7 38
Groups, continuous, finite substitution, introduction to 339—344
Groups, continuous, negative symmetric group 345—851
Groups, continuous, positive symmetric group 345 346 357
Gundelfinger 132 232
Harmonic quadrilateral 301
Harmonic range 191 192 203 207 272
Harmonically circumscribed conic 300
Harmonically concyclic points 209
Harmonically inscribed conic 300
Hesse 306
Hessian identically vanishes when quantic is a perfect nth power and conversely 193 235
Hessian is a covariant 3 16 17
Hessian of binary cubic defines the double point on the corresponding cubic curve 224
Hessian of ternary forms 249
Hessian points of a cubic 195 196 207 211 212
Hessian, defined 3
hilbert 145 169 274
Homographic ranges 187 188
Homographic ranges transformation 253
Hyperdeterminants 83 84 365
Identities, fundamental, for binary forms 19 321 368
Identities, fundamental, for ternary forms 257 258
Identities, fundamental, in general 349
Inflexion, points of 222—224
Invariants of binary forms, symbolical expression for 14 15 16
Invariants of ternary forms, symbolical expression for 250 251
| Invariants, defined 7 8
inversion 208
Involution 203 238
Irreducible solutions of Diophantine equations 102—105
Irreducible system of forms 85
Jacobian is a covariant 8 9
Jacobian of a Jacobian and another form is in general reducible 78
Jacobian of binary forms 8 77
Jacobian of pencil of cubics 241 242
Jacobian of ternary forms 249 251
Jacobian of two quadratics is harmonic to both 192
Jacobian of two quartics apolar to a third 245
Jacobian, any combinant of two binary quadratics is an invariant of their Jacobian 315
Jacobian, product of two 20 78—80 140
Jacobian, vanishing of 193
JORDAN 62 126 321 375 377
Kempe 366
Klein 374
Lie 38 366
Line coordinates 255
Linear forms with any number of variables 346
Linear forms, geometry of 279
Linear forms, invariants of a binary system of 33—35 85 86
Linear forms, invariants of a ternary system of 275i
Linear forms, invariants of any finite binary system and a 160 161
MacMahon 326 330
Maximum order 337
Meyer 245 317 368 374
Mixed concomitants 255
Number of independent covariants of degree three and given weight 65 67
Operator  for binary forms and generalised transvectants 83
Operator for binary forms and hyperdeterminants 84
Operator for binary forms, effect on symbolical product 23—25
Operator for binary forms, expansion of  173—175
Operator for binary forms, transvectants defined by 46
Operator for ternary forms and transvectants 295 296
Operator for ternary forms, effect on symbolical products 259—261
Order 9 255
Osculating plane 188 243
Parametric representation 236 305
Pascal 240 280
Peano 321 358 359
Pencil of cubics ( ) 241 242
Pencil of cubics ( ) 194—197
Pencil of quartics 197—208
Pencil of rays 188 189
Perpetuants 326—330 338 378
Polar conic 251 256
Polar forms are covariants 39 40
Polar forms, adjacent terms of 44
Polar forms, definition and symbolical expression of 12 13 345 357
Polar forms, difference between two terms of 42—55
Polar forms, expansion of one term in 55
Poncelet's porism 245
Porism 245 288
Projection 253
Quadratic, quaternary, complete system for 270
Quadratic, quaternary, geometry of 271—273
Quadratics, binary and geometry on a conic 235—240
Quadratics, binary, any finite system and one 165—168
Quadratics, binary, associated forms for one 157
Quadratics, binary, combinants of 315
Quadratics, binary, complete system for any number 161 162
Quadratics, binary, complete system for cubic and one 164 165
Quadratics, binary, complete system for one 86 121
Quadratics, binary, complete system for quartic and one 168
Quadratics, binary, covariant types of 321—328
Quadratics, binary, geometry on Argand diagram for 209—211
Quadratics, binary, geometry on straight line for 191—193
Quadratics, binary, possess invariants 1 2
Quadratics, binary, Syzygies for any number 162—164
Quadratics, ternary, complete system for one 275—277 298
Quadratics, ternary, complete system for two 280—286
Quadratics, ternary, geometry of two 288—294; see also “Apolarity”
Quadrics 272
Quantics defined 3
Quartic, binary, associated forms for 157
Quartic, binary, complete system for 91—94 122
Quartic, binary, cross ratio of roots of 204—207
Quartic, binary, defines a pencil of cubics 241 242
Quartic, binary, defines a twisted quartic curve 242—245
Quartic, binary, discriminant of 198 199
Quartic, binary, geometry and pencil of 197—208
Quartic, binary, irreducible invariant of five quartics 350
Quartic, binary, quadratic factors of sextic covariant of 200—203
Quartic, binary, Syzygy for 98 200
Quartic, binary, transvectants for 97—100 197
Quartic, ternary, canonical form for 313
Quartic, ternary, condition for an apolar conic 304
Quaternary forms 269—273 349 362
Quintic, binary, associated forms for 148—150
Quintic, binary, canonical form of 229—231
Quintic, binary, complete system for 128—132
Quintic, binary, elementary transvectants of 94 95
Quintic, binary, invariants of 133 136
Quintic, binary, linear covariants of 133
Quintic, binary, Syzygies for 143 144
Quintic, binary, typical representation of 145—147
Quintic, binary, values of transvectants of 135 137—140
Reciprocation 291
Rectangular hyperbola 303
Representation, typical 145—147
Reye 245
Richmond 245
Rosanes 245
Salmon 365
Schlesinger 307
Scott 367
Self-conjugate circle 302
Self-conjugate triangle 238 288
Seminvariant 28—30
Sextic, binary, associated system for 157
Sextic, binary, canonical form of 231 232
Sextic, binary, complete system for 150—156
Straight line, geometry on 183—189
Stroh 71 140 142 144 152 164 326
Stroh's series, deductions from 65—71
Stroh's series, obtained 62—64
Stroh's series, scheme used for 68
Stroh's series, used 99 100 328 329 336
Study 366 368
Stuefe 62
Sturm 245
Superosculation, points of 244
Sylvester 131 366
Syzygies for cubic 96 194
Syzygies for quadratics 162—164
Syzygies for quartic 98 198
Syzygies for quintic 143 144
Syzygies of second and higher kinds 145
Syzygies, finiteness of system of 177 178
Syzygies, reducibility of 144
Syzygies, Stroh's method of obtaining 140—148
Tangential equation 301
Transformations, linear form a group 5 6
Transformations, linear of binary symbolical product 13 14
Transformations, linear of ternary symbolical product 247 248
Transformations, linear, defined 4
Transformations, linear, geometrical interpretation of 184—189 208 251—254
Transformations, linear, modulus or determinant of 1 2 14—17 21—23 248 249
Translation principle for quaternary forms 271—273
Translation principle for ternary forms 265—268
Transvectants of ternary forms 296 297
Transvectants, adjacent terms of 49
Transvectants, calculation by means of polars of 47—49
Transvectants, defined 46
Transvectants, difference between two terms of 49—52
Transvectants, generalized 83
Transvectants, system obtained by transvection from two finite systems 107—109 111
Triad 194
|
|
|
| Реклама |
|
|
|
|
|
О проекте