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Grace J.H., Young A. — The Algebra of Invariants
Grace J.H., Young A. — The Algebra of Invariants

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Название: The Algebra of Invariants

Авторы: Grace J.H., Young A.

Аннотация:

This volume is produced from digital images created through the University of Michigan University Library's preservation reformatting program


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1903

Количество страниц: 384

Добавлена в каталог: 29.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 ($\mathrm{n} < \mathrm{m}$)      228
Apolarity of binary forms, the n linearly independent forms of order m apolar to a binary m-ic ($\mathrm{n} < \mathrm{m}$)      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 $\textrm{kf}+\lambda\textrm{H}$      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 $\Omega$ for binary forms and generalised transvectants      83
Operator $\Omega$ for binary forms and hyperdeterminants      84
Operator $\Omega$ for binary forms, effect on symbolical product      23—25
Operator $\Omega$ for binary forms, expansion of $\Omega^{\mathrm{m}} \left\{ (\xi\eta)^{\mathrm{n}} \mathrm{P} \right\}}$      173—175
Operator $\Omega$ for binary forms, transvectants defined by      46
Operator $\Omega$ for ternary forms and transvectants      295 296
Operator $\Omega$ 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 ($\lambda_1\mathrm{f}_1+\lambda_2\mathrm{f}$)      241 242
Pencil of cubics ($\textrm{kf}+\lambda\textrm{t}$)      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
1 2
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