x TABLE OF CONTENTS
PAGE
§ 24. Alternants 41
§ 25. Seminvariants as Leaders of Binary Covariants 42
§26. Number of Linearly Independent Seminvariants 43
§ 27. Hermite’s Law of Reciprocity 45
Exercises 46
• §§28-31. Fundamental System of Covariants 47
§§ 32,33. Canonical Form of Binary Quartic; Solution of Quartic Equations.. 50
§ 34. Seminvariants in Terms of the Roots 53
§ 35. Invariants in Terms of the Roots 54
Exercises 55
§ 36. Covariants in Terms of the Roots 56
Exercises 58
§ 37. Covariant with a Given Leader ... 58
§ 38. Differential Operators Producing Covariants 59
Exercises 61
PART III
Symbolic Notation
§§ 39-41. The Notation and its Immediate Consequences 63
Exercises 65, 66
§§ 42-45. Covariants as Functions of Two Symbolic Types 67
§ 46. Problem of Finiteness of Covariants , 70
§ 47. Reduction to Problem on Invariants 71
§ 48. Hilbert’s Theorem on a Set of Forms 72
§§ 49, 50. Finiteness of a Fundamental System of Invariants 73
§51. Finiteness of Syzygies 76
§ 52. Transvectants 77
§§ 53, 54. Binary Forms Apolar to Given Forms 78
§§ 55,56. Rational Plane Cubic Curves 81
§ 57. Rational Space Quartic Curves 83
§§ 58,59. Fundamental System of Covariants of Linear Forms; of a Quadratic
Form; Exercises 84
§ 60. Theorems on Transvectants; Convolution 85
§ 61. Irreducible Covariants Found by Induction 87
§ 62. Fundamental System for a Binary Cubic 89
§ 63. Results and References on Higher Binary Forms 91
§64. Hermite’s Law of Reciprocity Symbolically 91
§ 65. Ternary Form in Symbolic Notation 92
Exercises 93
§§ 66, 67. Concomitants of Ternary Forms 93
§ 68. Quaternary Forms 97
Index 99