Theory of algebraic invariants

Preface Introduction Part I. The Elements of Invariant Theory: 1. The forms 2. The linear transformation 3. The concept of an invariant 4. Properties of invariants and covariants 5. The operation symbols D and D 6. The smallest system of conditions for the determination of the invariants and covariants 7. The number of invariants of degree g 8. The invariants and covariants of degree two and three 9. Simultaneous invariants and covariants 10. Covariants of covariants 11. The invariants and covariants as functions of the roots 12. The invariants and covariants as functions of the one-sided derivatives 13. The symbolic representation of invariants and covariants Part II. The Theory of Invariant Fields: 14. Proof of the finitenesss of the full invariant system via representation by root differences 15. A generalizable proof for the finiteness of the full invariant system 16. The system of invariants I I1, I2, ..., Ik 17. The vanishing of the invariants 18. The ternary nullform 19. The finiteness of the number of irreducible syzygies and of the syzygy chain 20. The inflection point problem for plane curves of order three 21. The generalization of invariant theory 22. Observations about new types of coordinates.