Also such ideas as those of invariants, groups and of form, have modified the entire science.
The partition method of treating symmetrical algebra is one which has been singularly successful in indicating new paths of advance in the theory of invariants; the important theorem of expressibility is, directly we exclude unity from the partitions, a theorem concerning the expressibility of covariants, and involves the theory of the reducible forms and of the syzygies.
The important result is that the theory of invariants is from a certain point of view coincident with the theory of non-unitary symmetric functions.
An important notion in the theory of linear operators in general is that of MacMahon's multilinear operator (" Theory of a Multilinear partial Differential Operator with Applications to the Theories of Invariants and Reciprocants," Proc. Lond.
X i, x 2) is said to be a covariant of the quantic. The expression " invariantive forms " includes both invariants and covariants, and frequently also other analogous forms which will be met with.