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covariant's Usage Examples:

-2 _ ab 2an-2bn-2Crz z x () x x x, Each term on the right-hand side may be shown by permutation of a, b, c to be the symbolical representation of the same covariant; they are equivalent symbolic products, and we may accordingly write 2(ac) (bc)ai -1 bi -1 cx 2 =(ab)2a:-2b:-2c:, a relation which shows that the form on the left is the product of the two covariants n (ab) ay 2 by 2 and cZ.

For, if c(ao i ...x l, x 2) be a covariant of order e appertaining to a quantic of order n, t (T.

the orders of the quantic and covariant, and the degree and weight of the leading coefficient; calling these 'n, e,' 0, w respectively we can see that they are not independent integers, but that they are invariably connected by a certain relation n9 -2w = e.

It will be apparent that there are four numbers associated with a covariant, viz.

the order of the covariant) is P+P+T+...

The degree of the covariant in the coefficients is equal to the number of different symbols a, b, c, ...

For the cubic (ab) 2 axbx is a covariant because each symbol a, b occurs three times; we can first of all find its real expression as a simultaneous covariant of two cubics, and then, by supposing the two cubics to merge into identity, find the expression of the quadratic covariant, of the single cubic, commonly known as the Hessian.

If the forms be identical the sets of symbols are ultimately equated, and the form, provided it does not vanish, is a covariant of the form ate.

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.

+P=n1, j+k+...+T =n3, It will also be a covariant if the symbolic product be factorizable into portions each of which satisfies these conditions.

covariant's Meaning':

changing so that interrelations with another variable quantity or set of quantities remain unchanged

Synonyms:

variable,

Antonyms:

invariable, constant,