एक सजातीय बहुपद कम से कम दो चर

Noun:

दो या दो से अधिक चल राशियों का समघाती फल, समघातक, समघाती,

quantic's Usage Examples:

To find the effect of linear transformation on the symbolic form of quantic we will disuse the coefficients a 111 a 12, a21, a22, and employ A1, I�1, A2, �2.

For a single quantic of the first order (ab) is the symbol of a function of the coefficients which vanishes identically; thus (ab) =a1b2-a2bl= aw l -a1ao=0 and, indeed, from a remark made above we see that (ab) remains unchanged by interchange of a and b; but (ab), = -(ba), and these two facts necessitate (ab) = o.

We write;L 22 = a 1 a 2 .b 1 n-2 b2s 3 n - 3 3 n-3 3 n-3 3 a 3 = a 1 a 2 .b 1 b 2 .c 1 c2, and so on whenever we require to represent a product of real coefficients symbolically; we then have a one-to-one correspondence between the products of real coefficients and their symbolic forms. If we have a function of degree s in the coefficients, we may select any s sets of umbrae for use, and having made a selection we may when only one quantic is under consideration at any time permute the sets of umbrae in any manner without altering the real significance of the symbolism.

We consider the quantic to have any n number of equivalent representations a- b n -c n So that a 1 -k a 2 = b l -k b 2 - c 1 -k c 2 = ...

A particular quantic of the system may be of the same or different degrees in the pairs of variables which it involves, and these degrees may vary from quantic to quantic of the system.

This notion is fundamental in the present theory because we will find that one of the most valuable artifices for finding invariants of a single quantic is first to find simultaneous invariants of several different quantics, and subsequently to make all the quantics identical.

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.

Instead of a single quantic we may have several f(ao, a1, a2...; x1, x2), 4 (b o, b1, b2,...; x1, x2), ...

F(a ' a ' a, ...a) =r A F(ao, a1, a2,���an), 0 1 2 n the function F(ao, al, a2,...an) is then said to be an invariant of the quantic gud linear transformation.

In the theory of forms we seek functions of the coefficients and variables of the original quantic which, save as to a power of the modulus of transformation, are equal to the like functions of the coefficients and variables of the transformed quantic. We may have such a function which does not involve the variables, viz.

quantic's Meaning':

a homogeneous polynomial having at least two variables