एक सजातीय बहुपद कम से कम दो चर

Noun:

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

quantics's Usage Examples:

1-a'5 Accounts of further attempts in this direction will be found in Cayley's Memoirs on Quantics (Collected"Papers), in the papers of Sylvester and Franklin (Amer.

of the Memoir he discusses bi-ternary quantics, and in particular those which are lineo-linear, quadrato-linear, cubo-linear, quadrato-quadratic, cubo-cubic, and the system of two lineo-linear quantics.

Elliott, Algebra of Quantics, Art.

An important reference is " The Differential Equations satisfied by Concomitants of Quantics," by A.

+a"aa"-1 have been much studied by Sylvester, Hammond, Hilbert and Elliott (Elliott, Algebra of Quantics, ch.

Such quantics have been termed by Cayley multipartite.

in addition, and transform each pair to a new pair by substitutions, having the same coefficients a ll, a12, a 21, a 22 and arrive at functions of the original coefficients and variables (of one or more quantics) which possess the abovedefinied invariant property.

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.

From these formulae we derive two important relations, dp4 = or the function F, on the right which multiplies r, is said to be a simultaneous invariant or covariant of the system of quantics.

Under the general heading "Algebra and Theory of Numbers" occur the subheadings "Elements of Algebra," with the topics rational polynomials, permutations, 'c., partitions, probabilities; "Linear Substitutions," with the topics determinants, 'c., linear substitutions, general theory of quantics; "Theory of Algebraic Equations," with the topics existence of roots, separation of and approximation to, theory of Galois, 'c. "Theory of Numbers," with the topics congruences, quadratic residues, prime numbers, particular irrational and transcendental numbers.

quantics's Meaning':

a homogeneous polynomial having at least two variables