cover image: University of Calcuta Readership Lectures. Chapters on Algebra (being the first three chapters of matrices and determinoids)

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University of Calcuta Readership Lectures. Chapters on Algebra (being the first three chapters of matrices and determinoids)

1920

The eliminant of n functions is a resultant of n +1 functions of which one is linear, but it is a resultant of pre-eminent import- ance ; it serves to determine the exact number of the common roots of the n functions and the values of all symmetric functions of the common roots, and it serves the same purpose for the finite roots only and for the infinite roots only; if we denote it by E, then F. [...] Resultants of rational integral functions: properties of the resultant /I of a general homogeneous (or general) functions of a (or n - I ) variables ; the resultant is homogeneous in the coefficients of cads function, isobaric with respect to each variable, and it soluble; relations of R to the partial resultants and the common roots of PI - of the functions; resultants of function?' which are pr [...] Eliminants of rational integral functions, complete and partial elinii- mints ; properties of the X-eliminant E of n general homogeneous (or general) functions of n +1 (or ,a) variablm; it is the resultant of the a functions and ; it is a homogeneous rational integral function of the auxiliary parameters or the coefficients of I; terms of the highest degree in the individual parameters ; the elimi [...] function of x which does not vanish identically, and if there exists an identical equation of the form F=fg, where f and g are rational integral functions of then F is said to be divisible by f, f is called a Actor of F, and g is called the quotient in the division of F by f. At the same time F is divisible by g, g is a factor of . /P, and f is the quotient in the division of F by g. Neither of t [...] 1„, are in rational integral functions of Me n nuiables x,, . m1, no one of which vanishes identically, and it F. f, then the degree of F in all the variables is the sum of the degrees of f,„ in all the variables, also the degree of F any one variable xi is the sum of the degrees of f,, fs, f„, in xs.
technology medicine science
Pages
192
Published in
India
SARF Document ID
sarf.100014
Segment Pages Author Actions
Preface
i-x C.E. Cullis view
Chapter XX The Irresoluble and Irreducible Factors of Rational Integral Functions
1-56 unknown view
Chapter XXI Resultants and Eliminants of Rational Integral Functions
57-129 unknown view
Chapter XXII Symmetric Functions of the Elements of Similar Sequences
130-180 unknown view
Index
181-182 unknown view

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