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Multi-index notation is a mathematical notation that simplifies formulas used in multivariable calculus, partial differential equations and the theory of distributions, by generalising the concept of an integer index to an ordered tuple of indices.
With the multi-index notation for partial derivatives of functions of several variables, the Leibniz rule states more generally: =: () ().. This formula can be used to derive a formula that computes the symbol of the composition of differential operators.
In mathematics, specifically in commutative algebra, the elementary symmetric polynomials are one type of basic building block for symmetric polynomials, in the sense that any symmetric polynomial can be expressed as a polynomial in elementary symmetric polynomials.
A vector treated as an array of numbers by writing as a row vector or column vector (whichever is used depends on convenience or context): = (), = Index notation allows indication of the elements of the array by simply writing a i, where the index i is known to run from 1 to n, because of n-dimensions. [1]
The fundamental property of this norm is the Bombieri inequality: let , be two homogeneous polynomials respectively of degree () and () with variables, then, the following inequality holds:
Isaac Newton's notation for differentiation (also called the dot notation, fluxions, or sometimes, crudely, the flyspeck notation [12] for differentiation) places a dot over the dependent variable. That is, if y is a function of t , then the derivative of y with respect to t is