The elementary symmetric mean is based on elementary symmetric polynomials. If x is a tuple with and αp(x)- is the corresponding elementary symmetric term of order p, then the respective mean is In mathematics, specifically in commutative algebra, elementary symmetric polynomials are the basic building blocks for symmetric polynomials, in the sense that every symmetric polynomial can be expressed as a sum of products of the elementary symmetric polynomials. ... In mathematics, a tuple is a finite sequence of objects, that is, a list of a limited number of objects. ...
In mathematics and statistics, the arithmetic mean (or simply the mean) of a list of numbers is the sum of all the members of the list divided by the number of items in the list. ... The geometric mean of a set of positive data is defined as the nth root of the product of all the members of the set, where n is the number of members. ...
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