# Difference between revisions of "Elementary symmetric sum"

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## Revision as of 14:27, 4 January 2008

An **elementary symmetric sum** is a type of summation.

## Contents

## Definition

The -th **elmentary symmetric sum** of a set of numbers is the sum of all products of of those numbers (). For example, if , and our set of numbers is , then:

1st Symmetric Sum =

2nd Symmetric Sum =

3rd Symmetric Sum =

4th Symmetric Sum =

## Notation

The first elmentary symmetric sum of is often written . The th can be written

## Uses

Any symmetric sum can be written as a polynomial of the elmentary symmetric sum functions. For example, . This is often used to solve systems of equations involving power sums, combined with Vieta's.

Elmentary symmetric sums show up in Vieta's formulas. In a monic polynomial, the coefficient of the term is , and the coefficient of the term is .