Elementary symmetric sum

Revision as of 13:12, 24 July 2006 by JBL (talk | contribs)

Definition

The $k$-th symmetric sum of a set of $n$ numbers is the sum of all products of $k$ of those numbers ($1 \leq k \leq n). For example, if $n = 4$, and our set of numbers is $\{a, b, c, d\}$, then:

1st Symmetric Sum = $a+b+c+d$

2nd Symmetric Sum = $ab+ac+ad+bc+bd+cd$

3rd Symmetric Sum = $abc+abd+acd+bcd$

4th Symmetric Sum = $abcd$


Uses

Symmetric sums show up in Vieta's formulas

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