Difference between revisions of "Elementary symmetric sum"
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== Definition == | == Definition == | ||
| − | The ' | + | 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 | + | 1st Symmetric Sum = $a+b+c+d$ |
| − | 2nd Symmetric Sum = ab+ac+ad+bc+bd+cd | + | 2nd Symmetric Sum = $ab+ac+ad+bc+bd+cd$ |
| − | 3rd Symmetric Sum = abc+abd+acd+bcd | + | 3rd Symmetric Sum = $abc+abd+acd+bcd$ |
| − | 4th Symmetric Sum = abcd | + | 4th Symmetric Sum = $abcd$ |
Revision as of 13:12, 24 July 2006
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
