Difference between revisions of "Elementary symmetric sum"
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== Definition == | == Definition == | ||
| − | The | + | The <math>k</math>-th '''symmetric sum''' of a [[set]] of <math>n</math> numbers is the sum of all products of <math>k</math> of those numbers (<math>1 \leq k \leq n</math>). For example, if <math>n = 4</math>, and our set of numbers is <math>\{a, b, c, d\}</math>, then: |
| − | 1st Symmetric Sum = | + | 1st Symmetric Sum = <math>a+b+c+d</math> |
| − | 2nd Symmetric Sum = | + | 2nd Symmetric Sum = <math>ab+ac+ad+bc+bd+cd</math> |
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| + | 3rd Symmetric Sum = <math>abc+abd+acd+bcd</math> | ||
| + | 4th Symmetric Sum = <math>abcd</math> | ||
== Uses == | == Uses == | ||
Symmetric sums show up in [[Vieta's formulas]] | Symmetric sums show up in [[Vieta's formulas]] | ||
Revision as of 17:14, 26 July 2006
Definition
The 
-th 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 = 
Uses
Symmetric sums show up in Vieta's formulas
