Difference between revisions of "Elementary symmetric sum"
m ($ parity) |
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| + | A '''symmetric sum''' is a type of [[summation]]. | ||
== Definition == | == Definition == | ||
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4th Symmetric Sum = <math>abcd</math> | 4th Symmetric Sum = <math>abcd</math> | ||
| + | ==Notation== | ||
| + | The first symmetric sum of <math>f(x)</math> is often written <math>\sum_{sym}f(x)</math>. The <math>n</math>th can be written <math>\sum_{sym}^{n}f(x)</math> | ||
== Uses == | == Uses == | ||
Symmetric sums show up in [[Vieta's formulas]] | Symmetric sums show up in [[Vieta's formulas]] | ||
| + | ==See Also== | ||
| + | *[[Cyclic sum]] | ||
| + | |||
| + | [[Category:Algebra]] | ||
| + | [[Category:Definition]] | ||
Revision as of 18:44, 22 November 2007
A symmetric sum is a type of summation.
Contents
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 = 
Notation
The first symmetric sum of 
is often written 
. The th can be written 
Uses
Symmetric sums show up in Vieta's formulas
