Difference between revisions of "Elementary symmetric sum"

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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>
  
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==Notation==
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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]]
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==See Also==
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*[[Cyclic sum]]
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[[Category:Algebra]]
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[[Category:Definition]]

Revision as of 17:44, 22 November 2007

A symmetric sum is a type of summation.

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 = $abcd$

Notation

The first symmetric sum of $f(x)$ is often written $\sum_{sym}f(x)$. The $n$th can be written $\sum_{sym}^{n}f(x)$

Uses

Symmetric sums show up in Vieta's formulas

See Also

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