Difference between revisions of "Elementary symmetric sum"

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== Definition ==
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The ''n''th symmetric sum is the sum of a group of numbers, taken ''n'' at a time.  So if the numbers are a, b, c, and d, then:
 
The ''n''th symmetric sum is the sum of a group of numbers, taken ''n'' at a time.  So if the numbers are a, b, c, and d, then:
  
 
1st Symmetric Sum = a+b+c+d
 
1st Symmetric Sum = a+b+c+d
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2nd Symmetric Sum = ab+ac+ad+bc+bd+cd
 
2nd Symmetric Sum = ab+ac+ad+bc+bd+cd
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3rd Symmetric Sum = abc+abd+acd+bcd
 
3rd Symmetric Sum = abc+abd+acd+bcd
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4th Symmetric Sum = abcd
 
4th Symmetric Sum = abcd
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== Uses ==
  
 
Symmetric sums show up in [[Vieta's formula]]
 
Symmetric sums show up in [[Vieta's formula]]

Revision as of 13:13, 18 June 2006

Definition

The nth symmetric sum is the sum of a group of numbers, taken n at a time. So if the numbers are a, b, c, and 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 formula

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