Elementary symmetric sum: Difference between revisions
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== Definition == | |||
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 | ||
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 | ||
== 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
