elementary symmetric polynomial


The coefficient of xn-k in the polynomialMathworldPlanetmath (x+t1)(x+t2)(x+tn) is called the kth elementary symmetric polynomial in the n variablesMathworldPlanetmath t1,,tn. The elementary symmetric polynomials can also be constructed by taking the sum of all possible degree k monomials in t1,,tn having distinct factors.

The first few examples are:

n=1:

t1

n=2:

t1+t2t1t2

n=3:

t1+t2+t3t1t2+t2t3+t1t3t1t2t3

Title elementary symmetric polynomial
Canonical name ElementarySymmetricPolynomial
Date of creation 2013-03-22 12:09:01
Last modified on 2013-03-22 12:09:01
Owner djao (24)
Last modified by djao (24)
Numerical id 9
Author djao (24)
Entry type Definition
Classification msc 05E05