reduction algorithm for symmetric polynomials
Let be a symmetric polynomial. We reduce into elementary symmetric polynomials by induction on the height of . Let be the monomial term of maximal height in . Consider the polynomial
where is the –th elementary symmetric polynomial in the variables . Then is a symmetric polynomial of lower height than , so by the induction hypothesis, is a polynomial in , and it follows immediately that is also a polynomial in .
|Title||reduction algorithm for symmetric polynomials|
|Date of creation||2013-03-22 12:11:17|
|Last modified on||2013-03-22 12:11:17|
|Last modified by||djao (24)|