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polylib::representByElemSym -- represent symmetric by elementary symmetric polynomials

Introduction

polylib::representByElemSym(f, [x1,...,xn]) returns a polynomial g in the identifiers x1 through xn such that replacing each xi by the i-th elementary symmetric polynomial gives f.

Call(s)

polylib::representByElemSym(f, l)

Parameters

f - symmetric polynomial
l - list of indeterminates

Returns

The result is a polynomial having the same coefficient ring as f.

Related Functions

polylib::elemSym

Details

Example 1

The symmetric polynomial x^2+y^2 can be written as (x+y)^2 - 2*(x*y):

>> polylib::representByElemSym(poly(x^2+y^2), [u,v]);
   
                                2
                          poly(u  - 2 v, [u, v])

Example 2

polylib::representByElemSym works over domains also:

>> f:=poly(x^2+y^2, Dom::IntegerMod(7)):
   polylib::representByElemSym(f, [u,v])   
                      2
                poly(u  + 5 v, [u, v], Dom::IntegerMod(7))

Background

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