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polylib::representByElemSym

Represent symmetric by elementary symmetric polynomials

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Syntax

polylib::representByElemSym(f, l)

Description

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.

The list l must have as many operands as f has indeterminates.

The result is FAIL if the input is not symmetric.

Examples

Example 1

The symmetric polynomial x2 + y2 can be written as (x + y)2 - 2 (xy):

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

Example 2

polylib::representByElemSym works over domains also:

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

Parameters

f

Symmetric polynomial

l

List of indeterminates

Return Values

Result is a polynomial having the same coefficient ring as f.

Algorithms

It is a well-known theorem that every symmetric polynomial can be written in this way.

See Also

MuPAD Functions

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