polylib::representByElemSym --
represent symmetric by elementary symmetric polynomials
Introductionpolylib::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)
Parametersf |
- | symmetric polynomial |
l |
- | list of indeterminates |
ReturnsThe result is a polynomial having the same coefficient ring as
f.
Related
Functions
Detailsl must have as many operands as
f has indeterminates.
Example
1The 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
2polylib::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