polylib::representByElemSym
--
represent symmetric by elementary symmetric polynomialspolylib::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
.
polylib::representByElemSym(f, l)
f |
- | symmetric polynomial |
l |
- | list of indeterminates |
The result is a polynomial having the same coefficient ring as
f
.
l
must have as many operands as
f
has indeterminates.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])
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))