polylib::elemSym -- elementary
symmetric polynomials
Introductionpolylib::elemSym([x1,...,xn], k) returns
the k-th elementary symmetric polynomial in the given
variables x1 through xn.
Call(s)polylib::elemSym(l, k)
Parametersl |
- | list of indeterminatess |
k |
- | positive integer |
ReturnsThe result is a polynomial over the coefficient ring Expr. If k is greater than
the number of operands of l, undefined is returned.
Related
Functions
Detailsl is a valid first argument only if its
elements can be used as indeterminates of a polynomial .
Example
1The first elementary symmetric polynomial is just the sum of its variables:
>> polylib::elemSym([x,y,z], 1);
poly(x + y + z, [x, y, z])
Example
2Indeterminates may also be e.g. trigonometric functions:
>> polylib::elemSym([sin(u),cos(u), exp(u)], 2);
poly(sin(u) cos(u) + sin(u) exp(u) + cos(u) exp(u),
[sin(u), cos(u), exp(u)])
Background