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Elementary symmetric polynomials

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polylib::elemSym(l, k)


polylib::elemSym([x1,...,xn], k) returns the k-th elementary symmetric polynomial in the given variables x1 through xn.

A given list l is a valid first argument only if its elements can be used as indeterminates of a polynomial .


Example 1

The first elementary symmetric polynomial is just the sum of its variables:

polylib::elemSym([x,y,z], 1);

Example 2

Indeterminates may also be e.g. trigonometric functions:

polylib::elemSym([sin(u),cos(u), exp(u)], 2);



List of indeterminatess


Positive integer

Return Values

Result is a polynomial over the coefficient ring Expr. If k is greater than the number of operands of l, undefined is returned.


For more information about elementary symmetric polynomials, see v.d. Waerden, Algebra, vol. 1.

See Also

MuPAD Functions

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