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Symmetric polynomial as a polynomial on elementary symmetric polynomials

asked 2016-02-16 10:07:18 -0500

giomasce gravatar image

SymmetricFunctions, together with the various provided bases, is very good at writing a symmetric polynomial as the linear combination of what is called elementary functions here: mathworld.wolfram.com/SymmetricPolynomial.html. However, a different result says that a symmetric polynomial can be written as a polynomial on what is called elementary symmetric polynomials in the same paper. Can that be computed with Sage?

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answered 2016-02-17 11:45:17 -0500

giomasce gravatar image

The answer is actually implicit in the linked page: elementary functions have the property that (with Sage's notation) e[i, j, ...] = e[i]*e[j]*.... So there you have your polynomial.

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answered 2016-05-12 03:08:53 -0500

tmonteil gravatar image

See also the following answer to close question (and answer): http://ask.sagemath.org/question/3337...

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Asked: 2016-02-16 10:07:18 -0500

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Last updated: May 12 '16