Talk:Power sum symmetric polynomial
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To replace a redirect to Newton's identities I am preparing a page on the power sum symmetric polynomials to go along with those on the elementary symmetric polynomials and the complete homogeneous symmetric polynomials as well as other types of bases of symmetric polynomials that knowledgeable WPians can prepare short pages about. The power sum polynomials are of interest for many reasons not closely related to their (aso important) connection with Newton's identities. It is not appropriate to slip them as a minor topic into Newton's identities. I ask anyone who disagrees to please think it over carefully and discuss the matter before cancelling this page. Thank you. Zaslav 23:52, 25 March 2007 (UTC)
- Please overlook annoyed tone, which is the after-effect of a problem caused by some kind of stupid error of my own. Zaslav 20:57, 26 March 2007 (UTC)
I would be glad to see a complete proof that the p.s. polynomials form an algebraic basis for all symmetric polynomials over a field, written in here (similarly to elementary symmetric polynomials), to supplement the nice informal treatment at Newton's identities. Zaslav 01:08, 26 March 2007 (UTC)
- Surely it only works over characteristic 0? E.g. in characteristic 2, x^2+y^2=(x+y)^2, so F[x+y,x^2+y^2]=F[x+y] with rank one while F[x+y,xy] has rank two. —David Eppstein 02:00, 28 March 2007 (UTC)
