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Newton's identities

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Newton's identities
Dbpedia
Wikipedia articleDbpedia source
In mathematics, Newton's identities, also known as the Girard–Newton formulae, give relations between two types of symmetric polynomials, namely between power sums and elementary symmetric polynomials. Evaluated at the roots of a monic polynomial P in one variable, they allow expressing the sums of the k-th powers of all roots of P (counted with their multiplicity) in terms of the coefficients of P, without actually finding those roots. These identities were found by Isaac Newton around 1666, apparently in ignorance of earlier work (1629) by Albert Girard. They have applications in many areas of mathematics, including Galois theory, invariant theory, group theory, combinatorics, as well as further applications outside mathematics, including general relativity.
English Wikipedia http://en.wikipedia.org/wiki/Newton's_identities
Spanish wikipedia http://es.wikipedia.org/wiki/Identidades_de_Newton
Wiki page external link https://archive.org/details/appliedcombinato00tuck%7C https://archive.org/details/combinatorialspe0000berg http://stellar.mit.edu/S/course/6/sp10/6.256/courseMaterial/topics/topic2/lectureNotes/lecture-05/lecture-05.pdf http://mathworld.wolfram.com/Newton-GirardFormulas.html https://www.jstor.org/stable/2690982 https://www.math.rutgers.edu/~zeilberg/mamarimY/Zeilberger_y1984_p319.pdf https://archive.org/details/permutationgroup0000came

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Fecha publicación: 18.2.2022

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