Newton's identities
In mathematics, Newton's identities, also known as the Newton–Girard 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.
primaryTopic
Newton's identities
In mathematics, Newton's identities, also known as the Newton–Girard 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.
has abstract
25بك المحتوى هنا ينقصه الاستشه ...... يات، مثل نظرية النسبية العامة.
@ar
Em matemática, as identidades ...... ticularmente bases de Gröbner.
@pt
En Matemática, las identidades ...... uyendo la relatividad general.
@es
En mathématiques, et plus part ...... comme en relativité générale.
@fr
In der Mathematik, spezieller ...... lgemeinen Relativitätstheorie.
@de
In matematica, le identità di ...... pio nella relatività generale.
@it
In mathematics, Newton's ident ...... including general relativity.
@en
В математике тождества Ньютона ...... общей теории относительности.
@ru
Link from a Wikipage to an external page
Wikipage page ID
Wikipage revision ID
733,760,875
subject
comment
25بك المحتوى هنا ينقصه الاستشه ...... يات، مثل نظرية النسبية العامة.
@ar
Em matemática, as identidades ...... ticularmente bases de Gröbner.
@pt
En Matemática, las identidades ...... erior (1629) de Albert Girard.
@es
En mathématiques, et plus part ...... dans de nombreux domaines math
@fr
In der Mathematik, spezieller ...... lgemeinen Relativitätstheorie.
@de
In matematica, le identità di ...... r esempio nella relatività gen
@it
In mathematics, Newton's ident ...... including general relativity.
@en
В математике тождества Ньютона ...... общей теории относительности.
@ru
label
Identidades de Newton
@es
Identidades de Newton
@pt
Identità di Newton
@it
Identités de Newton
@fr
Newton's identities
@en
Newton-Identitäten
@de
Тождества Ньютона
@ru
متطابقات نيوتن
@ar