Symmetric Polynomial
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High Quality Content by WIKIPEDIA articles! In mathematics, a symmetric polynomial is a polynomial P(X1, X2, ?, Xn) in n variables, such that if any of the variables are interchanged, one obtains the same polynomial. Formally, P is a symmetric polynomial, if for any permutation ? of the subscripts 1, 2, ..., n one has P(X?(1), X?(2), ?, X?(n)) = P(X1, X2, ?, Xn). Symmetric polynomials arise naturally in the study of the relation between the roots of a polynomial in one variable and its coefficients, since the coefficients can be given by polynomial expressions in the roots, and all roots play a similar role in this setting. From this point of view the elementary symmetric polynomials are the most fundamental symmetric polynomials. A theorem states that any symmetric polynomial can be expressed in terms of elementary symmetric polynomials, which implies that every symmetric polynomial expression in the roots of a monic polynomial can alternatively be given as a polynomial expression in the coefficients of the polynomial.
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GarantieWeitere Informationen
- Allgemeine Informationen
- GTIN 09786130357467
- Editor Lambert M. Surhone, Miriam T. Timpledon, Susan F. Marseken
- Sprache Englisch
- Größe H220mm x B150mm x T7mm
- Jahr 2010
- EAN 9786130357467
- Format Kartonierter Einband
- ISBN 978-613-0-35746-7
- Titel Symmetric Polynomial
- Untertitel Mathematics, Polynomial Ring, Permutation, Elementary Symmetric Polynomial, Polynomial Expression, Polynomial, Complete Homogeneous Symmetric Polynomial, Representation Theory
- Gewicht 185g
- Herausgeber VDM Verlag Dr. Müller e.K.
- Anzahl Seiten 112
- Genre Mathematik
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