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单词 OppositePolynomial
释义

opposite polynomial


The opposite polynomialMathworldPlanetmathPlanetmath of a polynomial P in a polynomial ring R[X] is a polynomial  -P  such that

P+(-P)=𝟎,

where 0 denotes the zero polynomialMathworldPlanetmath.  It is clear that  -P  is obtained by changing the signs of all of the coefficients of P, i.e. (http://planetmath.org/Ie)

-ν=0naνXν=ν=0n(-aν)Xν.

The opposite polynomial may be used to define subtractionPlanetmathPlanetmath of polynomials:

P-Q=:P+(-Q)

Forming the opposite polynomial is a linear mapping   R[X]R[X].

Titleopposite polynomial
Canonical nameOppositePolynomial
Date of creation2013-03-22 14:47:41
Last modified on2013-03-22 14:47:41
Ownerpahio (2872)
Last modified bypahio (2872)
Numerical id9
Authorpahio (2872)
Entry typeDefinition
Classificationmsc 11C08
Classificationmsc 12E05
Classificationmsc 13P05
Related topicOppositeNumber
Related topicUnity
Related topicBasicPolynomial
Related topicMinimalPolynomialEndomorphism
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