opposite polynomial

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


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)


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


Forming the opposite polynomial is a linear mapping   R⁒[X]β†’R⁒[X].

Title opposite polynomial
Canonical name OppositePolynomial
Date of creation 2013-03-22 14:47:41
Last modified on 2013-03-22 14:47:41
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 9
Author pahio (2872)
Entry type Definition
Classification msc 11C08
Classification msc 12E05
Classification msc 13P05
Related topic OppositeNumber
Related topic Unity
Related topic BasicPolynomial
Related topic MinimalPolynomialEndomorphism