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1	Linear Transformation
1	Polynomial Ring
1	Basic Polynomial
1	Terms From Foreign Languages Used In Mathematics
1	Obvious
1	Subtraction
8	Zero Polynomial

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Opposite Polynomial

The opposite polynomial of a polynomial in a polynomial ring is a polynomial such that

$\displaystyle P+(-P) = \textbf{0},$

where $\textbf{0}$ denotes the zero polynomial. It is clear that

is obtained by changing the signs of all of the coefficients of

$\displaystyle -\sum_{\nu = 0}^n a_\nu X^\nu = \sum_{\nu = 0}^n (-a_\nu)X^\nu.$

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

$\displaystyle P-Q := P+(-Q)$

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