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Take the set of polynomials Poly.

We have, for all polynomials x and y and a in R,

(x + y)[a] = x[a] +R y[a]
(x - y)[a] = x[a] -R y[a]
(-x)[a] = -Rx[a]
(x * y)[a] = x[a] *R y[a]

i.e., polynomial evaluation is a homomorphism from Poly to R (for operations +, -, *).

Author: Wolfgang Schreiner
Last Modification: December 7, 1999

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