previous up next
Go backward to Polynomial Evaluation
Go up to Top
Go forward to Typical Notation
RISC-Linz logo

Polynomial Evaluation

Proposition: For all polynomials p and q and all reals c and a:

cPoly[a] = c,
x[a] = a,
(p+q)[a] = p[a] +R q[a],
(p*q)[a] = p[a] *R q[a].

When evaluating a polynomial p on a real a, we substitute aPoly for every occurrence of x in p and then use arithmetic on reals.

(x+1)[2] = 2+1 = 3
(x*x+2*x+1)[3] = 3*3+2*3+1 = 16

Author: Wolfgang Schreiner
Last Modification: November 16, 1999

previous up next