= Polynomial evaluation
{title2=$E_a(p)=p(a)$}
<Polynomial evaluation> replaces the <indeterminate> of a <polynomial> by an input value. For a fixed <scalar> $a$, the rule $E_a:p\mapsto p(a)$ is a <linear functional> on a <vector space> of <polynomials>, because evaluating a <linear combination> gives the same <linear combination> of the values. For $p(t)=1+2t+3t^2$, evaluation at zero gives one and evaluation at two gives seventeen. <Polynomial interpolation> uses these measurements to reconstruct a <polynomial> subject to a <polynomial degree> bound.
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