The EvaluatePolynomial command evaluates a dense univariate polynomial at a RealBox object. It does this in a manner that sometimes produces a smaller radius than simple evaluation using the standard arithmetic operations.

The first argument is a RealBox object, representing the value at which the polynomial is to be evaluated.

The second argument is a list of $n+1$ coefficients of the polynomial to be evaluated, where $n$ is the degree of the polynomial. The first entry is the constant coefficient, the second the linear coefficient, and so on. Each coefficient can be a RealBox object or a real constant.

$\mathrm{poly}≔292+72x-188x^2+49x^4$

$\mathrm{poly}≔49x^4-188x^2+72x+292$

$\mathrm{rb}≔\mathrm{RealBox}\left(-1.47\,0.01\right)$

$\mathrm{rb}≔⟨\text{RealBox:}-1.47\pm 0.01⟩$

$\mathrm{eval}\left(\mathrm{poly}\,x=\mathrm{rb}\right)$

$⟨\text{RealBox:}8.71575\pm 12.5558⟩$

$\mathrm{poly\_horner}≔\mathrm{convert}\left(\mathrm{poly}\,'\mathrm{horner}'\right)$

$\mathrm{poly\_horner}≔292+\left(72+\left(49x^2-188\right)x\right)x$

$\mathrm{eval}\left(\mathrm{poly\_horner}\,x=\mathrm{rb}\right)$

$⟨\text{RealBox:}8.71575\pm 6.30864⟩$

$\mathrm{plot}\left(\mathrm{poly}\,x=-1.48..-1.46\right)$

$\mathrm{Optimization}:-\mathrm{Minimize}\left(\mathrm{poly}\,x=-1.48..-1.46\right)$

$\left[8.71324004901427\,\left[x=\mathrm{-1.47236599608282}\right]\right]$

$\mathrm{eval}\left(\mathrm{poly}\,x=-1.46\right)$

$8.7814094$

$\mathrm{EvaluatePolynomial}\left(\mathrm{rb}\,\mathrm{PolynomialTools}:-\mathrm{CoefficientList}\left(\mathrm{poly}\,x\right)\right)$

$⟨\text{RealBox:}8.71575\pm 0.0662341⟩$

The RealBox:-EvaluatePolynomial command was introduced in Maple 2023.

For more information on Maple 2023 changes, see Updates in Maple 2023.