EvaluatePolynomial - Maple Help
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RealBox

  

EvaluatePolynomial

  

evaluate a univariate polynomial at a RealBox object

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

EvaluatePolynomial(a, [c0, c1, ..., cn])

EvaluatePolynomial(a, [c0, c1, ..., cn], precopt)

Parameters

a

-

a RealBox object

c0, c1, ..., cn

-

real constants or RealBox objects

precopt

-

(optional) equation of the form precision = n, where n is a positive integer

Description

• 

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  coefficients of the polynomial to be evaluated, where  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.

Examples

Consider the polynomial . Evaluate it at the RealBox object with center  and radius . We first use simple evaluation using the regular arithmetic operators.

(1)

(2)

(3)

The radius of the result is smaller if we first convert the polynomial to Horner form.

(4)

(5)

However, this is still a severe overestimation of the radius: the minimal value on this interval is about  and the maximal value of about  is achieved at . We verify these values numerically and graphically below.

(6)

(7)

So ideally we would like the result to have a center of about   and a radius of about . We don't quite achieve that with EvaluatePolynomial, but we get much closer than with the other options above.

(8)

Compatibility

• 

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

• 

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

See Also

ComplexBox:-EvaluatePolynomial

 


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