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##

Evaluation of a polynomial

The evaluation of a polynomial for a given value is implemented as:

REAL Evaluate_Polynomial_Interval(int Degree,VECTOR &Coeff,REAL P)
INTERVAL Evaluate_Polynomial_Interval(int Degree,INTERVAL_VECTOR &Coeff,REAL P)
INTERVAL Evaluate_Polynomial_Interval(int Degree,VECTOR &Coeff,INTERVAL P)
INTERVAL Evaluate_Polynomial_Interval(int Degree,INTERVAL_VECTOR &Coeff,INTERVAL P)
REAL Evaluate_Polynomial_Interval(int Degree,INTEGER_VECTOR &Coeff,REAL P);
int Evaluate_Polynomial_Interval(int Degree,INTEGER_VECTOR &Coeff,INT P);

with:
`Degree`: degree of the polynomial
`Coeff`: the `Degree+1` coefficients (which can
be `REAL`, `INT` or `INTERVAL` of the
polynomial in increasing degree
`P`: the point at which we want to compute the polynomial. It
may be `REAL`, `INT` or `INTERVAL`.

These procedures enable to get:
- the value of a polynomial with
`REAL` coefficients at a
point
- the interval value of a polynomial with interval coefficients at
a real point
- the interval value of a polynomial with
`REAL` coefficients at
for an interval value of the unknown. The first and second order
derivative of the polynomial are used to get sharp bounds
- the interval value of a polynomial with interval coefficients
for an interval value of the unknown. The first and second order
derivative of the polynomial are used to get sharp bounds

**Subsections**

** Next:** Evaluation in centered form
** Up:** Utilities
** Previous:** Multiplication of two polynomials
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Jean-Pierre Merlet
2012-12-20