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Derivative of a polynomial

The derivatives of a polynomial may be computed using the procedures:
VECTOR Derivative_Polynomial_Interval(int Degree,VECTOR &Coeff)
INTEGER_VECTOR Derivative_Polynomial_Interval(int Degree,INTEGER_VECTOR &Coeff);
VECTOR Nth_Derivative_Polynomial_Interval(int Degree,VECTOR &Coeff,int n)

These procedures enable to get the coefficients of the first and `n`-th derivative of a polynomial defined by its `REAL` or `INT`
coefficients.
Due to rounding errors there may be errors in the coefficients
provided by the previous procedures. The procedure:

INTERVAL_VECTOR Derivative_Polynomial_Safe_Interval(int Degree,VECTOR &Coeff);

will return an `INTERVAL_VECTOR` (i.e. a set of intervals) which
are guaranteed to include the true value of the coefficients of the
derivative.
A faster procedure may be used if "safe" interval values of the coefficients
have been pre-computed:
INTERVAL_VECTOR Derivative_Polynomial_Fast_Safe_Interval(int Degree,INTERVAL_VECTOR &Coeff);

If we deal with polynomial with interval coefficients the following procedures may be
used:

INTERVAL_VECTOR Derivative_Polynomial_Interval(int Degree,INTERVAL_VECTOR &Coeff)
INTERVAL_VECTOR Nth_Derivative_Polynomial_Interval(int Degree,
INTERVAL_VECTOR &Coeff,int n)

Jean-Pierre Merlet
2012-12-20