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Evaluating A Multiple Dimension Monomial And Its Derivatives

Syntax	monomial(n, k, p)
See Also	polval , polder

Description
Returns the derivative specified by k, of the multiple dimensional monomial specified by n, at the point specified by p. The return value is a column vector with the same type and row dimension as the integer, real, double-precision or complex matrix p. The j-th element of the return value is the derivative evaluated at the j-th row of p. The integer row vectors k and n have the same column dimension as p.

The monomial is defined by
             n(1)   n(2)           n(N)
     m(x) = x    * x   *  . . . * x
             1      2              N
where N is the length of the vector n. The vector k specifies the derivative
        k(1)     k(2)            k(N)
       d        d               d
     -------  -------  . . .  -------  m(x)
        k(1)     k(2)            k(N)
     d x      d x             d x
     
Hence, if all the elements of k are zero, the derivative is equal to m(x).

Example
Define the monomial
               2     3
     m(x)  =  x  *  x 
               1     2
The value of m(x) at the point [1, 2] is 8. We compute this value as follows
     n = [2, 3]
     k = [0, 0]
     p = [1, 2]
     monomial(n, k, p)
The partial of m(x) with respect to the second component of x at the point [1, 2] is 12. This can be computed by continuing the previous example with
     k = [0, 1]
     monomial(n, k, p)