
Dpoly - differential operator for polynomials

Calling sequence:
Dpoly(poly)
Dpoly([integer ...], poly)

Parameter:
poly      --  polynomial
integer   --  positive integer

Overloading:

2

Summary:

Dpoly, as the differential operator D, calculates the derivative of a polynomial.

 o  If p is a univariate polynomial then Dpoly(p) returns the derivative of
    p with respect to its variable.

 o  If p is a multivariate polynomial then Dpoly([i], p) returns the partial
    derivative of p with respect to the i-th variable.

    If i is greater than the number of variables then Dpoly returns the zero
    polynomial.

An expression of the form Dpoly([i,...j], p) is equivalent to Dpoly([i],...
Dpoly([j], p)...).  It is assumed that the partial derivatives commute.
Furthermore Dpoly([], p) returns p.

If the coefficients of the polynomial are elements of a domain Dom, then
this domain must have the method "intmult":  Dom::intmult(e,i) must
calculate the integer multiple i * e of a domain element e and a positive
integer i. Dpoly is a kernel function.

>>  Dpoly(poly(2*x^2 + x + 1));

      poly(4*x + 1, [x])

>>  Dpoly([1], poly(x^2*y + 3*x + y, [x,y]));

      poly(2*x*y + 3, [x,y])

>>  Dpoly([1,2], poly(x^2*y + 3*x + y, [x,y]));

      poly(2*x, [x,y])

See also:  D, diff

