polylib::Dpoly -- differential
operator for polynomials
IntroductionIf f is a polynomial in the indeterminates
x1 through xn,
polylib::Dpoly([i1,..,ik], f) computes the
k-th partial derivative (&partial;k
f)/(&partial;xi1 ...&partial;xik )
.
polylib::Dpoly(f) returns the derivative
of f with respect to its only variable for an univariate
polynomial f.
Call(s)polylib::Dpoly(f)
polylib::Dpoly(indexlist, f)
Parametersf |
- | polynomial |
indexlist |
- | list of positive integers |
Returnspolylib::Dpoly returns a polynomial in the same
indeterminates and over the same coefficient ring as the input.
f
Related
Functions
Detailsindexlist is greater than the
number of indeterminates of f, the zero polynomial is
returned.polylib::Dpoly([ ], p) returns
p.d, then this domain must have the method "intmult":
d::intmult(e,i), that must calculate the integer multiple of a
domain element e and a positive integer
i.polylib::Dpoly is a function of the system
kernel.
Example
1We differentiate a univariate polynomial with respect to its only indeterminate. In this case, we may leave out the first argument.
>> polylib::Dpoly(poly(2*x^2 + x + 1));
poly(4 x + 1, [x])
Example
2No we differentiate a bivariate polynomial, and must specify the indeterminate in this case.
>> polylib::Dpoly([1], poly(x^2*y + 3*x + y, [x, y]));
poly(2 x y + 3, [x, y])
Example
3It is also possible to compute second or higher partial derivatives.
>> polylib::Dpoly([1, 2], poly(x^2*y + 3*x + y, [x, y]));
poly(2 x, [x, y])
Dpoly