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polylib::Dpoly -- differential operator for polynomials

Introduction

If 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)

Parameters

f - polynomial
indexlist - list of positive integers

Returns

polylib::Dpoly returns a polynomial in the same indeterminates and over the same coefficient ring as the input.

Overloadable:

f

Related Functions

D, diff

Details

Example 1

We 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 2

No 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 3

It 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])

Changes




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