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# polylib::Dpoly

Differential operator for polynomials

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

```polylib::Dpoly(f)
polylib::Dpoly(indexlist, f)
```

## Description

If f is a polynomial in the indeterminates x1 through xn, polylib::Dpoly([i1,..,ik], f) computes the k-th partial derivative .

polylib::Dpoly(f) returns the derivative of f with respect to its only variable for an univariate polynomial f.

If some element of indexlist is greater than the number of indeterminates of f, the zero polynomial is returned.

polylib::Dpoly([], p) returns p.

If the coefficients of the polynomial are elements of a domain 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.

## Examples

### 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));`

### Example 2

Now 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]));`

### 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]));`

## Parameters

 f Polynomial indexlist List of positive integers

## Return Values

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