# Difference between revisions of "ApCoCoA-1:DA.NthDerivation"

## DA.NthDerivation

Computes the N-th derivation of a differential polynomial.

### Syntax

```DA.NthDerivation(F:POLY, N:INT):POLY
```

### Description

Computes the N-th derivation of the differential polynomial F. If the order of the result would exceed the given maximum order as implied by the current ring, an error is thrown.

• @param F A differential polynomial.

• @param N An integer.

• @return The N-th derivation of F.

#### Example

```Use QQ[x[1..2,0..20]];
F:=x[1,2]^2*x[1,1]-x[2,4]^3;
DA.NthDerivation(F, 2);
-------------------------------
5x[1,2]^2x[1,3] + 2x[1,1]x[1,3]^2 + 2x[1,1]x[1,2]x[1,4] - 6x[2,4]x[2,5]^2 - 3x[2,4]^2x[2,6]
-------------------------------
```

#### Example

```Use Q[x[1..2,0..20]];
F:=x[1,2]^2*x[1,1]-x[2,4]^3;
DA.NthDerivation(F, 20);
-------------------------------
ERROR: Maximum order is exceeded.
CONTEXT: Error(<quotes>Maximum order is exceeded.</quotes>)
-------------------------------
```