# ApCoCoA-1:DA.NthDerivation

From ApCoCoAWiki

## 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>) -------------------------------