# ApCoCoA-1:DA.NthDerivation

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## diffalg.NthDerivation

Computes the n-th derivation of a differential polynomial.

### Syntax

$diffalg.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.

#### Example

Use Q[x[1..2,0..20]]; F:=x[1,2]^2*x[1,1]-x[2,4]^3; $diffalg.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] ------------------------------- Use Q[x[1..2,0..20]]; F:=x[1,2]^2*x[1,1]-x[2,4]^3; $diffalg.NthDerivation(F, 20); ------------------------------- ERROR: Maximum order is exceeded. CONTEXT: Error("Maximum order is exceeded.") -------------------------------