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

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+ | {{Version|1}} | ||

<command> | <command> | ||

− | <title> | + | <title>DA.NthDerivation</title> |

− | <short_description>the | + | <short_description>Computes the <tt>N</tt>-th derivation of a differential polynomial.</short_description> |

<syntax> | <syntax> | ||

− | + | DA.NthDerivation(F:POLY, N:INT):POLY | |

</syntax> | </syntax> | ||

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

+ | <itemize> | ||

+ | <item>@param <em>F</em> A differential polynomial.</item> | ||

+ | <item>@param <em>N</em> An integer.</item> | ||

+ | <item>@return The <tt>N</tt>-th derivation of <tt>F</tt>.</item> | ||

+ | </itemize> | ||

<example> | <example> | ||

− | Use | + | Use QQ[x[1..2,0..20]]; |

F:=x[1,2]^2*x[1,1]-x[2,4]^3; | 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] | 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> | |

+ | <example> | ||

Use Q[x[1..2,0..20]]; | Use Q[x[1..2,0..20]]; | ||

F:=x[1,2]^2*x[1,1]-x[2,4]^3; | F:=x[1,2]^2*x[1,1]-x[2,4]^3; | ||

− | + | DA.NthDerivation(F, 20); | |

------------------------------- | ------------------------------- | ||

ERROR: Maximum order is exceeded. | ERROR: Maximum order is exceeded. | ||

Line 24: | Line 31: | ||

</example> | </example> | ||

</description> | </description> | ||

− | <see> | + | <types> |

− | <wiki-category>Package_diffalg</wiki-category> | + | <type>polynomial</type> |

+ | </types> | ||

+ | <see>ApCoCoA-1:DA.Differentiate|DA.Differentiate</see> | ||

+ | |||

+ | <key>NthDerivation</key> | ||

+ | <key>DA.NthDerivation</key> | ||

+ | <key>diffalg.NthDerivation</key> | ||

+ | <key>differential.NthDerivation</key> | ||

+ | <wiki-category>ApCoCoA-1:Package_diffalg</wiki-category> | ||

</command> | </command> |

## Latest revision as of 13:30, 29 October 2020

This article is about a function from ApCoCoA-1. |

## 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("Maximum order is exceeded.") -------------------------------