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

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<command> | <command> | ||

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

− | <short_description>the derivation of a differential polynomial</short_description> | + | <short_description>Computes the derivation of a differential polynomial.</short_description> |

<syntax> | <syntax> | ||

− | + | DA.Differentiate(F:POLY):POLY | |

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

<description> | <description> | ||

The function computes the derivation of the polynomial F. If the order of the result would exceed the given maximum order as implied by the current ring, an error is thrown. | The function computes the derivation of the polynomial F. 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 F A differential polynomial.</item> | ||

+ | <item>@return The derivation of F.</item> | ||

+ | </itemize> | ||

<example> | <example> | ||

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

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

− | + | DA.Differentiate(F); | |

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

x[1,2]x[1,4]^2 + 2x[1,1]x[1,4]x[1,5] - 3x[2,4]^2x[2,5] | x[1,2]x[1,4]^2 + 2x[1,1]x[1,4]x[1,5] - 3x[2,4]^2x[2,5] | ||

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

− | + | </example> | |

+ | <example> | ||

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

F:=x[1,20]^2*x[1,1]-x[2,4]^3; | F:=x[1,20]^2*x[1,1]-x[2,4]^3; | ||

− | + | DA.Differentiate(F); | |

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

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

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

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

− | <see> | + | <types> |

+ | <type>polynomial</type> | ||

+ | </types> | ||

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

+ | <key>Differentiate</key> | ||

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

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

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

<wiki-category>Package_diffalg</wiki-category> | <wiki-category>Package_diffalg</wiki-category> | ||

</command> | </command> |

## Revision as of 13:24, 22 April 2009

## DA.Differentiate

Computes the derivation of a differential polynomial.

### Syntax

DA.Differentiate(F:POLY):POLY

### Description

The function computes the derivation of the 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.

@return The derivation of F.

#### Example

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

#### Example

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