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

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{{Version|1}}
 
<command>
 
<command>
 
     <title>DA.NthDerivation</title>
 
     <title>DA.NthDerivation</title>
     <short_description>Computes the N-th derivation of a differential polynomial.</short_description>
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     <short_description>Computes the <tt>N</tt>-th derivation of a differential polynomial.</short_description>
 
<syntax>
 
<syntax>
 
DA.NthDerivation(F:POLY, N:INT):POLY
 
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.  
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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>
 
<itemize>
 
<item>@param <em>F</em> A differential polynomial.</item>
 
<item>@param <em>F</em> A differential polynomial.</item>
 
<item>@param <em>N</em> An integer.</item>
 
<item>@param <em>N</em> An integer.</item>
<item>@return The N-th derivation of F.</item>
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<item>@return The <tt>N</tt>-th derivation of <tt>F</tt>.</item>
 
</itemize>
 
</itemize>
 
<example>
 
<example>
Use Q[x[1..2,0..20]];
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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);
 
DA.NthDerivation(F, 2);
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<type>polynomial</type>
 
<type>polynomial</type>
 
</types>
 
</types>
<see>DA.Differentiate</see>
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<see>ApCoCoA-1:DA.Differentiate|DA.Differentiate</see>
  
 
<key>NthDerivation</key>
 
<key>NthDerivation</key>
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<key>diffalg.NthDerivation</key>
 
<key>diffalg.NthDerivation</key>
 
<key>differential.NthDerivation</key>
 
<key>differential.NthDerivation</key>
<wiki-category>Package_diffalg</wiki-category>
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<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.")
-------------------------------

DA.Differentiate