Difference between revisions of "ApCoCoA-1:DA.NthDerivation"
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<command> | <command> | ||
| − | <title> | + | <title>DA.NthDerivation</title> |
| − | <short_description>the n-th derivation of a differential polynomial</short_description> | + | <short_description>Computes the n-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 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. | ||
| + | <itemize> | ||
| + | <item>@param F A differential polynomial.</item> | ||
| + | <item>@param N An integer.</item> | ||
| + | <item>@return The N-th derivation of F.</item> | ||
| + | </itemize> | ||
<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, 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 30: | ||
</example> | </example> | ||
</description> | </description> | ||
| − | <see> | + | <types> |
| + | <type>polynomial</type> | ||
| + | </types> | ||
| + | <see>DA.Differentiate</see> | ||
| + | <key>NthDerivation</key> | ||
| + | <key>DA.NthDerivation</key> | ||
| + | <key>diffalg.NthDerivation</key> | ||
| + | <key>differential.NthDerivation</key> | ||
<wiki-category>Package_diffalg</wiki-category> | <wiki-category>Package_diffalg</wiki-category> | ||
</command> | </command> | ||
Revision as of 13:42, 22 April 2009
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 Q[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.")
-------------------------------
