ApCoCoA-1:DA.Sep: Difference between revisions
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<command> | <command> | ||
<title> | <title>DA.Sep</title> | ||
<short_description>the separand of a differential polynomial</short_description> | <short_description>Computes the separand of a differential polynomial.</short_description> | ||
<syntax> | <syntax> | ||
DA.Sep(F:POLY):POLY | |||
</syntax> | </syntax> | ||
<description> | <description> | ||
Sep returns the separand of polynomial F wrt. the current differential term ordering, or the hereby induced ranking, respectivly. | DA.Sep returns the separand of polynomial F wrt. the current differential term ordering, or the hereby induced ranking, respectivly. | ||
The | The seperand of F is just the initial of the derivative of F. | ||
<itemize> | |||
<item>@param F A differential polynomial.</item> | |||
<item>@return The seperand of F wrt. to the current differential term ordering.</item> | |||
</itemize> | |||
<example> | <example> | ||
Use Q[x[1..2,0..20]]; | Use Q[x[1..2,0..20]]; | ||
Use Q[x[1..2,0..20]], Ord( | Use Q[x[1..2,0..20]], Ord(DA.DiffTO("Lex")); | ||
F:=x[1,2]^3x[2,2]^2 + x[1,1]^3x[2,2]^2 + 1/4x[1,2]; | F:=x[1,2]^3x[2,2]^2 + x[1,1]^3x[2,2]^2 + 1/4x[1,2]; | ||
G:= | G:=DA.Differentiate(F); | ||
DA.Initial(G); | |||
------------------------------- | ------------------------------- | ||
2x[1,2]^3x[2,2] + 2x[1,1]^3x[2,2] | 2x[1,2]^3x[2,2] + 2x[1,1]^3x[2,2] | ||
------------------------------- | ------------------------------- | ||
DA.Sep(F); | |||
------------------------------- | ------------------------------- | ||
2x[1,2]^3x[2,2] + 2x[1,1]^3x[2,2] | 2x[1,2]^3x[2,2] + 2x[1,1]^3x[2,2] | ||
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</example> | </example> | ||
</description> | </description> | ||
<see> | <types> | ||
<see> | <type>polynomial</type> | ||
<see> | </types> | ||
<see>DA.DiffTO</see> | |||
<see>DA.Differentiate</see> | |||
<see>DA.Initial</see> | |||
<key>Sep</key> | |||
<key>DA.Sep</key> | |||
<key>diffalg.Sep</key> | |||
<key>differential.Sep</key> | |||
<wiki-category>Package_diffalg</wiki-category> | <wiki-category>Package_diffalg</wiki-category> | ||
</command> | </command> | ||
Revision as of 13:58, 22 April 2009
DA.Sep
Computes the separand of a differential polynomial.
Syntax
DA.Sep(F:POLY):POLY
Description
DA.Sep returns the separand of polynomial F wrt. the current differential term ordering, or the hereby induced ranking, respectivly.
The seperand of F is just the initial of the derivative of F.
@param F A differential polynomial.
@return The seperand of F wrt. to the current differential term ordering.
Example
Use Q[x[1..2,0..20]];
Use Q[x[1..2,0..20]], Ord(DA.DiffTO("Lex"));
F:=x[1,2]^3x[2,2]^2 + x[1,1]^3x[2,2]^2 + 1/4x[1,2];
G:=DA.Differentiate(F);
DA.Initial(G);
-------------------------------
2x[1,2]^3x[2,2] + 2x[1,1]^3x[2,2]
-------------------------------
DA.Sep(F);
-------------------------------
2x[1,2]^3x[2,2] + 2x[1,1]^3x[2,2]
-------------------------------
