Difference between revisions of "ApCoCoA-1:DA.Sep"
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S schuster (talk | contribs) (Applied style principles.) |
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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] | ||
| Line 28: | Line 33: | ||
</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]
-------------------------------
