Difference between revisions of "ApCoCoA-1:DA.Sep"
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| + | {{Version|1}} | ||
<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, | + | <ref>ApCoCoA-1:DA.Sep|DA.Sep</ref> returns the separand of polynomial <tt>F</tt> wrt. the current differential term ordering, or the hereby induced ranking, respectively. The seperand of <tt>F</tt> is just the initial of the derivative of <tt>F</tt>. |
| − | The | + | <itemize> |
| + | <item>@param <em>F</em> A differential polynomial.</item> | ||
| + | <item>@return The seperand of <tt>F</tt> wrt. to the current differential term ordering.</item> | ||
| + | </itemize> | ||
<example> | <example> | ||
| − | Use | + | Use QQ[x[1..2,0..20]]; |
| − | Use | + | Use QQ[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] | ||
------------------------------- | ------------------------------- | ||
| + | </example> | ||
| + | </description> | ||
| + | <types> | ||
| + | <type>polynomial</type> | ||
| + | </types> | ||
| + | <see>ApCoCoA-1:DA.DiffTO|DA.DiffTO</see> | ||
| + | <see>ApCoCoA-1:DA.Differentiate|DA.Differentiate</see> | ||
| + | <see>ApCoCoA-1:DA.Initial|DA.Initial</see> | ||
| − | < | + | <key>Sep</key> |
| − | </ | + | <key>DA.Sep</key> |
| − | < | + | <key>diffalg.Sep</key> |
| − | < | + | <key>differential.Sep</key> |
| − | < | + | <wiki-category>ApCoCoA-1:Package_diffalg</wiki-category> |
| − | <wiki-category>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.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, respectively. 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 QQ[x[1..2,0..20]];
Use QQ[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]
-------------------------------
