ApCoCoA-1:DA.Initial: Difference between revisions
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{{Version|1}} | |||
<command> | <command> | ||
<title> | <title>DA.Initial</title> | ||
<short_description>the initial of a differential polynomial</short_description> | <short_description>Computes the initial of a differential polynomial.</short_description> | ||
<syntax> | <syntax> | ||
DA.Initial(F:POLY):POLY | |||
</syntax> | </syntax> | ||
<description> | <description> | ||
Initial returns the initial of polynomial F wrt. the current differential term ordering, or the hereby induced ranking, respectively. | <ref>ApCoCoA-1:DA.Initial|DA.Initial</ref> returns the initial of polynomial <tt>F</tt> wrt. the current differential term ordering, or the hereby induced ranking, respectively. | ||
<itemize> | |||
<item>@param <em>F</em> A differential polynomial.</item> | |||
<item>@return The initial of <tt>F</tt>.</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]; | ||
DA.LD(F); | |||
------------------------------- | ------------------------------- | ||
x[2,2] | x[2,2] | ||
------------------------------- | ------------------------------- | ||
DA.LPot(F); | |||
------------------------------- | ------------------------------- | ||
x[2,2]^2 | x[2,2]^2 | ||
------------------------------- | ------------------------------- | ||
DA.Initial(F); | |||
------------------------------- | ------------------------------- | ||
x[1,2]^3 + x[1,1]^3 | x[1,2]^3 + x[1,1]^3 | ||
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</example> | </example> | ||
</description> | </description> | ||
<see> | <types> | ||
<see> | <type>polynomial</type> | ||
<see> | </types> | ||
<wiki-category>Package_diffalg</wiki-category> | <see>ApCoCoA-1:DA.LD|DA.LD</see> | ||
<see>ApCoCoA-1:DA.LPot|DA.LPot</see> | |||
<see>ApCoCoA-1:DA.DiffTO|DA.DiffTO</see> | |||
<key>Initial</key> | |||
<key>DA.Initial</key> | |||
<key>diffalg.Initial</key> | |||
<key>differential.Initial</key> | |||
<wiki-category>ApCoCoA-1:Package_diffalg</wiki-category> | |||
</command> | </command> | ||
Latest revision as of 13:29, 29 October 2020
| This article is about a function from ApCoCoA-1. |
DA.Initial
Computes the initial of a differential polynomial.
Syntax
DA.Initial(F:POLY):POLY
Description
DA.Initial returns the initial of polynomial F wrt. the current differential term ordering, or the hereby induced ranking, respectively.
@param F A differential polynomial.
@return The initial of F.
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];
DA.LD(F);
-------------------------------
x[2,2]
-------------------------------
DA.LPot(F);
-------------------------------
x[2,2]^2
-------------------------------
DA.Initial(F);
-------------------------------
x[1,2]^3 + x[1,1]^3
-------------------------------
