Difference between revisions of "ApCoCoA-1:DA.Initial"
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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 | ||
| Line 29: | Line 32: | ||
</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
-------------------------------
