Difference between revisions of "ApCoCoA-1:DA.Initial"

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{{Version|1}}
 
<command>
 
<command>
 
     <title>DA.Initial</title>
 
     <title>DA.Initial</title>
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</syntax>
 
</syntax>
 
<description>
 
<description>
Initial returns the initial of polynomial F wrt. the current differential term ordering, or the hereby induced ranking, respectively.
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<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>
 
<itemize>
 
<item>@param <em>F</em> A differential polynomial.</item>
 
<item>@param <em>F</em> A differential polynomial.</item>
<item>@return The initial of F.</item>
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<item>@return The initial of <tt>F</tt>.</item>
 
</itemize>
 
</itemize>
 
<example>
 
<example>
Use Q[x[1..2,0..20]];
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Use QQ[x[1..2,0..20]];
Use Q[x[1..2,0..20]], Ord(DA.DiffTO(<quotes>Lex</quotes>));
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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];
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<type>polynomial</type>
 
<type>polynomial</type>
 
</types>
 
</types>
<see>DA.LD</see>
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<see>ApCoCoA-1:DA.LD|DA.LD</see>
<see>DA.LPot</see>
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<see>ApCoCoA-1:DA.LPot|DA.LPot</see>
<see>DA.DiffTO</see>
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<see>ApCoCoA-1:DA.DiffTO|DA.DiffTO</see>
  
 
<key>Initial</key>
 
<key>Initial</key>
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<key>diffalg.Initial</key>
 
<key>diffalg.Initial</key>
 
<key>differential.Initial</key>
 
<key>differential.Initial</key>
<wiki-category>Package_diffalg</wiki-category>
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<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
-------------------------------

DA.LD

DA.LPot

DA.DiffTO