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

From ApCoCoAWiki
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<command>
 
<command>
     <title>diffalg.Initial</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>
$diffalg.Initial(F:POLY):POLY
+
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.
 
Initial returns the initial of polynomial F wrt. the current differential term ordering, or the hereby induced ranking, respectively.
 
+
<itemize>
 
+
<item>@param F A differential polynomial.</item>
 +
<item>@return The initial of F.</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($diffalg.DiffTO("Lex"));
+
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];
  
$diffalg.LD(F);
+
DA.LD(F);
 
-------------------------------
 
-------------------------------
 
x[2,2]
 
x[2,2]
 
-------------------------------
 
-------------------------------
$diffalg.LPot(F);
+
DA.LPot(F);
 
-------------------------------
 
-------------------------------
 
x[2,2]^2
 
x[2,2]^2
 
-------------------------------
 
-------------------------------
$diffalg.Initial(F);
+
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>Diffalg.LD</see>
+
<types>
<see>Diffalg.LPot</see>
+
<type>polynomial</type>
<see>Diffalg.DiffTO</see>
+
</types>
 +
<see>DA.LD</see>
 +
<see>DA.LPot</see>
 +
<see>DA.DiffTO</see>
 +
<key>Initial</key>
 +
<key>DA.Initial</key>
 +
<key>diffalg.Initial</key>
 +
<key>differential.Initial</key>
 
<wiki-category>Package_diffalg</wiki-category>
 
<wiki-category>Package_diffalg</wiki-category>
 
</command>
 
</command>

Revision as of 13:27, 22 April 2009

DA.Initial

Computes the initial of a differential polynomial.

Syntax

DA.Initial(F:POLY):POLY

Description

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 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];

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