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

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{{Version|1}}
 
<command>
 
<command>
 
     <title>DA.Sep</title>
 
     <title>DA.Sep</title>
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</syntax>
 
</syntax>
 
<description>
 
<description>
DA.Sep returns the separand of polynomial F wrt. the current differential term ordering, or the hereby induced ranking, respectivly. The seperand of F is just the initial of the derivative of F.
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<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>.
  
 
<itemize>
 
<itemize>
 
<item>@param <em>F</em> A differential polynomial.</item>
 
<item>@param <em>F</em> A differential polynomial.</item>
<item>@return The seperand of F wrt. to the current differential term ordering.</item>
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<item>@return The seperand of <tt>F</tt> wrt. to the current differential term ordering.</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("Lex"));
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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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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>
 
</example>
 
</description>
 
</description>
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</types>
 
</types>
  
<see>DA.DiffTO</see>
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<see>ApCoCoA-1:DA.DiffTO|DA.DiffTO</see>
<see>DA.Differentiate</see>
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<see>ApCoCoA-1:DA.Differentiate|DA.Differentiate</see>
<see>DA.Initial</see>
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<see>ApCoCoA-1:DA.Initial|DA.Initial</see>
  
 
<key>Sep</key>
 
<key>Sep</key>
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<key>diffalg.Sep</key>
 
<key>diffalg.Sep</key>
 
<key>differential.Sep</key>
 
<key>differential.Sep</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 13:30, 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]
-------------------------------


DA.DiffTO

DA.Differentiate

DA.Initial