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

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{{Version|1}}
 
<command>
 
<command>
 
     <title>DA.InitialOfDer</title>
 
     <title>DA.InitialOfDer</title>
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</syntax>
 
</syntax>
 
<description>
 
<description>
<ref>DA.InitialOfDer</ref> returns the polynomial leading coefficient of polynomial <tt>F</tt> regarded as polynomial in the derivative <tt>X</tt>.
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<ref>ApCoCoA-1:DA.InitialOfDer|DA.InitialOfDer</ref> returns the polynomial leading coefficient of polynomial <tt>F</tt> regarded as polynomial in the derivative <tt>X</tt>.
 
<itemize>
 
<itemize>
 
<item>@param <em>F</em> A differential polynomial.</item>
 
<item>@param <em>F</em> A differential polynomial.</item>
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<example>
 
<example>
 
Use QQ[x[1..2,0..20]];
 
Use QQ[x[1..2,0..20]];
Use QQ[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.Initial</see>
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<see>ApCoCoA-1:DA.Initial|DA.Initial</see>
<see>DA.DiffTO</see>
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<see>ApCoCoA-1:DA.DiffTO|DA.DiffTO</see>
  
 
<key>InitialOfDer</key>
 
<key>InitialOfDer</key>

Latest revision as of 13:29, 29 October 2020

This article is about a function from ApCoCoA-1.

DA.InitialOfDer

Computes the initial wrt. a given derivative.

Syntax

DA.InitialOfDer(F:POLY, X:INDET):POLY

Description

DA.InitialOfDer returns the polynomial leading coefficient of polynomial F regarded as polynomial in the derivative X.

  • @param F A differential polynomial.

  • @param X A indeterminate.

  • @return Initial of F wrt. X.

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.InitialOfDer(F, x[1,2]);
-------------------------------
x[2,2]^2
-------------------------------

DA.Initial

DA.DiffTO