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

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(New page: <command> <title>diffalg.InitialOfDer</title> <short_description>Returns the initial wrt. a given indeterminate.</short_description> <syntax> $diffalg.InitialOfDer(F:POLY, X:INDET)...)
 
m (replaced <quotes> tag by real quotes)
 
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{{Version|1}}
 
<command>
 
<command>
     <title>diffalg.InitialOfDer</title>
+
     <title>DA.InitialOfDer</title>
     <short_description>Returns the initial wrt. a given indeterminate.</short_description>
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     <short_description>Computes the initial wrt. a given derivative.</short_description>
 
<syntax>
 
<syntax>
$diffalg.InitialOfDer(F:POLY, X:INDET):POLY
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DA.InitialOfDer(F:POLY, X:INDET):POLY
 
</syntax>
 
</syntax>
 
<description>
 
<description>
InitialOfDer returns the polynomial leading coefficient of polynomial F regarded as polynomial in the derivative X.
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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>.
 
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<itemize>
 +
<item>@param <em>F</em> A differential polynomial.</item>
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<item>@param <em>X</em> A indeterminate.</item>
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<item>@return Initial of <tt>F</tt> wrt. <tt>X</tt>.</item>
 +
</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($diffalg.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];
  
$diffalg.InitialOfDer(F, x[1,2]);
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DA.InitialOfDer(F, x[1,2]);
 
-------------------------------
 
-------------------------------
 
x[2,2]^2
 
x[2,2]^2
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</example>
 
</example>
 
</description>
 
</description>
<see>Diffalg.Initial</see>
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<types>
<see>Diffalg.DiffTO</see>
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<type>polynomial</type>
<wiki-category>Package_diffalg</wiki-category>
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</types>
 +
<see>ApCoCoA-1:DA.Initial|DA.Initial</see>
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<see>ApCoCoA-1:DA.DiffTO|DA.DiffTO</see>
 +
 
 +
<key>InitialOfDer</key>
 +
<key>DA.InitialOfDer</key>
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<key>diffalg.InitialOfDer</key>
 +
<key>differential.InitialOfDer</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.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