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

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(New page: <command> <title>diffalg.DiffReduce</title> <short_description>Compute a differential normal form of a differential Polynomial wrt. a list of differential polynomials.</short_descr...)
 
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{{Version|1}}
 
<command>
 
<command>
     <title>diffalg.DiffReduce</title>
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     <title>DA.DiffReduce</title>
     <short_description>Compute a differential normal form of a differential Polynomial wrt. a list of differential polynomials.</short_description>
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     <short_description>Computes a differential normal form of a differential polynomial wrt. a list of differential polynomials.</short_description>
 
<syntax>
 
<syntax>
$diffalg.DiffReduce(F:POLY, G:LIST):POLY
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DA.DiffReduce(F:POLY, G:LIST):POLY
 
</syntax>
 
</syntax>
 
<description>
 
<description>
DiffReduce computes the differential normal form of F wrt. the set of differential polynomials G.
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<ref>ApCoCoA-1:DA.DiffReduce|DA.DiffReduce</ref> computes the differential normal form of <tt>F</tt> wrt. the set of differential polynomials <tt>G</tt>.
To this end, the elements of G are differentiated sufficiently often and the usual normal form is built.
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To this end, the elements of <tt>G</tt> are differentiated sufficiently often and the usual normal form is built.
 
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<itemize>
 +
<item>@param <em>F</em> Differential polynomial to compute the normal form of.</item>
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<item>@param <em>G</em> List of differential polynomials to wrt. which the normal form of <tt>F</tt> is computed.</item>
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<item>@return Normal form of <tt>F</tt> wrt. <tt>G</tt>.</item>
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</itemize>
 
<example>
 
<example>
Use Q[x[1..1,0..20]];
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Use QQ[x[1..1,0..20]];
Use Q[x[1..1,0..20]], Ord($diffalg.DiffTO("Lex"));
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Use QQ[x[1..1,0..20]], Ord(DA.DiffTO("Lex"));
$diffalg.DiffReduce(x[1,2]^2+x[1,0]^2+3, [x[1,1]+3x[1,0]]);
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DA.DiffReduce(x[1,2]^2+x[1,0]^2+3, [x[1,1]+3x[1,0]]);
 
-------------------------------
 
-------------------------------
 
82x[1,0]^2 + 3
 
82x[1,0]^2 + 3
 
-------------------------------
 
-------------------------------
 
 
</example>
 
</example>
 
</description>
 
</description>
<see>Diffalg.DiffTO</see>
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<types>
<wiki-category>Package_diffalg</wiki-category>
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<type>polynomial</type>
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</types>
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<see>ApCoCoA-1:DA.DiffTO|DA.DiffTO</see>
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<key>DiffReduce</key>
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<key>DA.DiffReduce</key>
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<key>diffalg.DiffReduce</key>
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<key>differential.DiffReduce</key>
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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.DiffReduce

Computes a differential normal form of a differential polynomial wrt. a list of differential polynomials.

Syntax

DA.DiffReduce(F:POLY, G:LIST):POLY

Description

DA.DiffReduce computes the differential normal form of F wrt. the set of differential polynomials G.

To this end, the elements of G are differentiated sufficiently often and the usual normal form is built.

  • @param F Differential polynomial to compute the normal form of.

  • @param G List of differential polynomials to wrt. which the normal form of F is computed.

  • @return Normal form of F wrt. G.

Example

Use QQ[x[1..1,0..20]];
Use QQ[x[1..1,0..20]], Ord(DA.DiffTO("Lex"));
DA.DiffReduce(x[1,2]^2+x[1,0]^2+3, [x[1,1]+3x[1,0]]);
-------------------------------
82x[1,0]^2 + 3
-------------------------------

DA.DiffTO