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

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(Corrected example.)
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{{Version|1}}
 
<command>
 
<command>
 
     <title>DA.DiffReduce</title>
 
     <title>DA.DiffReduce</title>
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</syntax>
 
</syntax>
 
<description>
 
<description>
DA.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.
 
<itemize>
 
<itemize>
 
<item>@param <em>F</em> Differential polynomial to compute the normal form of.</item>
 
<item>@param <em>F</em> Differential polynomial to compute the normal form of.</item>
<item>@param <em>G</em> List of differential polynomials to wrt. which the normal form of F is computed.</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>
<item>@return Normal form of F wrt. G.</item>
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<item>@return Normal form of <tt>F</tt> wrt. <tt>G</tt>.</item>
 
</itemize>
 
</itemize>
 
<example>
 
<example>
 
Use QQ[x[1..1,0..20]];
 
Use QQ[x[1..1,0..20]];
Use QQ[x[1..1,0..20]], Ord(DA.DiffTO(<quotes>Lex</quotes>));
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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]]);
 
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>
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<type>polynomial</type>
 
<type>polynomial</type>
 
</types>
 
</types>
<see>DA.DiffTO</see>
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<see>ApCoCoA-1:DA.DiffTO|DA.DiffTO</see>
 
<key>DiffReduce</key>
 
<key>DiffReduce</key>
 
<key>DA.DiffReduce</key>
 
<key>DA.DiffReduce</key>
 
<key>diffalg.DiffReduce</key>
 
<key>diffalg.DiffReduce</key>
 
<key>differential.DiffReduce</key>
 
<key>differential.DiffReduce</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 13:29, 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