Difference between revisions of "ApCoCoA-1:DA.DiffReduce"
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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. | + | <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. | + | 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> | + | <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> | + | <item>@return Normal form of <tt>F</tt> wrt. <tt>G</tt>.</item> |
</itemize> | </itemize> | ||
<example> | <example> | ||
| − | Use | + | Use QQ[x[1..1,0..20]]; |
| − | Use | + | 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> | + | <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> | + | <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
-------------------------------
