Difference between revisions of "ApCoCoA-1:DA.DiffGB"
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| + | {{Version|1}} | ||
<command> | <command> | ||
<title>DA.DiffGB</title> | <title>DA.DiffGB</title> | ||
| − | <short_description> | + | <short_description>Computes a differential Groebner basis.</short_description> |
<syntax> | <syntax> | ||
DA.DiffGB(I:IDEAL):LIST | DA.DiffGB(I:IDEAL):LIST | ||
</syntax> | </syntax> | ||
<description> | <description> | ||
| − | Returns a differential Groebner basis of the ideal I which is differentially generated by | + | Returns a differential Groebner basis of the ideal <tt>I</tt> which is differentially generated by a set of differential polynomials wrt. the current differential term ordering. This function only terminates if the ideal <tt>I</tt> is zero dimensional and has a finite differential Groebner basis. |
<itemize> | <itemize> | ||
| − | <item>@param I A differential ideal.</item> | + | <item>@param <em>I</em> A differential ideal.</item> |
| − | <item>@return If terminating, a list of differential polynomials that form a differential Groebner basis of I.</item> | + | <item>@return If terminating, a list of differential polynomials that form a differential Groebner basis of <tt>I</tt>.</item> |
</itemize> | </itemize> | ||
| − | <example>Use | + | <example>Use QQ[x[1..1,0..20]]; |
| − | Use | + | Use QQ[x[1..1,0..20]], Ord(DA.DiffTO("Lex")); |
DA.DiffGB([x[1,1]^4+x[1,0]]); | DA.DiffGB([x[1,1]^4+x[1,0]]); | ||
------------------------------- | ------------------------------- | ||
| Line 21: | Line 22: | ||
<types> | <types> | ||
<type>polynomial</type> | <type>polynomial</type> | ||
| + | <type>ideal</type> | ||
<type>groebner</type> | <type>groebner</type> | ||
</types> | </types> | ||
| + | |||
<key>DiffGB</key> | <key>DiffGB</key> | ||
<key>DA.DiffGB</key> | <key>DA.DiffGB</key> | ||
<key>diffalg.DiffGB</key> | <key>diffalg.DiffGB</key> | ||
<key>differential.DiffGB</key> | <key>differential.DiffGB</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.DiffGB
Computes a differential Groebner basis.
Syntax
DA.DiffGB(I:IDEAL):LIST
Description
Returns a differential Groebner basis of the ideal I which is differentially generated by a set of differential polynomials wrt. the current differential term ordering. This function only terminates if the ideal I is zero dimensional and has a finite differential Groebner basis.
@param I A differential ideal.
@return If terminating, a list of differential polynomials that form a differential Groebner basis of I.
Example
Use QQ[x[1..1,0..20]];
Use QQ[x[1..1,0..20]], Ord(DA.DiffTO("Lex"));
DA.DiffGB([x[1,1]^4+x[1,0]]);
-------------------------------
[x[1,3] - 8x[1,1]x[1,2]^3, x[1,1]^2x[1,2]^2 + 1/4x[1,2], x[1,0]x[1,2] - 1/4x[1,1]^2, x[1,1]^4 + x[1,0]]
-------------------------------
