Difference between revisions of "ApCoCoA-1:DA.DiffGB"
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<command> | <command> | ||
| − | <title> | + | <title>DA.DiffGB</title> |
| − | <short_description> | + | <short_description>Calculates a differential Groebner basis.</short_description> |
<syntax> | <syntax> | ||
| − | + | DA.DiffGB(I:IDEAL):LIST | |
</syntax> | </syntax> | ||
<description> | <description> | ||
Returns a differential Groebner basis of the ideal I which is differentially generated by G wrt. the current differential term ordering. This function only terminates if the ideal I is zero dimensional and has a finite differential Groebner basis. | Returns a differential Groebner basis of the ideal I which is differentially generated by G wrt. the current differential term ordering. This function only terminates if the ideal I is zero dimensional and has a finite differential Groebner basis. | ||
| + | <itemize> | ||
| + | <item>@param I A differential ideal.</item> | ||
| + | <item>@return If terminating, a list of differential polynomials that form a differential Groebner basis of I.</item> | ||
| + | </itemize> | ||
<example>Use Q[x[1..1,0..20]]; | <example>Use Q[x[1..1,0..20]]; | ||
| − | Use Q[x[1..1,0..20]], Ord( | + | Use Q[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]] | [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]] | ||
| Line 15: | Line 19: | ||
</example> | </example> | ||
</description> | </description> | ||
| + | <types> | ||
| + | <type>polynomial</type> | ||
| + | <type>groebner</type> | ||
| + | </types> | ||
| + | <key>DiffGB</key> | ||
| + | <key>DA.DiffGB</key> | ||
| + | <key>diffalg.DiffGB</key> | ||
| + | <key>differential.DiffGB</key> | ||
<wiki-category>Package_diffalg</wiki-category> | <wiki-category>Package_diffalg</wiki-category> | ||
</command> | </command> | ||
Revision as of 12:34, 22 April 2009
DA.DiffGB
Calculates 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 G 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 Q[x[1..1,0..20]];
Use Q[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]]
-------------------------------
