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

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{{Version|1}}
 
<command>
 
<command>
     <title>diffalg.DiffGB</title>
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     <title>DA.DiffGB</title>
     <short_description>calculate a differential Groebner basis</short_description>
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     <short_description>Computes a differential Groebner basis.</short_description>
 
<syntax>
 
<syntax>
$diffalg.DiffGB(I:IDEAL):LIST
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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.
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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.
<example>Use Q[x[1..1,0..20]];
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<itemize>
Use Q[x[1..1,0..20]], Ord($diffalg.DiffTO("Lex"));
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<item>@param <em>I</em> A differential ideal.</item>
$diffalg.DiffGB([x[1,1]^4+x[1,0]]);
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<item>@return If terminating, a list of differential polynomials that form a differential Groebner basis of <tt>I</tt>.</item>
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</itemize>
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<example>Use QQ[x[1..1,0..20]];
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Use QQ[x[1..1,0..20]], Ord(DA.DiffTO("Lex"));
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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]]
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</example>
 
</example>
 
</description>
 
</description>
<wiki-category>Package_diffalg</wiki-category>
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<types>
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<type>polynomial</type>
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<type>ideal</type>
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<type>groebner</type>
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</types>
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<key>DiffGB</key>
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<key>DA.DiffGB</key>
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<key>diffalg.DiffGB</key>
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<key>differential.DiffGB</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.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]]
-------------------------------