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

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m (ApCoCoA:Diffalg.DiffGB moved to ApCoCoA:DA.DiffGB: To comply with style principles.)
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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>
 
<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 I.</item>
 
</itemize>
 
</itemize>
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<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>

Revision as of 10:59, 23 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]]
-------------------------------