Difference between revisions of "ApCoCoA-1:BB.BBasis"

From ApCoCoAWiki
(Types section update.)
(Types section update.)
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</example>
 
</example>
 
     </description>
 
     </description>
<types>
 
<type>ideal</type>
 
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       <see>GBasis5, and more</see>
 
       <see>GBasis5, and more</see>
 
       <see>BB.BorderBasis</see>
 
       <see>BB.BorderBasis</see>
 
     <types>
 
     <types>
       <type>ideal</type>
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       <type>apcocoaserver</type>
      <type>list</type>
 
      <type>cocoaserver</type>
 
 
     </types>
 
     </types>
 
     <key>BBasis</key>
 
     <key>BBasis</key>

Revision as of 11:27, 23 April 2009

BBasis

Compute the border basis of a zero-dimensional ideal.

Syntax

BBasis(I:IDEAL):LIST of POLY

Description

Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.

Let <formula>\sigma</formula> be a degree compatible term ordering. The function BBasis calls the ApCoCoAServer to compute the <formula>\mathcal{O}_\sigma(I)</formula>-border basis of the zero-dimensional input ideal I and returns it as a list of polynomials.

The return value will be the computed border basis.

  • @param I A zero-dimensional ideal of which to compute a border basis.

  • @return A list of border basis polynomials.

Example

Use Q[x, y], DegLex;
I := Ideal([x^2, xy + y^2]);
BB := BBasis(I);
BB;

-------------------------------
[xy + y^2, x^2, y^3, xy^2]
-------------------------------

GBasis5, and more

BB.BorderBasis