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

From ApCoCoAWiki
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<command>
 
<command>
 
   <title>BB.BBasisForOI</title>
 
   <title>BB.BBasisForOI</title>
   <short_description>Compute the border basis of an ideal w.r.t. a given order ideal.</short_description>
+
   <short_description>Computes the border basis of an ideal w.r.t. a given order ideal.</short_description>
 
    
 
    
 
<syntax>
 
<syntax>
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   <types>
 
   <types>
 
     <type>borderbasis</type>
 
     <type>borderbasis</type>
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    <type>ideal</type>
 
   </types>
 
   </types>
 
   <see>BB.BBasis</see>
 
   <see>BB.BBasis</see>

Revision as of 12:40, 28 April 2009

BB.BBasisForOI

Computes the border basis of an ideal w.r.t. a given order ideal.

Syntax

BB.BBasisForOI(F:LIST,OO:LIST):LIST

Description

Computes the border basis of the ideal I = <F> with respect to the order ideal OO. Gives an error messages if no border basis exists. Uses the O_sigma(I) border basis and the border basis transformation algorithm. The inputs are a list of polynomials F and a list OO of terms that specify an order ideal. The output is a list of polynomials.

  • @param F Generators of a zero-dimensional ideal whose border basis should be computed.

  • @param OO A list of terms representing an order ideal.

  • @return A list of border basis polynomials.

Example

Use QQ[x,y];
BB.BBasisForOI([x^2, xy + y^2], [1,x,y,y^2]);

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

BB.BBasis