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

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   <title>BB.NDgens</title>
 
   <title>BB.NDgens</title>
 
   <short_description>Compute the generators of the vanishing ideal of a border basis scheme.</short_description>
 
   <short_description>Compute the generators of the vanishing ideal of a border basis scheme.</short_description>
   <syntax>BB.NDgens(K:INT,OO:LIST):LIST</syntax>
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 +
<syntax>
 +
BB.NDgens(K:INT,OO:LIST):LIST
 +
</syntax>
 
   <description>
 
   <description>
 
Computes the generators of the vanishing ideal of the border basis scheme corresponding to the lifting of the K-th element of <ref>BB.NDneighbors</ref>(OO). The inputs are an integer K in the range 1..<ref>Len</ref>(<ref>BB.NDneighbors</ref>(OO)) and a list OO of terms that specify an order ideal. The output is a list of polynomials in the ring BBS=K[c_{ij}].
 
Computes the generators of the vanishing ideal of the border basis scheme corresponding to the lifting of the K-th element of <ref>BB.NDneighbors</ref>(OO). The inputs are an integer K in the range 1..<ref>Len</ref>(<ref>BB.NDneighbors</ref>(OO)) and a list OO of terms that specify an order ideal. The output is a list of polynomials in the ring BBS=K[c_{ij}].

Revision as of 14:50, 24 April 2009

BB.NDgens

Compute the generators of the vanishing ideal of a border basis scheme.

Syntax

BB.NDgens(K:INT,OO:LIST):LIST

Description

Computes the generators of the vanishing ideal of the border basis scheme corresponding to the lifting of the K-th element of BB.NDneighbors(OO). The inputs are an integer K in the range 1..Len(BB.NDneighbors(OO)) and a list OO of terms that specify an order ideal. The output is a list of polynomials in the ring BBS=K[c_{ij}].

  • @param K The generators of the vanishing ideal of the border basis scheme corresponding to the lifting of the K-th element of the list returned by BB.NDneighbors(OO) will be computed.

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

  • @return A list of generators of the vanishing ideal of the border basis scheme corresponding to the lifting of the K-th element of the list returned by BB.NDneighbors(OO). The polynomials will belong to the ring BBS=K[c_{ij}].

Example

Use QQ[x,y,z];
BB.NDgens(1, [1,x]);
[BBS :: c[1,5]c[2,1] - c[1,3], BBS :: c[2,1]c[2,5] + c[1,1] - c[2,3]]
-------------------------------


BB.ASgens

BB.HomASgens

BB.HomNDgens