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

From ApCoCoAWiki
(Updated parameter and return value list.)
(Key and see section update.)
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     <see>BB.HomASgens</see>
 
     <see>BB.HomASgens</see>
 
     <see>BB.HomNDgens</see>
 
     <see>BB.HomNDgens</see>
     <key>kreuzer</key>
+
     <key>NDgens</key>
     <key>bb.ndgens</key>
+
     <key>BB.NDgens</key>
     <key>borderbasis.ndgens</key>
+
     <key>borderbasis.NDgens</key>
 
     <wiki-category>Package_borderbasis</wiki-category>
 
     <wiki-category>Package_borderbasis</wiki-category>
 
</command>
 
</command>

Revision as of 18:52, 22 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 NDneighbors(OO). The inputs are an integer K in the range 1..Len(NDneighbors(OO)) and a list OO of terms that specify an order ideal. The output is a list of polynomials in the ring <formula>BBS=K[c_{ij}]</formula>.

  • @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 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 NDneighbors(OO). The polynomials will belong to the ring BBS=K[c_{ij}].

Example

Use Q[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