Difference between revisions of "ApCoCoA-1:BB.NDgens"
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<item>@param <em>K</em> 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.</item> | <item>@param <em>K</em> 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.</item> | ||
<item>@param <em>OO</em> A list of terms representing an order ideal.</item> | <item>@param <em>OO</em> A list of terms representing an order ideal.</item> | ||
| − | <item>@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).</item> | + | <item>@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}].</item> |
</itemize> | </itemize> | ||
<example> | <example> | ||
Revision as of 16:21, 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]] -------------------------------
