Difference between revisions of "ApCoCoA-1:BB.ASgens"
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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 ASneighbors(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 ASneighbors(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 ASneighbors(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 ASneighbors(OO). The polynomials will belong to the ring BBS=K[c_{ij}].</item> |
</itemize> | </itemize> | ||
<example> | <example> | ||
Revision as of 16:47, 22 April 2009
BB.ASgens
Compute the generators of the vanishing ideal of a border basis scheme.
Syntax
BB.ASgens(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 the list returned by ASneighbors(OO). The inputs are an integer K in the range 1..Len(ASneighbors(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 ASneighbors(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 ASneighbors(OO). The polynomials will belong to the ring BBS=K[c_{ij}].
Example
Use Q[x,y,z]; BB.ASgens(1, [1,x,y,z]); [BBS :: c[1,5]c[2,1] - c[1,3]c[2,2] + c[1,4]c[3,1] - c[1,2]c[3,2] + c[1,2]c[4,1] - c[1,1]c[4,2], BBS :: c[2,2]c[2,3] - c[2,1]c[2,5] - c[2,4]c[3,1] + c[2,2]c[3,2] - c[2,2]c[4,1] + c[2,1]c[4,2], BBS :: c[3,2]^2 + c[2,2]c[3,3] - c[3,1]c[3,4] - c[2,1]c[3,5] - c[3,2]c[4,1] + c[3,1]c[4,2] - c[1,1], BBS :: c[3,2]c[4,2] + c[2,2]c[4,3] - c[3,1]c[4,4] - c[2,1]c[4,5] + c[1,2]] -------------------------------
