Difference between revisions of "ApCoCoA-1:BB.ASgens"
From ApCoCoAWiki
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<command> | <command> | ||
| − | + | <title>BB.ASgens</title> | |
| − | + | <short_description>Compute the generators of the vanishing ideal of a border basis scheme.</short_description> | |
| − | <syntax> | + | <syntax>BB.ASgens(K:INT,OO:LIST):LIST</syntax> |
| − | BB.ASgens(K:INT,OO:LIST):LIST | + | <description> |
| − | </syntax> | + | 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 <ref>ASneighbors</ref>(OO). The inputs are an integer K in the range 1..Len(<ref>ASneighbors</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 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 | ||
<itemize> | <itemize> | ||
| − | <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 <ref>ASneighbors</ref>(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). The polynomials will belong to the ring BBS=K[c_{ij}].</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 <ref>ASneighbors</ref>(OO). The polynomials will belong to the ring BBS=K[c_{ij}].</item> |
</itemize> | </itemize> | ||
<example> | <example> | ||
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------------------------------- | ------------------------------- | ||
</example> | </example> | ||
| − | + | </description> | |
| − | <types> | + | <types> |
| − | <type>list</type> | + | <type>list</type> |
| − | <type>int</type> | + | <type>int</type> |
| − | <type>integer</type> | + | <type>integer</type> |
| − | </types> | + | </types> |
| − | + | <see>BB.HomASgens</see> | |
| − | + | <see>BB.HomNDgens</see> | |
| − | + | <see>BB.NDgens</see> | |
| − | + | <key>ASgens</key> | |
| − | + | <key>BB.ASgens</key> | |
| − | + | <key>borderbasis.ASgens</key> | |
| − | + | <wiki-category>Package_borderbasis</wiki-category> | |
</command> | </command> | ||
Revision as of 10:58, 24 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 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 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 QQ[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]] -------------------------------
