Difference between revisions of "ApCoCoA-1:BB.ASgens"
From ApCoCoAWiki
| Line 1: | Line 1: | ||
<command> | <command> | ||
<title>BB.ASgens</title> | <title>BB.ASgens</title> | ||
| − | <short_description> | + | <short_description>Computes the generators of the vanishing ideal of a border basis scheme.</short_description> |
<syntax> | <syntax> | ||
| Line 7: | Line 7: | ||
</syntax> | </syntax> | ||
<description> | <description> | ||
| − | + | This command computes the generators of the vanishing ideal of the border basis scheme corresponding to the lifting of the <tt>K</tt>-th element of the list returned by <ref>BB.ASneighbors</ref><tt>(OO)</tt>. | |
<itemize> | <itemize> | ||
| − | <item>@param <em>K</em> | + | <item>@param <em>K</em> An integer in the range 1..Len(<ref>BB.ASneighbors</ref>(OO)).</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 | + | <item>@return A list of generators of the vanishing ideal. The polynomials will belong to the ring <tt>BBS=K[c_{ij}]</tt>.</item> |
</itemize> | </itemize> | ||
<example> | <example> | ||
Revision as of 14:33, 8 July 2009
BB.ASgens
Computes the generators of the vanishing ideal of a border basis scheme.
Syntax
BB.ASgens(K:INT,OO:LIST):LIST
Description
This command 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 BB.ASneighbors(OO).
@param K An integer in the range 1..Len(BB.ASneighbors(OO)).
@param OO A list of terms representing an order ideal.
@return A list of generators of the vanishing ideal. 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]] -------------------------------
