Difference between revisions of "ApCoCoA-1:BB.ASgens"
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| + | {{Version|1}} | ||
<command> | <command> | ||
| − | + | <title>BB.ASgens</title> | |
| − | + | <short_description>Computes the generators of the vanishing ideal of a border basis scheme.</short_description> | |
| + | |||
<syntax> | <syntax> | ||
| − | + | BB.ASgens(K:INT,OO:LIST):LIST | |
</syntax> | </syntax> | ||
| − | + | <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>ApCoCoA-1:BB.ASneighbors|BB.ASneighbors</ref><tt>(OO)</tt>. | |
| − | + | <itemize> | |
| − | <key> | + | <item>@param <em>K</em> An integer in the range 1..Len(<ref>ApCoCoA-1:BB.ASneighbors|BB.ASneighbors</ref>(OO)).</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. The polynomials will belong to the ring <tt>BBS=K[c_{ij}]</tt>.</item> | |
| − | + | </itemize> | |
| + | <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]] | ||
| + | ------------------------------- | ||
| + | </example> | ||
| + | </description> | ||
| + | <types> | ||
| + | <type>borderbasis</type> | ||
| + | </types> | ||
| + | <see>ApCoCoA-1:BB.HomASgens|BB.HomASgens</see> | ||
| + | <see>ApCoCoA-1:BB.HomNDgens|BB.HomNDgens</see> | ||
| + | <see>ApCoCoA-1:BB.NDgens|BB.NDgens</see> | ||
| + | <key>ASgens</key> | ||
| + | <key>BB.ASgens</key> | ||
| + | <key>borderbasis.ASgens</key> | ||
| + | <wiki-category>ApCoCoA-1:Package_borderbasis</wiki-category> | ||
</command> | </command> | ||
Latest revision as of 09:38, 7 October 2020
| This article is about a function from ApCoCoA-1. |
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]] -------------------------------
