Difference between revisions of "ApCoCoA-1:BB.NDgens"
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| + | {{Version|1}} | ||
<command> | <command> | ||
| − | + | <title>BB.NDgens</title> | |
| − | + | <short_description>Computes the generators of the vanishing ideal of a border basis scheme.</short_description> | |
| + | |||
<syntax> | <syntax> | ||
| − | BB.NDgens(K:INT,OO:LIST):LIST | + | BB.NDgens(K:INT,OO:LIST):LIST of POLY |
</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 <ref>ApCoCoA-1:BB.NDneighbors|BB.NDneighbors</ref>(OO). | |
<itemize> | <itemize> | ||
| − | <item>@param <em>K</em> | + | <item>@param <em>K</em> An integer in the range 1..<ref>ApCoCoA-1:Len|Len</ref>(<ref>ApCoCoA-1:BB.NDneighbors|BB.NDneighbors</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> | ||
| − | Use | + | Use QQ[x,y,z]; |
BB.NDgens(1, [1,x]); | 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]] | [BBS :: c[1,5]c[2,1] - c[1,3], BBS :: c[2,1]c[2,5] + c[1,1] - c[2,3]] | ||
------------------------------- | ------------------------------- | ||
</example> | </example> | ||
| − | </ | + | </description> |
| − | <see>BB.ASgens</see> | + | <types> |
| − | + | <type>borderbasis</type> | |
| − | + | <type>ideal</type> | |
| − | + | </types> | |
| − | + | ||
| − | + | <see>ApCoCoA-1:BB.ASgens|BB.ASgens</see> | |
| − | + | <see>ApCoCoA-1:BB.HomASgens|BB.HomASgens</see> | |
| + | <see>ApCoCoA-1:BB.HomNDgens|BB.HomNDgens</see> | ||
| + | |||
| + | <key>NDgens</key> | ||
| + | <key>BB.NDgens</key> | ||
| + | <key>borderbasis.NDgens</key> | ||
| + | <wiki-category>ApCoCoA-1:Package_borderbasis</wiki-category> | ||
</command> | </command> | ||
Latest revision as of 09:42, 7 October 2020
| This article is about a function from ApCoCoA-1. |
BB.NDgens
Computes the generators of the vanishing ideal of a border basis scheme.
Syntax
BB.NDgens(K:INT,OO:LIST):LIST of POLY
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 BB.NDneighbors(OO).
@param K An integer in the range 1..Len(BB.NDneighbors(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.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]] -------------------------------
