Difference between revisions of "ApCoCoA-1:BB.ASgens"

From ApCoCoAWiki
m
(new alias)
Line 1: Line 1:
 
<command>
 
<command>
     <title>borderbasis.ASgens</title>
+
     <title>BB.ASgens</title>
 
     <short_description>generators from vanishing ideal of a border basis scheme</short_description>
 
     <short_description>generators from vanishing ideal of a border basis scheme</short_description>
 
<syntax>
 
<syntax>
$borderbasis.ASgens(K:INT,OO:LIST):LIST
+
BB.ASgens(K:INT,OO:LIST):LIST
 
</syntax>
 
</syntax>
 
     <description>
 
     <description>
Line 9: Line 9:
 
<example>
 
<example>
 
Use Q[x,y,z];
 
Use Q[x,y,z];
$borderbasis.ASgens(1, [1,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[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[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],
Line 17: Line 17:
 
</example>
 
</example>
 
     </description>
 
     </description>
     <see>borderbasis.HomASgens</see>
+
     <see>BB.HomASgens</see>
     <see>borderbasis.HomNDgens</see>
+
     <see>BB.HomNDgens</see>
     <see>borderbasis.NDgens</see>
+
     <see>BB.NDgens</see>
 
     <key>kreuzer</key>
 
     <key>kreuzer</key>
 +
    <key>bb.asgens</key>
 
     <key>borderbasis.asgens</key>
 
     <key>borderbasis.asgens</key>
 
     <wiki-category>Package_borderbasis</wiki-category>
 
     <wiki-category>Package_borderbasis</wiki-category>
 
</command>
 
</command>

Revision as of 19:41, 8 November 2007

BB.ASgens

generators from 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>.

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]]
-------------------------------

BB.HomASgens

BB.HomNDgens

BB.NDgens