Difference between revisions of "ApCoCoA-1:BB.ASgens"
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<command> | <command> | ||
| − | <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> | ||
| − | + | BB.ASgens(K:INT,OO:LIST):LIST | |
</syntax> | </syntax> | ||
<description> | <description> | ||
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<example> | <example> | ||
Use Q[x,y,z]; | 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[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> | + | <see>BB.HomASgens</see> |
| − | <see> | + | <see>BB.HomNDgens</see> |
| − | <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]] -------------------------------
