Difference between revisions of "ApCoCoA-1:BB.ASgens"
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KHiddemann (talk | contribs) (removing Kaspar's command refs in the descriptions since the man pages look strange) |
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<command> | <command> | ||
<title>borderbasis.ASgens</title> | <title>borderbasis.ASgens</title> | ||
| − | <short_description> | + | <short_description>compute generators of vanishing ideal of border basis scheme</short_description> |
<syntax> | <syntax> | ||
$borderbasis.ASgens(K:INT,OO:LIST):LIST | $borderbasis.ASgens(K:INT,OO:LIST):LIST | ||
</syntax> | </syntax> | ||
<description> | <description> | ||
| − | Computes the generators of the vanishing ideal of the border basis scheme corresponding to the lifting of the K-th element of ASneighbors(OO). The input is an integer K | + | 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 input is an integer K in the range 1..Len(ASneighbors(OO)) and a list of terms OO that specifies 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]; | ||
| + | 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> | </description> | ||
| + | <see>borderbasis.HomASgens</see> | ||
| + | <see>borderbasis.HomNDgens</see> | ||
| + | <see>borderbasis.NDgens</see> | ||
<key>Kreuzer</key> | <key>Kreuzer</key> | ||
<key>borderbasis.asgens</key> | <key>borderbasis.asgens</key> | ||
Revision as of 20:08, 7 November 2007
borderbasis.ASgens
compute generators of vanishing ideal of border basis scheme
Syntax
$borderbasis.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 input is an integer K in the range 1..Len(ASneighbors(OO)) and a list of terms OO that specifies 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]; 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]] -------------------------------
