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

From ApCoCoAWiki
(removing Kaspar's command refs in the descriptions since the man pages look strange)
(Reviewed text and added example)
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<command>
 
<command>
 
     <title>borderbasis.ASgens</title>
 
     <title>borderbasis.ASgens</title>
     <short_description>Compute gens of vanishing ideal of BB scheme corresp. to lifting of an element of ASneighbors(OO)</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 In 1..Len(ASneighbors(OO)) and a list of terms OO (2nd element of type POLY). The output is a list of poly in the ring <formula>BBS=K[c_{ij}]</formula>.
+
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]]
-------------------------------

borderbasis.HomASgens

borderbasis.HomNDgens

borderbasis.NDgens