Difference between revisions of "ApCoCoA-1:BB.LiftND"
From ApCoCoAWiki
m (ApCoCoA:Borderbasis.LiftND moved to ApCoCoA:BB.LiftND: new alias) |
(Inserted example, updated "see" section) |
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| Line 1: | Line 1: | ||
<command> | <command> | ||
<title>BB.LiftND</title> | <title>BB.LiftND</title> | ||
| − | <short_description> | + | <short_description>BBS generators from lifting of ND neighbors</short_description> |
<syntax> | <syntax> | ||
BB.LiftND(OO:LIST):LIST | BB.LiftND(OO:LIST):LIST | ||
| Line 7: | Line 7: | ||
<description> | <description> | ||
Compute the equations defining the border basis scheme and coming from the lifting of next-door neighbors. The input is 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>. | Compute the equations defining the border basis scheme and coming from the lifting of next-door neighbors. The input is 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>. | ||
| + | <example> | ||
| + | Use Q[x,y], DegRevLex; | ||
| + | BB.LiftND([Poly(1), x, y, xy]); | ||
| + | |||
| + | [BBS :: c[1,2]c[2,1] + c[1,4]c[4,1] - c[1,3], | ||
| + | BBS :: c[2,1]c[2,2] + c[2,4]c[4,1] + c[1,1] - c[2,3], | ||
| + | BBS :: c[2,1]c[3,2] + c[3,4]c[4,1] - c[3,3], | ||
| + | BBS :: c[2,1]c[4,2] + c[4,1]c[4,4] + c[3,1] - c[4,3], | ||
| + | BBS :: c[1,1]c[3,2] + c[1,3]c[4,2] - c[1,4], | ||
| + | BBS :: c[2,1]c[3,2] + c[2,3]c[4,2] - c[2,4], | ||
| + | BBS :: c[3,1]c[3,2] + c[3,3]c[4,2] + c[1,2] - c[3,4], | ||
| + | BBS :: c[3,2]c[4,1] + c[4,2]c[4,3] + c[2,2] - c[4,4]] | ||
| + | ------------------------------- | ||
| + | </example> | ||
</description> | </description> | ||
<key>kreuzer</key> | <key>kreuzer</key> | ||
<key>bb.liftnd</key> | <key>bb.liftnd</key> | ||
<key>borderbasis.liftnd</key> | <key>borderbasis.liftnd</key> | ||
| + | <see>BB.LiftAS</see> | ||
| + | <see>BB.LiftASViaServer</see> | ||
| + | <see>BB.LiftHomAS</see> | ||
| + | <see>BB.LiftNDViaServer</see> | ||
| + | <see>BB.LiftHomND</see> | ||
<wiki-category>Package_borderbasis</wiki-category> | <wiki-category>Package_borderbasis</wiki-category> | ||
</command> | </command> | ||
Revision as of 17:18, 25 July 2008
BB.LiftND
BBS generators from lifting of ND neighbors
Syntax
BB.LiftND(OO:LIST):LIST
Description
Compute the equations defining the border basis scheme and coming from the lifting of next-door neighbors. The input is 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>.
Example
Use Q[x,y], DegRevLex; BB.LiftND([Poly(1), x, y, xy]); [BBS :: c[1,2]c[2,1] + c[1,4]c[4,1] - c[1,3], BBS :: c[2,1]c[2,2] + c[2,4]c[4,1] + c[1,1] - c[2,3], BBS :: c[2,1]c[3,2] + c[3,4]c[4,1] - c[3,3], BBS :: c[2,1]c[4,2] + c[4,1]c[4,4] + c[3,1] - c[4,3], BBS :: c[1,1]c[3,2] + c[1,3]c[4,2] - c[1,4], BBS :: c[2,1]c[3,2] + c[2,3]c[4,2] - c[2,4], BBS :: c[3,1]c[3,2] + c[3,3]c[4,2] + c[1,2] - c[3,4], BBS :: c[3,2]c[4,1] + c[4,2]c[4,3] + c[2,2] - c[4,4]] -------------------------------
