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

From ApCoCoAWiki
(Inserted example, updated "see" section)
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<command>
 
<command>
 
     <title>BB.LiftAS</title>
 
     <title>BB.LiftAS</title>
     <short_description>border basis scheme for the lifting of across-the-street neighbors</short_description>
+
     <short_description>BBS generators from lifting of AS neighbors</short_description>
 
<syntax>
 
<syntax>
 
BB.LiftAS(OO:LIST):LIST
 
BB.LiftAS(OO:LIST):LIST
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     <description>
 
     <description>
 
Compute the equations defining the border basis scheme and coming from the lifting of across-the-street 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 across-the-street 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>.
    </description>
+
<example>
 +
Use Q[x,y], DegRevLex;
 +
BB.LiftAS([Poly(1), x, y, xy]);
 +
 
 +
[BBS :: c[1,2]c[2,3] - c[1,1]c[3,4] + c[1,4]c[4,3] - c[1,3]c[4,4],
 +
BBS :: c[2,2]c[2,3] - c[2,1]c[3,4] + c[2,4]c[4,3] - c[2,3]c[4,4] + c[1,3],
 +
BBS :: c[2,3]c[3,2] - c[3,1]c[3,4] + c[3,4]c[4,3] - c[3,3]c[4,4] - c[1,4],
 +
BBS :: c[3,4]c[4,1] - c[2,3]c[4,2] + c[2,4] - c[3,3]]
 +
-------------------------------
 +
</example>
 +
</description>
 
     <key>kreuzer</key>
 
     <key>kreuzer</key>
 
     <key>bb.liftas</key>
 
     <key>bb.liftas</key>
 
     <key>borderbasis.liftas</key>
 
     <key>borderbasis.liftas</key>
 +
    <see>BB.LiftASViaServer</see>
 +
    <see>BB.LiftHomAS</see>
 +
    <see>BB.LiftND</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 17:16, 25 July 2008

BB.LiftAS

BBS generators from lifting of AS neighbors

Syntax

BB.LiftAS(OO:LIST):LIST

Description

Compute the equations defining the border basis scheme and coming from the lifting of across-the-street 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.LiftAS([Poly(1), x, y, xy]);

[BBS :: c[1,2]c[2,3] - c[1,1]c[3,4] + c[1,4]c[4,3] - c[1,3]c[4,4],
 BBS :: c[2,2]c[2,3] - c[2,1]c[3,4] + c[2,4]c[4,3] - c[2,3]c[4,4] + c[1,3],
 BBS :: c[2,3]c[3,2] - c[3,1]c[3,4] + c[3,4]c[4,3] - c[3,3]c[4,4] - c[1,4],
 BBS :: c[3,4]c[4,1] - c[2,3]c[4,2] + c[2,4] - c[3,3]]
-------------------------------


BB.LiftASViaServer

BB.LiftHomAS

BB.LiftND

BB.LiftNDViaServer

BB.LiftHomND