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

From ApCoCoAWiki
(Types section update.)
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<command>
 
<command>
 
   <title>BB.LiftAS</title>
 
   <title>BB.LiftAS</title>
   <short_description>Compute the border basis scheme ideal generators obtained from lifting of AS neighbors.</short_description>
+
   <short_description>Computes the border basis scheme ideal generators obtained from lifting of AS neighbors.</short_description>
 
   <syntax>BB.LiftAS(OO:LIST):LIST</syntax>
 
   <syntax>BB.LiftAS(OO:LIST):LIST</syntax>
 
   <description>
 
   <description>
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   </description>
 
   </description>
 
   <types>
 
   <types>
    <type>list</type>
 
 
     <type>borderbasis</type>
 
     <type>borderbasis</type>
 
   </types>
 
   </types>
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   <see>BB.LiftNDViaServer</see>
 
   <see>BB.LiftNDViaServer</see>
 
   <see>BB.LiftHomND</see>
 
   <see>BB.LiftHomND</see>
 +
 
   <key>LiftAS</key>
 
   <key>LiftAS</key>
 
   <key>BB.LiftAS</key>
 
   <key>BB.LiftAS</key>

Revision as of 13:44, 24 April 2009

BB.LiftAS

Computes the border basis scheme ideal generators obtained from lifting of AS neighbors.

Syntax

BB.LiftAS(OO:LIST):LIST

Description

Computes the generators of the border basis scheme ideal I(B_O) that result 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 BBS=K[c_{ij}].

  • @param OO A list of terms representing an order ideal.

  • @return A list of generators of the border basis scheme ideal I(B_O) that results from the lifting of across-the-street neighbors in the border of OO. The polynomials will belong to the ring BBS=K[c_{ij}].

Example

Use QQ[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