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

From ApCoCoAWiki
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<command>
 
<command>
 
   <title>BB.LiftHomND</title>
 
   <title>BB.LiftHomND</title>
   <short_description>Compute the homogeneous border basis scheme ideal generators obtained from lifting of ND neighbors.</short_description>
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   <short_description>Computes the homogeneous border basis scheme ideal generators obtained from lifting of next-door neighbors.</short_description>
 
    
 
    
 
<syntax>
 
<syntax>
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</syntax>
 
</syntax>
 
   <description>
 
   <description>
Computes the generators of the border basis scheme ideal I(B^hom_O) that result 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 BBS=K[c_{ij}].
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This command computes the generators of the border basis scheme ideal <tt>I(B^hom_O)</tt> that result from the lifting of next-door (ND) neighbors.  
 
<itemize>
 
<itemize>
   <item>@param <em>OO</em> A list of terms representing an order ideal.</item>
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   <item>@param <em>OO</em> A list of terms representing an order ideal. The second element is of type <tt>POLY</tt>.</item>
   <item>@return A list of generators of the homogeneous border basis scheme ideal I(B_O) that results from the lifting of next-door neighbors in the border of OO. The polynomials will belong to the ring BBS=K[c_{ij}].</item>
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   <item>@return A list of generators of the homogeneous border basis scheme ideal. The polynomials will belong to the ring <tt>BBS=K[c_{ij}]</tt>.</item>
 
</itemize>
 
</itemize>
 
<example>
 
<example>

Revision as of 15:40, 8 July 2009

BB.LiftHomND

Computes the homogeneous border basis scheme ideal generators obtained from lifting of next-door neighbors.

Syntax

BB.LiftHomND(OO:LIST):LIST

Description

This command computes the generators of the border basis scheme ideal I(B^hom_O) that result from the lifting of next-door (ND) neighbors.

  • @param OO A list of terms representing an order ideal. The second element is of type POLY.

  • @return A list of generators of the homogeneous border basis scheme ideal. The polynomials will belong to the ring BBS=K[c_{ij}].

Example

Use QQ[x,y,z], DegRevLex;
BB.LiftHomND([Poly(1), x, y, xy]);

[BBS :: c[3,1]c[4,4] + c[2,1] - c[4,2],
 BBS :: c[2,1]c[4,5] + c[3,1] - c[4,3]]
-------------------------------

BB.LiftAS

BB.LiftASViaServer

BB.LiftHomAS

BB.LiftND

BB.LiftNDViaServer