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

From ApCoCoAWiki
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<command>
 
<command>
 
   <title>BB.LiftND</title>
 
   <title>BB.LiftND</title>
   <short_description>Computes the border basis scheme ideal generators obtained from lifting of ND neighbors.</short_description>
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   <short_description>Computes the border basis scheme ideal generators obtained from lifting of ND neighbours.</short_description>
 
    
 
    
 
<syntax>
 
<syntax>
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</syntax>
 
</syntax>
 
   <description>
 
   <description>
Computes the generators of the border basis scheme ideal I(B_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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Computes the generators of the border basis scheme ideal I(B_O) that result from the lifting of next-door neighbours. 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}].
 
<itemize>
 
<itemize>
 
   <item>@param <em>OO</em> A list of terms representing an order ideal.</item>
 
   <item>@param <em>OO</em> A list of terms representing an order ideal.</item>
   <item>@return A list of generators of the 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 border basis scheme ideal I(B_O) that results from the lifting of next-door neighbours in the border of OO. The polynomials will belong to the ring BBS=K[c_{ij}].</item>
 
</itemize>
 
</itemize>
 
<example>
 
<example>
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   <types>
 
   <types>
 
     <type>borderbasis</type>
 
     <type>borderbasis</type>
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    <type>ideal</type>
 
   </types>
 
   </types>
 
   <see>BB.LiftAS</see>
 
   <see>BB.LiftAS</see>

Revision as of 12:50, 28 April 2009

BB.LiftND

Computes the border basis scheme ideal generators obtained from lifting of ND neighbours.

Syntax

BB.LiftND(OO:LIST):LIST

Description

Computes the generators of the border basis scheme ideal I(B_O) that result from the lifting of next-door neighbours. 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 next-door neighbours in the border of OO. The polynomials will belong to the ring BBS=K[c_{ij}].

Example

Use QQ[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]]
-------------------------------

BB.LiftAS

BB.LiftASViaServer

BB.LiftHomAS

BB.LiftNDViaServer

BB.LiftHomND