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

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     <description>
 
     <description>
 
Computes the generators of the border basis scheme ideal <formula>I(\mathbb{B}_\mathcal{O})</formula> 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 <formula>BBS=K[c_{ij}]</formula>.
 
Computes the generators of the border basis scheme ideal <formula>I(\mathbb{B}_\mathcal{O})</formula> 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 <formula>BBS=K[c_{ij}]</formula>.
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<itemize>
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  <item>@param <em>OO</em> A list of terms representing an order ideal.</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 across-the-street neighbors in the border of OO. The polynomials will belong to the ring BBS=K[c_{ij}].</item>
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</itemize>
 
<example>
 
<example>
 
Use Q[x,y], DegRevLex;
 
Use Q[x,y], DegRevLex;

Revision as of 16:28, 22 April 2009

BB.LiftAS

Compute 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 <formula>I(\mathbb{B}_\mathcal{O})</formula> 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 <formula>BBS=K[c_{ij}]</formula>.

  • @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 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