ApCoCoA-1:BB.LiftHomND: Difference between revisions

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{{Version|1}}
<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>
   <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}].
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>
   <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>
   <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>
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     <type>borderbasis</type>
     <type>borderbasis</type>
   </types>
   </types>
   <see>BB.LiftAS</see>
   <see>ApCoCoA-1:BB.LiftAS|BB.LiftAS</see>
   <see>BB.LiftASViaServer</see>
   <see>ApCoCoA-1:BB.LiftASViaServer|BB.LiftASViaServer</see>
   <see>BB.LiftHomAS</see>
   <see>ApCoCoA-1:BB.LiftHomAS|BB.LiftHomAS</see>
   <see>BB.LiftND</see>
   <see>ApCoCoA-1:BB.LiftND|BB.LiftND</see>
   <see>BB.LiftNDViaServer</see>
   <see>ApCoCoA-1:BB.LiftNDViaServer|BB.LiftNDViaServer</see>


   <key>LiftHomND</key>
   <key>LiftHomND</key>
   <key>BB.LiftHomND</key>
   <key>BB.LiftHomND</key>
   <key>borderbasis.LiftHomND</key>
   <key>borderbasis.LiftHomND</key>
   <wiki-category>Package_borderbasis</wiki-category>
   <wiki-category>ApCoCoA-1:Package_borderbasis</wiki-category>
</command>
</command>

Latest revision as of 09:42, 7 October 2020

This article is about a function from ApCoCoA-1.

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