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

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{{Version|1}}
 
<command>
 
<command>
    <title>borderbasis.LiftHomND</title>
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  <title>BB.LiftHomND</title>
    <short_description>Compute eqns defining hom. BB scheme and coming 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>
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<syntax>
 
<syntax>
$borderbasis.LiftHomND(OO:LIST):LIST
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BB.LiftHomND(OO:LIST):LIST
 
</syntax>
 
</syntax>
    <description>
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  <description>
Compute the equations defining the homogeneous border basis scheme and coming 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.  
    </description>
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<itemize>
     <key>Kreuzer</key>
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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>
    <key>borderbasis.lifthomnd</key>
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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>
    <key>borderbasislifthomnd</key>
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</itemize>
    <wiki-category>Package_borderbasis</wiki-category>
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<example>
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Use QQ[x,y,z], DegRevLex;
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BB.LiftHomND([Poly(1), x, y, xy]);
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[BBS :: c[3,1]c[4,4] + c[2,1] - c[4,2],
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BBS :: c[2,1]c[4,5] + c[3,1] - c[4,3]]
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-------------------------------
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</example>
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  </description>
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  <types>
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     <type>borderbasis</type>
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  </types>
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  <see>ApCoCoA-1:BB.LiftAS|BB.LiftAS</see>
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  <see>ApCoCoA-1:BB.LiftASViaServer|BB.LiftASViaServer</see>
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  <see>ApCoCoA-1:BB.LiftHomAS|BB.LiftHomAS</see>
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  <see>ApCoCoA-1:BB.LiftND|BB.LiftND</see>
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  <see>ApCoCoA-1:BB.LiftNDViaServer|BB.LiftNDViaServer</see>
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 +
  <key>LiftHomND</key>
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  <key>BB.LiftHomND</key>
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  <key>borderbasis.LiftHomND</key>
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  <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