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

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{{Version|1}}
 
<command>
 
<command>
    <title>borderbasis.LiftAS</title>
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  <title>BB.LiftAS</title>
    <short_description>Compute the equations defining the border basis scheme and coming from the lifting of across-the-street neighbors</short_description>
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  <short_description>Computes the border basis scheme ideal generators obtained from lifting of AS neighbours.</short_description>
 +
 
 
<syntax>
 
<syntax>
$borderbasis.LiftAS(OO:LIST):LIST
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BB.LiftAS(OO:LIST):LIST
 
</syntax>
 
</syntax>
    <description>
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  <description>
Compute the equations defining the border basis scheme and coming 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 BBS=K[c_{ij}].
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This command computes the generators of the border basis scheme ideal <tt>I(B_O)</tt> that result from the lifting of across-the-street neighbours.
     </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 with second element of type <tt>POLY</tt>.</item>
    <key>borderbasis.liftas</key>
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  <item>@return A list of generators of the border basis scheme ideal. The polynomials will belong to the ring BBS=K[c_{ij}].</item>
    <key>borderbasisliftas</key>
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</itemize>
    <wiki-category>Package_borderbasis|LiftAS</wiki-category>
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<example>
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Use QQ[x,y], DegRevLex;
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BB.LiftAS([Poly(1), x, y, xy]);
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[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],
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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],
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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],
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BBS :: c[3,4]c[4,1] - c[2,3]c[4,2] + c[2,4] - c[3,3]]
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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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     <type>ideal</type>
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  </types>
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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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  <see>ApCoCoA-1:BB.LiftHomND|BB.LiftHomND</see>
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 +
  <key>LiftAS</key>
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  <key>BB.LiftAS</key>
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  <key>borderbasis.LiftAS</key>
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  <wiki-category>ApCoCoA-1:Package_borderbasis</wiki-category>
 
</command>
 
</command>

Latest revision as of 09:41, 7 October 2020

This article is about a function from ApCoCoA-1.

BB.LiftAS

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

Syntax

BB.LiftAS(OO:LIST):LIST

Description

This command computes the generators of the border basis scheme ideal I(B_O) that result from the lifting of across-the-street neighbours.

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

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

Example

Use QQ[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