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

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{{Version|1}}
 
<command>
 
<command>
    <title>BB.LiftND</title>
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  <title>BB.LiftND</title>
    <short_description>Compute 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 next-door neighbours.</short_description>
 +
 
 
<syntax>
 
<syntax>
 
BB.LiftND(OO:LIST):LIST
 
BB.LiftND(OO:LIST):LIST
 
</syntax>
 
</syntax>
    <description>
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  <description>
Computes the generators of the border basis scheme ideal <formula>I(\mathbb{B}_\mathcal{O})</formula> 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 <formula>BBS=K[c_{ij}]</formula>.
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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 next-door (ND) neighbours.
 
<itemize>
 
<itemize>
   <item>@param <em>OO</em> A list of terms representing an order ideal.</item>
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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>
   <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. The polynomials will belong to the ring <tt>BBS=K[c_{ij}]</tt>.</item>
 
</itemize>
 
</itemize>
 
<example>
 
<example>
Use Q[x,y], DegRevLex;
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Use QQ[x,y], DegRevLex;
 
BB.LiftND([Poly(1), x, y, xy]);
 
BB.LiftND([Poly(1), x, y, xy]);
  
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-------------------------------
 
-------------------------------
 
</example>
 
</example>
     </description>
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  </description>
     <see>BB.LiftAS</see>
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  <types>
    <see>BB.LiftASViaServer</see>
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     <type>borderbasis</type>
    <see>BB.LiftHomAS</see>
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     <type>ideal</type>
    <see>BB.LiftNDViaServer</see>
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  </types>
    <see>BB.LiftHomND</see>
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  <see>ApCoCoA-1:BB.LiftAS|BB.LiftAS</see>
    <key>LiftND</key>
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  <see>ApCoCoA-1:BB.LiftASViaServer|BB.LiftASViaServer</see>
    <key>BB.LiftND</key>
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  <see>ApCoCoA-1:BB.LiftHomAS|BB.LiftHomAS</see>
    <key>borderbasis.LiftND</key>
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  <see>ApCoCoA-1:BB.LiftNDViaServer|BB.LiftNDViaServer</see>
    <wiki-category>Package_borderbasis</wiki-category>
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  <see>ApCoCoA-1:BB.LiftHomND|BB.LiftHomND</see>
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 +
  <key>LiftND</key>
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  <key>BB.LiftND</key>
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  <key>borderbasis.LiftND</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.LiftND

Computes the border basis scheme ideal generators obtained from lifting of next-door neighbours.

Syntax

BB.LiftND(OO:LIST):LIST

Description

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

  • @param OO A list of terms representing an order ideal. The second element is 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.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