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

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{{Version|1}}
 
<command>
 
<command>
    <title>borderbasis.NDneighbors</title>
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  <title>BB.NDneighbors</title>
    <short_description>Computes the list of next-door neighbors in the border of OO</short_description>
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  <short_description>Computes a list of next-door neighbors.</short_description>
 +
 
 
<syntax>
 
<syntax>
$borderbasis.NDneighbors(OO:LIST):LIST
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BB.NDneighbors(OO:LIST):LIST
 
</syntax>
 
</syntax>
    <description>
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  <description>
Computes the list of next-door neighbors in the border of OO. The input is a list of terms OO (2nd element of type POLY). The output is a list of triples [i,j,k] s.t. b_i = x_k * b_j.
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This command computes the list of next-door neighbors in the border of the order ideal <tt>OO</tt>. The input is a list <tt>OO</tt> of terms that specify an order ideal. The output is a list of triples <tt>[i,j,k]</tt> such that <tt>b_i = x_k * b_j</tt> where the border terms <tt>b_i</tt> and <tt>b_j</tt> correspond to the <tt>i</tt>-th and <tt>j</tt>-th element of the list returned by the command <ref>ApCoCoA-1:BB.Border|BB.Border</ref>(OO).
    </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.</item>
    <key>borderbasis.ndneighbors</key>
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  <item>@return A list of next-door neighbors of <tt>OO</tt>.</item>
    <key>borderbasisndneighbors</key>
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</itemize>
    <wiki-category>Package_borderbasis|NDneighbors</wiki-category>
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<example>
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Use QQ[x,y,z];
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BB.Border([1,x]);
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BB.NDneighbors([1,x]);
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[z, y, xz, xy, x^2]
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-------------------------------
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[[3, 1, 1], [4, 2, 1]]
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-- E.g. the first triple of the result can be interpreted
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-- as x*z = xz
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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.ASneighbors|BB.ASneighbors</see>
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 +
  <key>NDneighbors</key>
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  <key>BB.NDneighbors</key>
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  <key>borderbasis.NDneighbors</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.NDneighbors

Computes a list of next-door neighbors.

Syntax

BB.NDneighbors(OO:LIST):LIST

Description

This command computes the list of next-door neighbors in the border of the order ideal OO. The input is a list OO of terms that specify an order ideal. The output is a list of triples [i,j,k] such that b_i = x_k * b_j where the border terms b_i and b_j correspond to the i-th and j-th element of the list returned by the command BB.Border(OO).

  • @param OO A list of terms representing an order ideal.

  • @return A list of next-door neighbors of OO.

Example

Use QQ[x,y,z];
BB.Border([1,x]);
BB.NDneighbors([1,x]);

[z, y, xz, xy, x^2]
-------------------------------
[[3, 1, 1], [4, 2, 1]]

-- E.g. the first triple of the result can be interpreted
-- as x*z = xz

BB.ASneighbors