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

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{{Version|1}}
 
<command>
 
<command>
    <title>borderbasis.ASneighbors</title>
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  <title>BB.ASneighbors</title>
    <short_description>list of across-the-street neighbors</short_description>
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  <short_description>Computes a list of across-the-street neighbors.</short_description>
 +
 
 
<syntax>
 
<syntax>
$borderbasis.ASneighbors(OO:LIST):LIST
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BB.ASneighbors(OO:LIST):LIST
 
</syntax>
 
</syntax>
    <description>
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  <description>
Computes the list of across-the-street 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 quadruples <formula>[i,j,k,l]</formula> such that <formula>x_k * b_i = x_l * b_j</formula>.
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This command computes the list of across-the-street 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 quadruples <tt>[i,j,k,l]</tt> such that <tt>x_k * b_i = x_l * 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).
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<itemize>
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  <item>@param <em>OO</em> A list of terms representing an order ideal.</item>
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  <item>@return A list of across-the-street neighbors of <tt>OO</tt>.</item>
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</itemize>
 
<example>
 
<example>
Use Q[x,y,z];
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Use QQ[x,y,z];
$borderbasis.ASneighbors([1,x]);
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BB.Border([1,x]);
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BB.ASneighbors([1,x]);
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 +
[z, y, xz, xy, x^2]
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-------------------------------
 
[[1, 2, 2, 3], [3, 4, 2, 3], [3, 5, 1, 3], [4, 5, 1, 2]]
 
[[1, 2, 2, 3], [3, 4, 2, 3], [3, 5, 1, 3], [4, 5, 1, 2]]
-------------------------------
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 +
-- E.g. the first quadruple of the result can be interpreted
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-- as that y*z = z*y
 
</example>
 
</example>
    </description>
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  </description>
     <see>borderbasis.NDneighbors</see>
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  <types>
    <key>Kreuzer</key>
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     <type>borderbasis</type>
    <key>borderbasis.asneighbors</key>
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  </types>
    <key>borderbasisasneighbors</key>
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  <see>ApCoCoA-1:BB.NDneighbors|BB.NDneighbors</see>
    <wiki-category>Package_borderbasis</wiki-category>
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  <key>ASneighbors</key>
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  <key>BB.ASneighbors</key>
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  <key>borderbasis.ASneighbors</key>
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  <wiki-category>ApCoCoA-1:Package_borderbasis</wiki-category>
 
</command>
 
</command>

Latest revision as of 09:38, 7 October 2020

This article is about a function from ApCoCoA-1.

BB.ASneighbors

Computes a list of across-the-street neighbors.

Syntax

BB.ASneighbors(OO:LIST):LIST

Description

This command computes the list of across-the-street 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 quadruples [i,j,k,l] such that x_k * b_i = x_l * 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 across-the-street neighbors of OO.

Example

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

[z, y, xz, xy, x^2]
-------------------------------
[[1, 2, 2, 3], [3, 4, 2, 3], [3, 5, 1, 3], [4, 5, 1, 2]]

-- E.g. the first quadruple of the result can be interpreted
-- as that y*z = z*y

BB.NDneighbors