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

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(Updated description and example.)
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</syntax>
 
</syntax>
 
   <description>
 
   <description>
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>.
+
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>BB.Border</ref>(OO).
 
<itemize>
 
<itemize>
 
   <item>@param <em>OO</em> A list of terms representing an order ideal.</item>
 
   <item>@param <em>OO</em> A list of terms representing an order ideal.</item>
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<example>
 
<example>
 
Use QQ[x,y,z];
 
Use QQ[x,y,z];
 +
BB.Border([1,x]);
 
BB.NDneighbors([1,x]);
 
BB.NDneighbors([1,x]);
 +
 +
[z, y, xz, xy, x^2]
 +
-------------------------------
 
[[3, 1, 1], [4, 2, 1]]
 
[[3, 1, 1], [4, 2, 1]]
-------------------------------
+
 
 +
-- E.g. the first triple of the result can be interpreted
 +
-- as that x*z = xz
 
</example>
 
</example>
 
   </description>
 
   </description>

Revision as of 14:03, 26 May 2010

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 that x*z = xz

BB.ASneighbors