ApCoCoA:BB.ASneighbors

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<command>

 <title>BB.ASneighbors</title>
 <short_description>Computes a list of across-the-street neighbors.</short_description>
 

<syntax> BB.ASneighbors(OO:LIST):LIST </syntax>

 <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 <ref>BB.Border</ref>(OO). <itemize>

 <item>@param OO A list of terms representing an order ideal.</item>
 <item>@return A list of across-the-street neighbors of OO.</item>

</itemize> <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 </example>

 </description>
 <types>
   <type>borderbasis</type>
 </types>
 <see>BB.NDneighbors</see>
 <key>ASneighbors</key>
 <key>BB.ASneighbors</key>
 <key>borderbasis.ASneighbors</key>
 <wiki-category>Package_borderbasis</wiki-category>

</command>