Difference between revisions of "ApCoCoA-1:BB.ASneighbors"
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| + | {{Version|1}} | ||
<command> | <command> | ||
<title>BB.ASneighbors</title> | <title>BB.ASneighbors</title> | ||
| − | <short_description> | + | <short_description>Computes a list of across-the-street neighbors.</short_description> |
<syntax> | <syntax> | ||
| Line 7: | Line 8: | ||
</syntax> | </syntax> | ||
<description> | <description> | ||
| − | + | 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). | |
<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> | ||
| − | <item>@return A list of across-the-street neighbors of OO.</item> | + | <item>@return A list of across-the-street neighbors of <tt>OO</tt>.</item> |
</itemize> | </itemize> | ||
<example> | <example> | ||
Use QQ[x,y,z]; | Use QQ[x,y,z]; | ||
| + | BB.Border([1,x]); | ||
BB.ASneighbors([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]] | [[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> | </example> | ||
</description> | </description> | ||
| Line 22: | Line 29: | ||
<type>borderbasis</type> | <type>borderbasis</type> | ||
</types> | </types> | ||
| − | <see>BB.NDneighbors</see> | + | <see>ApCoCoA-1:BB.NDneighbors|BB.NDneighbors</see> |
<key>ASneighbors</key> | <key>ASneighbors</key> | ||
<key>BB.ASneighbors</key> | <key>BB.ASneighbors</key> | ||
<key>borderbasis.ASneighbors</key> | <key>borderbasis.ASneighbors</key> | ||
| − | <wiki-category>Package_borderbasis</wiki-category> | + | <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
