Difference between revisions of "ApCoCoA-1:BB.NDneighbors"
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| + | {{Version|1}} | ||
<command> | <command> | ||
| − | + | <title>BB.NDneighbors</title> | |
| − | + | <short_description>Computes a list of next-door neighbors.</short_description> | |
| + | |||
<syntax> | <syntax> | ||
| − | + | BB.NDneighbors(OO:LIST):LIST | |
</syntax> | </syntax> | ||
| − | + | <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> 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> | ||
| + | <item>@param <em>OO</em> A list of terms representing an order ideal.</item> | ||
| + | <item>@return A list of next-door neighbors of <tt>OO</tt>.</item> | ||
| + | </itemize> | ||
<example> | <example> | ||
| − | NDneighbors([1,x]); | + | 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]] | [[3, 1, 1], [4, 2, 1]] | ||
| − | ---- | + | |
| + | -- E.g. the first triple of the result can be interpreted | ||
| + | -- as x*z = xz | ||
</example> | </example> | ||
| − | + | </description> | |
| − | <see> | + | <types> |
| − | + | <type>borderbasis</type> | |
| − | + | </types> | |
| − | + | <see>ApCoCoA-1:BB.ASneighbors|BB.ASneighbors</see> | |
| − | + | ||
| + | <key>NDneighbors</key> | ||
| + | <key>BB.NDneighbors</key> | ||
| + | <key>borderbasis.NDneighbors</key> | ||
| + | <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
