Difference between revisions of "ApCoCoA-1:BB.NDneighbors"
From ApCoCoAWiki
(Updated description and example.) |
|||
| Line 7: | Line 7: | ||
</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> | ||
| Line 14: | Line 14: | ||
<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
