Difference between revisions of "ApCoCoA-1:BB.LiftND"
From ApCoCoAWiki
(Initial version) |
m (insert version info) |
||
| (23 intermediate revisions by 5 users not shown) | |||
| Line 1: | Line 1: | ||
| + | {{Version|1}} | ||
<command> | <command> | ||
| − | + | <title>BB.LiftND</title> | |
| − | + | <short_description>Computes the border basis scheme ideal generators obtained from lifting of next-door neighbours.</short_description> | |
| + | |||
<syntax> | <syntax> | ||
| − | + | BB.LiftND(OO:LIST):LIST | |
</syntax> | </syntax> | ||
| − | + | <description> | |
| − | + | This command computes the generators of the border basis scheme ideal <tt>I(B_O)</tt> that result from the lifting of next-door (ND) neighbours. | |
| − | </ | + | <itemize> |
| − | <key> | + | <item>@param <em>OO</em> A list of terms representing an order ideal. The second element is of type <tt>POLY</tt>.</item> |
| − | + | <item>@return A list of generators of the border basis scheme ideal. The polynomials will belong to the ring <tt>BBS=K[c_{ij}]</tt>.</item> | |
| − | + | </itemize> | |
| − | + | <example> | |
| + | Use QQ[x,y], DegRevLex; | ||
| + | BB.LiftND([Poly(1), x, y, xy]); | ||
| + | |||
| + | [BBS :: c[1,2]c[2,1] + c[1,4]c[4,1] - c[1,3], | ||
| + | BBS :: c[2,1]c[2,2] + c[2,4]c[4,1] + c[1,1] - c[2,3], | ||
| + | BBS :: c[2,1]c[3,2] + c[3,4]c[4,1] - c[3,3], | ||
| + | BBS :: c[2,1]c[4,2] + c[4,1]c[4,4] + c[3,1] - c[4,3], | ||
| + | BBS :: c[1,1]c[3,2] + c[1,3]c[4,2] - c[1,4], | ||
| + | BBS :: c[2,1]c[3,2] + c[2,3]c[4,2] - c[2,4], | ||
| + | BBS :: c[3,1]c[3,2] + c[3,3]c[4,2] + c[1,2] - c[3,4], | ||
| + | BBS :: c[3,2]c[4,1] + c[4,2]c[4,3] + c[2,2] - c[4,4]] | ||
| + | ------------------------------- | ||
| + | </example> | ||
| + | </description> | ||
| + | <types> | ||
| + | <type>borderbasis</type> | ||
| + | <type>ideal</type> | ||
| + | </types> | ||
| + | <see>ApCoCoA-1:BB.LiftAS|BB.LiftAS</see> | ||
| + | <see>ApCoCoA-1:BB.LiftASViaServer|BB.LiftASViaServer</see> | ||
| + | <see>ApCoCoA-1:BB.LiftHomAS|BB.LiftHomAS</see> | ||
| + | <see>ApCoCoA-1:BB.LiftNDViaServer|BB.LiftNDViaServer</see> | ||
| + | <see>ApCoCoA-1:BB.LiftHomND|BB.LiftHomND</see> | ||
| + | |||
| + | <key>LiftND</key> | ||
| + | <key>BB.LiftND</key> | ||
| + | <key>borderbasis.LiftND</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.LiftND
Computes the border basis scheme ideal generators obtained from lifting of next-door neighbours.
Syntax
BB.LiftND(OO:LIST):LIST
Description
This command computes the generators of the border basis scheme ideal I(B_O) that result from the lifting of next-door (ND) neighbours.
@param OO A list of terms representing an order ideal. The second element is of type POLY.
@return A list of generators of the border basis scheme ideal. The polynomials will belong to the ring BBS=K[c_{ij}].
Example
Use QQ[x,y], DegRevLex; BB.LiftND([Poly(1), x, y, xy]); [BBS :: c[1,2]c[2,1] + c[1,4]c[4,1] - c[1,3], BBS :: c[2,1]c[2,2] + c[2,4]c[4,1] + c[1,1] - c[2,3], BBS :: c[2,1]c[3,2] + c[3,4]c[4,1] - c[3,3], BBS :: c[2,1]c[4,2] + c[4,1]c[4,4] + c[3,1] - c[4,3], BBS :: c[1,1]c[3,2] + c[1,3]c[4,2] - c[1,4], BBS :: c[2,1]c[3,2] + c[2,3]c[4,2] - c[2,4], BBS :: c[3,1]c[3,2] + c[3,3]c[4,2] + c[1,2] - c[3,4], BBS :: c[3,2]c[4,1] + c[4,2]c[4,3] + c[2,2] - c[4,4]] -------------------------------
