Difference between revisions of "ApCoCoA-1:BB.LiftND"
From ApCoCoAWiki
| Line 1: | Line 1: | ||
<command> | <command> | ||
<title>BB.LiftND</title> | <title>BB.LiftND</title> | ||
| − | <short_description>Computes the border basis scheme ideal generators obtained from lifting of | + | <short_description>Computes the border basis scheme ideal generators obtained from lifting of next-door neighbours.</short_description> |
<syntax> | <syntax> | ||
| Line 7: | Line 7: | ||
</syntax> | </syntax> | ||
<description> | <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> | <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. The second element is of type <tt>POLY</tt>.</item> |
| − | <item>@return A list of generators of the border basis scheme ideal | + | <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> | </itemize> | ||
<example> | <example> | ||
Revision as of 15:42, 8 July 2009
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]] -------------------------------
