Difference between revisions of "ApCoCoA-1:BB.LiftAS"
From ApCoCoAWiki
(Key and see section update.) |
(Types section update.) |
||
| Line 22: | Line 22: | ||
</example> | </example> | ||
</description> | </description> | ||
| + | <types> | ||
| + | <type>list</type> | ||
| + | </types> | ||
<see>BB.LiftASViaServer</see> | <see>BB.LiftASViaServer</see> | ||
<see>BB.LiftHomAS</see> | <see>BB.LiftHomAS</see> | ||
Revision as of 11:04, 23 April 2009
BB.LiftAS
Compute the border basis scheme ideal generators obtained from lifting of AS neighbors.
Syntax
BB.LiftAS(OO:LIST):LIST
Description
Computes the generators of the border basis scheme ideal <formula>I(\mathbb{B}_\mathcal{O})</formula> that result from the lifting of across-the-street neighbors. The input is a list of terms OO (2nd element of type POLY). The output is a list of poly in the ring <formula>BBS=K[c_{ij}]</formula>.
@param OO A list of terms representing an order ideal.
@return A list of generators of the border basis scheme ideal I(B_O) that results from the lifting of across-the-street neighbors in the border of OO. The polynomials will belong to the ring BBS=K[c_{ij}].
Example
Use Q[x,y], DegRevLex; BB.LiftAS([Poly(1), x, y, xy]); [BBS :: c[1,2]c[2,3] - c[1,1]c[3,4] + c[1,4]c[4,3] - c[1,3]c[4,4], BBS :: c[2,2]c[2,3] - c[2,1]c[3,4] + c[2,4]c[4,3] - c[2,3]c[4,4] + c[1,3], BBS :: c[2,3]c[3,2] - c[3,1]c[3,4] + c[3,4]c[4,3] - c[3,3]c[4,4] - c[1,4], BBS :: c[3,4]c[4,1] - c[2,3]c[4,2] + c[2,4] - c[3,3]] -------------------------------
