Difference between revisions of "ApCoCoA-1:BB.LiftHomND"
From ApCoCoAWiki
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<description> | <description> | ||
Computes the generators of the border basis scheme ideal <formula>I(\mathbb{B}^{\textrm{hom}}_\mathcal{O})</formula> that result from the lifting of next-door 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>. | Computes the generators of the border basis scheme ideal <formula>I(\mathbb{B}^{\textrm{hom}}_\mathcal{O})</formula> that result from the lifting of next-door 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>. | ||
| + | <example> | ||
| + | Use Q[x,y,z], DegRevLex; | ||
| + | BB.LiftHomND([Poly(1), x, y, xy]); | ||
| + | |||
| + | [BBS :: c[3,1]c[4,4] + c[2,1] - c[4,2], | ||
| + | BBS :: c[2,1]c[4,5] + c[3,1] - c[4,3]] | ||
| + | ------------------------------- | ||
| + | </example> | ||
</description> | </description> | ||
<key>kreuzer</key> | <key>kreuzer</key> | ||
Revision as of 20:26, 29 July 2008
BB.LiftHomND
homogeneous BBS ideal generators from lifting of ND neighbors
Syntax
BB.LiftHomND(OO:LIST):LIST
Description
Computes the generators of the border basis scheme ideal <formula>I(\mathbb{B}^{\textrm{hom}}_\mathcal{O})</formula> that result from the lifting of next-door 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>.
Example
Use Q[x,y,z], DegRevLex; BB.LiftHomND([Poly(1), x, y, xy]); [BBS :: c[3,1]c[4,4] + c[2,1] - c[4,2], BBS :: c[2,1]c[4,5] + c[3,1] - c[4,3]] -------------------------------
