Difference between revisions of "ApCoCoA-1:BB.LiftASViaServer"
From ApCoCoAWiki
(Corrected example) |
(Updated description) |
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<command> | <command> | ||
<title>BB.LiftASViaServer</title> | <title>BB.LiftASViaServer</title> | ||
| − | <short_description>BBS generators from lifting of AS neighbors</short_description> | + | <short_description>BBS ideal generators from lifting of AS neighbors</short_description> |
<syntax> | <syntax> | ||
| − | BB.LiftASViaServer(OO:LIST,Border:LIST):LIST | + | BB.LiftASViaServer(OO:LIST,Border:LIST,HomogeneousLift:BOOL):LIST |
</syntax> | </syntax> | ||
<description> | <description> | ||
| − | + | If <tt>HomogeneousLift</tt> is set to <tt>False</tt>, 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 will computed by using the ApCoCoAServer. The input is a list of terms <tt>OO</tt> representing an order ideal and a list of terms <tt>Border</tt> representing the border of the order ideal. If <tt>HomogeneousLift</tt> is set to <tt>True</tt>, generators of <formula>I(\mathbb{B}^{\textrm{hom}}_\mathcal{O})</formula> will be computed instead. The output is a list of polynomials in the ring <formula>BBS=K[c_{ij}]</formula>. | |
<example> | <example> | ||
Use Q[x,y], DegRevLex; | Use Q[x,y], DegRevLex; | ||
| − | BB.LiftASViaServer([Poly(1), x, y, xy], [y^2, x^2, xy^2, x^2y]); | + | BB.LiftASViaServer([Poly(1), x, y, xy], [y^2, x^2, xy^2, x^2y], False); |
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Revision as of 20:13, 29 July 2008
BB.LiftASViaServer
BBS ideal generators from lifting of AS neighbors
Syntax
BB.LiftASViaServer(OO:LIST,Border:LIST,HomogeneousLift:BOOL):LIST
Description
If HomogeneousLift is set to False, 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 will computed by using the ApCoCoAServer. The input is a list of terms OO representing an order ideal and a list of terms Border representing the border of the order ideal. If HomogeneousLift is set to True, generators of <formula>I(\mathbb{B}^{\textrm{hom}}_\mathcal{O})</formula> will be computed instead. The output is a list of polynomials in the ring <formula>BBS=K[c_{ij}]</formula>.
Example
Use Q[x,y], DegRevLex; BB.LiftASViaServer([Poly(1), x, y, xy], [y^2, x^2, xy^2, x^2y], False); ------------------------------- [BBS :: c[3,4]c[4,1] - c[2,3]c[4,2] + c[2,4] - c[3,3], 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[1,2]c[2,3] + c[1,1]c[3,4] - c[1,4]c[4,3] + c[1,3]c[4,4]] -------------------------------
