Difference between revisions of "ApCoCoA-1:BB.LiftNDViaServer"
From ApCoCoAWiki
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<command> | <command> | ||
<title>BB.LiftNDViaServer</title> | <title>BB.LiftNDViaServer</title> | ||
| − | <short_description>BBS generators from lifting of ND neighbors</short_description> | + | <short_description>BBS ideal generators from lifting of ND neighbors</short_description> |
<syntax> | <syntax> | ||
| − | BB.LiftNDViaServer(OO:LIST,Border:LIST):LIST | + | BB.LiftNDViaServer(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 next-door 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.LiftNDViaServer([Poly(1), x, y, xy], [y^2, x^2, xy^2, x^2y]); | + | BB.LiftNDViaServer([Poly(1), x, y, xy], [y^2, x^2, xy^2, x^2y], False); |
------------------------------- | ------------------------------- | ||
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BBS :: c[3,1]c[3,2] + c[3,3]c[4,2] + c[1,2] - c[3,4], | BBS :: c[3,1]c[3,2] + c[3,3]c[4,2] + c[1,2] - c[3,4], | ||
BBS :: c[1,1]c[3,2] + c[1,3]c[4,2] - c[1,4]] | BBS :: c[1,1]c[3,2] + c[1,3]c[4,2] - c[1,4]] | ||
| + | ------------------------------- | ||
| + | |||
| + | Use Q[x,y,z], DegRevLex; | ||
| + | BB.LiftNDViaServer([Poly(1), x, y, xy], [z, yz, xz, y^2, x^2, xyz, xy^2, x^2y], True); | ||
| + | |||
| + | ------------------------------- | ||
| + | [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> | </example> | ||
Revision as of 20:16, 29 July 2008
BB.LiftNDViaServer
BBS ideal generators from lifting of ND neighbors
Syntax
BB.LiftNDViaServer(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 next-door 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.LiftNDViaServer([Poly(1), x, y, xy], [y^2, x^2, xy^2, x^2y], False); ------------------------------- [BBS :: c[2,1]c[4,2] + c[4,1]c[4,4] + c[3,1] - c[4,3], 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[1,2]c[2,1] + c[1,4]c[4,1] - c[1,3], BBS :: c[3,2]c[4,1] + c[4,2]c[4,3] + c[2,2] - c[4,4], 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[1,1]c[3,2] + c[1,3]c[4,2] - c[1,4]] ------------------------------- Use Q[x,y,z], DegRevLex; BB.LiftNDViaServer([Poly(1), x, y, xy], [z, yz, xz, y^2, x^2, xyz, xy^2, x^2y], True); ------------------------------- [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]] -------------------------------
