Difference between revisions of "ApCoCoA-1:BB.LiftASViaServer"
From ApCoCoAWiki
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<example> | <example> | ||
Use Q[x,y], DegRevLex; | Use Q[x,y], DegRevLex; | ||
| − | BB. | + | BB.LiftASViaServer([Poly(1), x, y, xy], [y^2, x^2, xy^2, x^2y]); |
------------------------------- | ------------------------------- | ||
| − | [BBS :: c[ | + | [BBS :: c[3,4]c[4,1] - c[2,3]c[4,2] + c[2,4] - c[3,3], |
| − | BBS :: c[2, | + | 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 :: | + | 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[ | ||
| − | |||
------------------------------- | ------------------------------- | ||
</example> | </example> | ||
Revision as of 17:13, 25 July 2008
BB.LiftASViaServer
BBS generators from lifting of AS neighbors
Syntax
BB.LiftASViaServer(OO:LIST,Border:LIST):LIST
Description
Compute the equations defining the border basis scheme and coming from the lifting of across-the-street neighbors 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. 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]); ------------------------------- [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]] -------------------------------
