Difference between revisions of "ApCoCoA-1:BB.LiftNDViaServer"
m (Bot: fixed typo) |
m (insert version info) |
||
| (One intermediate revision by the same user not shown) | |||
| Line 1: | Line 1: | ||
| + | {{Version|1}} | ||
<command> | <command> | ||
<title>BB.LiftNDViaServer</title> | <title>BB.LiftNDViaServer</title> | ||
| Line 47: | Line 48: | ||
</types> | </types> | ||
| − | <see>Introduction to CoCoAServer</see> | + | <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see> |
| − | <see>BB.LiftAS</see> | + | <see>ApCoCoA-1:BB.LiftAS|BB.LiftAS</see> |
| − | <see>BB.LiftASViaServer</see> | + | <see>ApCoCoA-1:BB.LiftASViaServer|BB.LiftASViaServer</see> |
| − | <see>BB.LiftHomAS</see> | + | <see>ApCoCoA-1:BB.LiftHomAS|BB.LiftHomAS</see> |
| − | <see>BB.LiftND</see> | + | <see>ApCoCoA-1:BB.LiftND|BB.LiftND</see> |
| − | <see>BB.LiftHomND</see> | + | <see>ApCoCoA-1:BB.LiftHomND|BB.LiftHomND</see> |
<key>LiftNDViaServer</key> | <key>LiftNDViaServer</key> | ||
Latest revision as of 09:42, 7 October 2020
| This article is about a function from ApCoCoA-1. |
BB.LiftNDViaServer
Computes the border basis scheme ideal generators obtained from lifting of next-door neighbors.
Syntax
BB.LiftNDViaServer(OO:LIST,Border:LIST,HomogeneousLift:BOOL):LIST
Description
Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.
If HomogeneousLift is set to FALSE, the generators of the border basis scheme ideal I(B_O) that result from the lifting of next-door neighbors will computed by using the ApCoCoAServer. If HomogeneousLift is set to TRUE, generators of I(B^hom_O) will be computed instead.
@param OO A list of terms representing an order ideal.
@param Border A list of terms representing the border of the order ideal.
@param Homogeneous Set to TRUE if you want to compute the generators of the homogeneous border basis scheme.
@return A list of generators of the border basis scheme ideal. The polynomials will belong to the ring BBS=K[c_{ij}].
Example
Use QQ[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]] -------------------------------
Example
Use QQ[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]] -------------------------------
