Difference between revisions of "ApCoCoA-1:BB.LiftASViaServer"
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</description> | </description> | ||
<types> | <types> | ||
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<type>borderbasis</type> | <type>borderbasis</type> | ||
<type>apcocoaserver</type> | <type>apcocoaserver</type> | ||
</types> | </types> | ||
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| + | <see>Introduction to CoCoAServer</see> | ||
<see>BB.LiftAS</see> | <see>BB.LiftAS</see> | ||
<see>BB.LiftHomAS</see> | <see>BB.LiftHomAS</see> | ||
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<see>BB.LiftNDViaServer</see> | <see>BB.LiftNDViaServer</see> | ||
<see>BB.LiftHomND</see> | <see>BB.LiftHomND</see> | ||
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<key>LiftASViaServer</key> | <key>LiftASViaServer</key> | ||
<key>BB.LiftASViaServer</key> | <key>BB.LiftASViaServer</key> | ||
Revision as of 13:45, 24 April 2009
BB.LiftASViaServer
Compute the border basis scheme ideal generators obtained from lifting of AS neighbors.
Syntax
BB.LiftASViaServer(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 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 I(B^hom_O) will be computed instead. The output is a list of polynomials in the ring BBS=K[c_{ij}].
@param OO A list of terms representing an order ideal.
@param Border A list of terms representing the border of OO
@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 I(B_O) that results from the lifting of across-the-street neighbors. The polynomials will belong to the ring BBS=K[c_{ij}].
Example
Use QQ[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]] -------------------------------
