Difference between revisions of "ApCoCoA-1:BB.LiftASViaServer"
| Line 1: | Line 1: | ||
<command> | <command> | ||
<title>BB.LiftASViaServer</title> | <title>BB.LiftASViaServer</title> | ||
| − | <short_description> | + | <short_description>Computes the border basis scheme ideal generators obtained from lifting of AS neighbours.</short_description> |
<syntax> | <syntax> | ||
| Line 14: | Line 14: | ||
<item>@param <em>Border</em> A list of terms representing the border of OO</item> | <item>@param <em>Border</em> A list of terms representing the border of OO</item> | ||
<item>@param <em>Homogeneous</em> Set to <em>TRUE</em> if you want to compute the generators of the homogeneous border basis scheme.</item> | <item>@param <em>Homogeneous</em> Set to <em>TRUE</em> if you want to compute the generators of the homogeneous border basis scheme.</item> | ||
| − | <item>@return A list of generators of the border basis scheme ideal I(B_O) that results from the lifting of across-the-street | + | <item>@return A list of generators of the border basis scheme ideal I(B_O) that results from the lifting of across-the-street neighbours. The polynomials will belong to the ring BBS=K[c_{ij}].</item> |
</itemize> | </itemize> | ||
<example> | <example> | ||
| Line 30: | Line 30: | ||
<types> | <types> | ||
<type>borderbasis</type> | <type>borderbasis</type> | ||
| + | <type>ideal</type> | ||
<type>apcocoaserver</type> | <type>apcocoaserver</type> | ||
</types> | </types> | ||
Revision as of 12:49, 28 April 2009
BB.LiftASViaServer
Computes the border basis scheme ideal generators obtained from lifting of AS neighbours.
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 neighbours. 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]] -------------------------------
