ApCoCoA-1:BB.LiftNDViaServer: Difference between revisions
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<command> | <command> | ||
<title>BB.LiftNDViaServer</title> | |||
<short_description>Compute the border basis scheme ideal generators obtained from lifting of ND neighbors.</short_description> | |||
<syntax> | <syntax>BB.LiftNDViaServer(OO:LIST,Border:LIST,HomogeneousLift:BOOL):LIST</syntax> | ||
BB.LiftNDViaServer(OO:LIST,Border:LIST,HomogeneousLift:BOOL):LIST | |||
</syntax> | |||
<description> | <description> | ||
<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | |||
<par/> | |||
If <tt>HomogeneousLift</tt> is set to <tt>False</tt>, the generators of the border basis scheme ideal | If <tt>HomogeneousLift</tt> is set to <tt>False</tt>, 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. 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 I(B^hom_O) will be computed instead. The output is a list of polynomials in the ring BBS=K[c_{ij}]. | ||
<itemize> | <itemize> | ||
<item>@param <em>OO</em> A list of terms representing an order ideal.</item> | <item>@param <em>OO</em> A list of terms representing an order ideal.</item> | ||
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------------------------------- | ------------------------------- | ||
</example> | </example> | ||
</description> | |||
<types> | <types> | ||
<type>list</type> | |||
<type>boolean</type> | |||
<type>apcocoaserver</type> | |||
</types> | </types> | ||
<see>BB.LiftAS</see> | |||
<see>BB.LiftASViaServer</see> | |||
<see>BB.LiftHomAS</see> | |||
<see>BB.LiftND</see> | |||
<see>BB.LiftHomND</see> | |||
<key>LiftNDViaServer</key> | |||
<key>BB.LiftNDViaServer</key> | |||
<key>borderbasis.LiftNDViaServer</key> | |||
<wiki-category>Package_borderbasis</wiki-category> | |||
</command> | </command> | ||
Revision as of 11:37, 24 April 2009
BB.LiftNDViaServer
Compute the border basis scheme ideal generators obtained from lifting of ND 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. 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 next-door neighbors. 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]] -------------------------------
