Difference between revisions of "ApCoCoA-1:BB.LiftNDViaServer"
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| + | {{Version|1}} | ||
<command> | <command> | ||
| − | + | <title>BB.LiftNDViaServer</title> | |
| − | + | <short_description>Computes the border basis scheme ideal generators obtained from lifting of next-door neighbors.</short_description> | |
| + | |||
<syntax> | <syntax> | ||
BB.LiftNDViaServer(OO:LIST,Border:LIST,HomogeneousLift:BOOL):LIST | BB.LiftNDViaServer(OO:LIST,Border:LIST,HomogeneousLift:BOOL):LIST | ||
</syntax> | </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> | + | If <tt>HomogeneousLift</tt> is set to <tt>FALSE</tt>, the generators of the border basis scheme ideal <tt>I(B_O)</tt> that result from the lifting of next-door neighbors will computed by using the ApCoCoAServer. If <tt>HomogeneousLift</tt> is set to <tt>TRUE</tt>, generators of <tt>I(B^hom_O)</tt> will be computed instead. |
<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> | ||
| − | <item>@param <em>Border</em> A list of terms representing the border of | + | <item>@param <em>Border</em> A list of terms representing the border of the order ideal.</item> |
| − | <item>@param <em>Homogeneous</em> Set to < | + | <item>@param <em>Homogeneous</em> Set to <tt>TRUE</tt> 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 | + | <item>@return A list of generators of the border basis scheme ideal. The polynomials will belong to the ring <tt>BBS=K[c_{ij}]</tt>.</item> |
</itemize> | </itemize> | ||
<example> | <example> | ||
| − | Use | + | Use QQ[x,y], DegRevLex; |
BB.LiftNDViaServer([Poly(1), x, y, xy], [y^2, x^2, xy^2, x^2y], False); | BB.LiftNDViaServer([Poly(1), x, y, xy], [y^2, x^2, xy^2, x^2y], False); | ||
| Line 29: | Line 31: | ||
BBS :: c[1,1]c[3,2] + c[1,3]c[4,2] - c[1,4]] | BBS :: c[1,1]c[3,2] + c[1,3]c[4,2] - c[1,4]] | ||
------------------------------- | ------------------------------- | ||
| − | + | </example> | |
| − | Use | + | <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); | BB.LiftNDViaServer([Poly(1), x, y, xy], [z, yz, xz, y^2, x^2, xyz, xy^2, x^2y], True); | ||
| Line 38: | Line 41: | ||
------------------------------- | ------------------------------- | ||
</example> | </example> | ||
| − | </ | + | </description> |
| − | <see>BB.LiftAS</see> | + | <types> |
| − | + | <type>borderbasis</type> | |
| − | + | <type>ideal</type> | |
| − | + | <type>apcocoaserver</type> | |
| − | + | </types> | |
| − | + | ||
| − | + | <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see> | |
| − | + | <see>ApCoCoA-1:BB.LiftAS|BB.LiftAS</see> | |
| − | + | <see>ApCoCoA-1:BB.LiftASViaServer|BB.LiftASViaServer</see> | |
| + | <see>ApCoCoA-1:BB.LiftHomAS|BB.LiftHomAS</see> | ||
| + | <see>ApCoCoA-1:BB.LiftND|BB.LiftND</see> | ||
| + | <see>ApCoCoA-1:BB.LiftHomND|BB.LiftHomND</see> | ||
| + | |||
| + | <key>LiftNDViaServer</key> | ||
| + | <key>BB.LiftNDViaServer</key> | ||
| + | <key>borderbasis.LiftNDViaServer</key> | ||
| + | <wiki-category>ApCoCoA-1:Package_borderbasis</wiki-category> | ||
</command> | </command> | ||
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]] -------------------------------
