Difference between revisions of "ApCoCoA-1:BB.LiftASViaServer"
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<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> | ||
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<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. | <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/> | <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 across-the-street neighbors will be 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 order ideal.</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 | + | <item>@return A list of generators of the border basis scheme ideal. The polynomials will belong to the ring BBS=K[c_{ij}].</item> |
</itemize> | </itemize> | ||
<example> | <example> | ||
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<types> | <types> | ||
<type>borderbasis</type> | <type>borderbasis</type> | ||
| + | <type>ideal</type> | ||
<type>apcocoaserver</type> | <type>apcocoaserver</type> | ||
</types> | </types> | ||
<see>Introduction to CoCoAServer</see> | <see>Introduction to CoCoAServer</see> | ||
| − | <see>BB.LiftAS</see> | + | <see>ApCoCoA-1:BB.LiftAS|BB.LiftAS</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.LiftNDViaServer</see> | + | <see>ApCoCoA-1:BB.LiftNDViaServer|BB.LiftNDViaServer</see> |
| − | <see>BB.LiftHomND</see> | + | <see>ApCoCoA-1:BB.LiftHomND|BB.LiftHomND</see> |
<key>LiftASViaServer</key> | <key>LiftASViaServer</key> | ||
<key>BB.LiftASViaServer</key> | <key>BB.LiftASViaServer</key> | ||
<key>borderbasis.LiftASViaServer</key> | <key>borderbasis.LiftASViaServer</key> | ||
| − | <wiki-category>Package_borderbasis</wiki-category> | + | <wiki-category>ApCoCoA-1:Package_borderbasis</wiki-category> |
</command> | </command> | ||
Latest revision as of 09:41, 7 October 2020
| This article is about a function from ApCoCoA-1. |
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 be 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 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.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]] -------------------------------
