Difference between revisions of "ApCoCoA-1:BB.LiftHomND"
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<command> | <command> | ||
| − | + | <title>BB.LiftHomND</title> | |
| − | + | <short_description>Computes the homogeneous border basis scheme ideal generators obtained from lifting of next-door neighbors.</short_description> | |
| + | |||
<syntax> | <syntax> | ||
BB.LiftHomND(OO:LIST):LIST | BB.LiftHomND(OO:LIST):LIST | ||
</syntax> | </syntax> | ||
| − | + | <description> | |
| − | + | This command computes the generators of the border basis scheme ideal <tt>I(B^hom_O)</tt> that result from the lifting of next-door (ND) neighbors. | |
| − | + | <itemize> | |
| − | <key> | + | <item>@param <em>OO</em> A list of terms representing an order ideal. The second element is of type <tt>POLY</tt>.</item> |
| − | + | <item>@return A list of generators of the homogeneous border basis scheme ideal. The polynomials will belong to the ring <tt>BBS=K[c_{ij}]</tt>.</item> | |
| − | + | </itemize> | |
| − | + | <example> | |
| + | Use QQ[x,y,z], DegRevLex; | ||
| + | BB.LiftHomND([Poly(1), x, y, xy]); | ||
| + | |||
| + | [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]] | ||
| + | ------------------------------- | ||
| + | </example> | ||
| + | </description> | ||
| + | <types> | ||
| + | <type>borderbasis</type> | ||
| + | </types> | ||
| + | <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.LiftNDViaServer|BB.LiftNDViaServer</see> | ||
| + | |||
| + | <key>LiftHomND</key> | ||
| + | <key>BB.LiftHomND</key> | ||
| + | <key>borderbasis.LiftHomND</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.LiftHomND
Computes the homogeneous border basis scheme ideal generators obtained from lifting of next-door neighbors.
Syntax
BB.LiftHomND(OO:LIST):LIST
Description
This command computes the generators of the border basis scheme ideal I(B^hom_O) that result from the lifting of next-door (ND) neighbors.
@param OO A list of terms representing an order ideal. The second element is of type POLY.
@return A list of generators of the homogeneous border basis scheme ideal. The polynomials will belong to the ring BBS=K[c_{ij}].
Example
Use QQ[x,y,z], DegRevLex; BB.LiftHomND([Poly(1), x, y, xy]); [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]] -------------------------------
