Difference between revisions of "ApCoCoA-1:BB.LiftND"
From ApCoCoAWiki
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<command> | <command> | ||
| − | + | <title>BB.LiftND</title> | |
| − | + | <short_description>Compute the border basis scheme ideal generators obtained from lifting of ND neighbors.</short_description> | |
| − | <syntax> | + | <syntax>BB.LiftND(OO:LIST):LIST</syntax> |
| − | BB.LiftND(OO:LIST):LIST | + | <description> |
| − | </syntax> | + | Computes the generators of the border basis scheme ideal I(B_O) that result from the lifting of next-door neighbors. The input is a list of terms OO (2nd element of type POLY). The output is a list of poly in the ring BBS=K[c_{ij}]. |
| − | |||
| − | Computes the generators of the border basis scheme ideal | ||
<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>list</type> |
| − | </types> | + | </types> |
| − | + | <see>BB.LiftAS</see> | |
| − | + | <see>BB.LiftASViaServer</see> | |
| − | + | <see>BB.LiftHomAS</see> | |
| − | + | <see>BB.LiftNDViaServer</see> | |
| − | + | <see>BB.LiftHomND</see> | |
| − | + | <key>LiftND</key> | |
| − | + | <key>BB.LiftND</key> | |
| − | + | <key>borderbasis.LiftND</key> | |
| − | + | <wiki-category>Package_borderbasis</wiki-category> | |
</command> | </command> | ||
Revision as of 11:38, 24 April 2009
BB.LiftND
Compute the border basis scheme ideal generators obtained from lifting of ND neighbors.
Syntax
BB.LiftND(OO:LIST):LIST
Description
Computes the generators of the border basis scheme ideal I(B_O) that result from the lifting of next-door neighbors. The input is a list of terms OO (2nd element of type POLY). The output is a list of poly in the ring BBS=K[c_{ij}].
@param OO A list of terms representing an order ideal.
@return A list of generators of the border basis scheme ideal I(B_O) that results from the lifting of next-door neighbors in the border of OO. The polynomials will belong to the ring BBS=K[c_{ij}].
Example
Use QQ[x,y], DegRevLex; BB.LiftND([Poly(1), x, y, xy]); [BBS :: c[1,2]c[2,1] + c[1,4]c[4,1] - c[1,3], 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[2,1]c[4,2] + c[4,1]c[4,4] + c[3,1] - c[4,3], BBS :: c[1,1]c[3,2] + c[1,3]c[4,2] - c[1,4], 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[3,2]c[4,1] + c[4,2]c[4,3] + c[2,2] - c[4,4]] -------------------------------
