Difference between revisions of "ApCoCoA-1:BB.LiftAS"
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| + | {{Version|1}} | ||
<command> | <command> | ||
| − | + | <title>BB.LiftAS</title> | |
| − | + | <short_description>Computes the border basis scheme ideal generators obtained from lifting of AS neighbours.</short_description> | |
| + | |||
<syntax> | <syntax> | ||
| − | + | BB.LiftAS(OO:LIST):LIST | |
</syntax> | </syntax> | ||
| − | + | <description> | |
| − | + | This command computes the generators of the border basis scheme ideal <tt>I(B_O)</tt> that result from the lifting of across-the-street neighbours. | |
| − | </ | + | <itemize> |
| − | <key> | + | <item>@param <em>OO</em> A list of terms representing an order ideal with second element of type <tt>POLY</tt>.</item> |
| − | + | <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> | |
| + | <example> | ||
| + | Use QQ[x,y], DegRevLex; | ||
| + | BB.LiftAS([Poly(1), x, y, xy]); | ||
| + | |||
| + | [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], | ||
| + | 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[3,4]c[4,1] - c[2,3]c[4,2] + c[2,4] - c[3,3]] | ||
| + | ------------------------------- | ||
| + | </example> | ||
| + | </description> | ||
| + | <types> | ||
| + | <type>borderbasis</type> | ||
| + | <type>ideal</type> | ||
| + | </types> | ||
| + | <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> | ||
| + | <see>ApCoCoA-1:BB.LiftHomND|BB.LiftHomND</see> | ||
| + | |||
| + | <key>LiftAS</key> | ||
| + | <key>BB.LiftAS</key> | ||
| + | <key>borderbasis.LiftAS</key> | ||
| + | <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.LiftAS
Computes the border basis scheme ideal generators obtained from lifting of AS neighbours.
Syntax
BB.LiftAS(OO:LIST):LIST
Description
This command computes the generators of the border basis scheme ideal I(B_O) that result from the lifting of across-the-street neighbours.
@param OO A list of terms representing an order ideal with second element of type POLY.
@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.LiftAS([Poly(1), x, y, xy]); [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], 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[3,4]c[4,1] - c[2,3]c[4,2] + c[2,4] - c[3,3]] -------------------------------
