Difference between revisions of "ApCoCoA-1:BB.LiftAS"
From ApCoCoAWiki
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<command> | <command> | ||
<title>BB.LiftAS</title> | <title>BB.LiftAS</title> | ||
| − | <short_description> | + | <short_description>Computes the border basis scheme ideal generators obtained from lifting of AS neighbours.</short_description> |
| − | <syntax>BB.LiftAS(OO:LIST):LIST</syntax> | + | |
| + | <syntax> | ||
| + | BB.LiftAS(OO:LIST):LIST | ||
| + | </syntax> | ||
<description> | <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> | <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 with second element of type <tt>POLY</tt>.</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> | ||
| Line 21: | Line 25: | ||
</description> | </description> | ||
<types> | <types> | ||
| − | <type> | + | <type>borderbasis</type> |
| + | <type>ideal</type> | ||
</types> | </types> | ||
| − | <see>BB.LiftASViaServer</see> | + | <see>ApCoCoA-1:BB.LiftASViaServer|BB.LiftASViaServer</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>LiftAS</key> | <key>LiftAS</key> | ||
<key>BB.LiftAS</key> | <key>BB.LiftAS</key> | ||
<key>borderbasis.LiftAS</key> | <key>borderbasis.LiftAS</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.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]] -------------------------------
