ApCoCoA-1:BB.LiftAS: Difference between revisions
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<command> | <command> | ||
<title>BB.LiftAS</title> | |||
<short_description>Compute the border basis scheme ideal generators obtained from lifting of AS neighbors.</short_description> | |||
<syntax> | <syntax>BB.LiftAS(OO:LIST):LIST</syntax> | ||
BB.LiftAS(OO:LIST):LIST | <description> | ||
</syntax> | Computes the generators of the border basis scheme ideal I(B_O) that result from the lifting of across-the-street 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> | </description> | ||
<types> | <types> | ||
<type>list</type> | <type>list</type> | ||
</types> | </types> | ||
<see>BB.LiftASViaServer</see> | |||
<see>BB.LiftHomAS</see> | |||
<see>BB.LiftND</see> | |||
<see>BB.LiftNDViaServer</see> | |||
<see>BB.LiftHomND</see> | |||
<key>LiftAS</key> | |||
<key>BB.LiftAS</key> | |||
<key>borderbasis.LiftAS</key> | |||
<wiki-category>Package_borderbasis</wiki-category> | |||
</command> | </command> | ||
Revision as of 11:10, 24 April 2009
BB.LiftAS
Compute the border basis scheme ideal generators obtained from lifting of AS neighbors.
Syntax
BB.LiftAS(OO:LIST):LIST
Description
Computes the generators of the border basis scheme ideal I(B_O) that result from the lifting of across-the-street 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 across-the-street neighbors in the border of OO. 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]] -------------------------------
