Difference between revisions of "ApCoCoA-1:BB.BBscheme"

From ApCoCoAWiki
(Shortened short description)
m (insert version info)
 
(22 intermediate revisions by 5 users not shown)
Line 1: Line 1:
 +
{{Version|1}}
 
<command>
 
<command>
    <title>borderbasis.BBscheme</title>
+
  <title>BB.BBscheme</title>
    <short_description>Compute defining eqns of BB scheme</short_description>
+
  <short_description>Computes the defining equations of a border basis scheme.</short_description>
 +
 
 
<syntax>
 
<syntax>
$borderbasis.BBscheme(OO:LIST):IDEAL
+
BB.BBscheme(OO:LIST):IDEAL
 
</syntax>
 
</syntax>
    <description>
+
  <description>
Computes the defining equations of the border basis scheme using the commutators of the multiplication matrices. The input is an order ideal OO (2nd element of type POLY). The output is an ideal in the ring BBS = K[c_{ij}].
+
Computes the defining equations of the border basis scheme using the commutators of the multiplication matrices. The input is a list <tt>OO</tt> of terms that specify an order ideal. The second element of <tt>OO</tt> must be a non-constant polynomial. The output is an ideal in the ring <tt>BBS = K[c_{ij}]</tt>.
    </description>
+
<itemize>
     <key>Kreuzer</key>
+
  <item>@param <em>OO</em> A list of terms representing an order ideal.</item>
    <key>borderbasis.bbscheme</key>
+
  <item>@return A list of polynomials representing the defining equations of the border basis scheme. The polynomials will belong to the ring <tt>BBS=K[c_{ij}]</tt>.</item>
    <key>borderbasisbbscheme</key>
+
</itemize>
    <wiki-category>Package_borderbasis</wiki-category>
+
<example>
 +
Use QQ[x,y,z];
 +
BB.BBscheme([1,x]);
 +
BBS :: Ideal(c[1,5]c[2,2] - c[1,4], c[1,2]c[1,5] - c[1,5]c[2,4] + c[1,4]c[2,5],
 +
c[2,2]c[2,5] + c[1,2] - c[2,4], c[1,5]c[2,2] - c[1,4], c[1,5]c[2,1] - c[1,3],
 +
c[1,1]c[1,5] - c[1,5]c[2,3] + c[1,3]c[2,5], c[2,1]c[2,5] + c[1,1] - c[2,3],
 +
c[1,5]c[2,1] - c[1,3], c[1,4]c[2,1] - c[1,3]c[2,2],
 +
c[1,2]c[1,3] - c[1,1]c[1,4] + c[1,4]c[2,3] - c[1,3]c[2,4],
 +
c[1,2]c[2,1] - c[1,1]c[2,2] + c[2,2]c[2,3] - c[2,1]c[2,4], c[1,4]c[2,1] - c[1,3]c[2,2])
 +
-------------------------------
 +
</example>
 +
  </description>
 +
  <types>
 +
     <type>borderbasis</type>
 +
  </types>
 +
  <see>ApCoCoA-1:BB.HomBBscheme|BB.HomBBscheme</see>
 +
  <key>BBscheme</key>
 +
  <key>BB.BBscheme</key>
 +
  <key>borderbasis.BBscheme</key>
 +
  <wiki-category>ApCoCoA-1:Package_borderbasis</wiki-category>
 
</command>
 
</command>

Latest revision as of 09:39, 7 October 2020

This article is about a function from ApCoCoA-1.

BB.BBscheme

Computes the defining equations of a border basis scheme.

Syntax

BB.BBscheme(OO:LIST):IDEAL

Description

Computes the defining equations of the border basis scheme using the commutators of the multiplication matrices. The input is a list OO of terms that specify an order ideal. The second element of OO must be a non-constant polynomial. The output is an ideal in the ring BBS = K[c_{ij}].

  • @param OO A list of terms representing an order ideal.

  • @return A list of polynomials representing the defining equations of the border basis scheme. The polynomials will belong to the ring BBS=K[c_{ij}].

Example

Use QQ[x,y,z];
BB.BBscheme([1,x]);
BBS :: Ideal(c[1,5]c[2,2] - c[1,4], c[1,2]c[1,5] - c[1,5]c[2,4] + c[1,4]c[2,5],
c[2,2]c[2,5] + c[1,2] - c[2,4], c[1,5]c[2,2] - c[1,4], c[1,5]c[2,1] - c[1,3],
c[1,1]c[1,5] - c[1,5]c[2,3] + c[1,3]c[2,5], c[2,1]c[2,5] + c[1,1] - c[2,3],
c[1,5]c[2,1] - c[1,3], c[1,4]c[2,1] - c[1,3]c[2,2],
c[1,2]c[1,3] - c[1,1]c[1,4] + c[1,4]c[2,3] - c[1,3]c[2,4],
c[1,2]c[2,1] - c[1,1]c[2,2] + c[2,2]c[2,3] - c[2,1]c[2,4], c[1,4]c[2,1] - c[1,3]c[2,2])
-------------------------------

BB.HomBBscheme