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

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<command>
 
<command>
 
   <title>BB.BBscheme</title>
 
   <title>BB.BBscheme</title>
   <short_description>Compute the defining equations of a border basis scheme.</short_description>
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   <short_description>Computes the defining equations of a border basis scheme.</short_description>
   <syntax>BB.BBscheme(OO:LIST):IDEAL</syntax>
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<syntax>
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BB.BBscheme(OO:LIST):IDEAL
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</syntax>
 
   <description>
 
   <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}].
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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>.
 
<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>
   <item>@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}].</item>
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   <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>
 
</itemize>
 
</itemize>
 
<example>
 
<example>
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     <type>borderbasis</type>
 
     <type>borderbasis</type>
 
   </types>
 
   </types>
   <see>BB.HomBBscheme</see>
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   <see>ApCoCoA-1:BB.HomBBscheme|BB.HomBBscheme</see>
 
   <key>BBscheme</key>
 
   <key>BBscheme</key>
 
   <key>BB.BBscheme</key>
 
   <key>BB.BBscheme</key>
 
   <key>borderbasis.BBscheme</key>
 
   <key>borderbasis.BBscheme</key>
   <wiki-category>Package_borderbasis</wiki-category>
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   <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