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

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{{Version|1}}
 
<command>
 
<command>
 
   <title>BB.GenericBB</title>
 
   <title>BB.GenericBB</title>
   <short_description>Compute a generic border basis.</short_description>
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   <short_description>Computes a generic border basis.</short_description>
   <syntax>BB.GenericBB(OO:LIST):LIST</syntax>
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<syntax>
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BB.GenericBB(OO:LIST):LIST
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</syntax>
 
   <description>
 
   <description>
Computes the <quotes>generic</quotes> border basis w.r.t. an order ideal OO i.e. the polynomials g_j = b_j - \sum_i c_{ij} * t_i. The input is a list of terms OO (2nd element of type POLY). The output is a list of POLY in a <quotes>universal family ring</quotes> UF where UF=K[x_1,..,x_n,c_{ij}].
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Computes the "generic" border basis w.r.t. an order ideal <tt>OO</tt> i.e. the polynomials <tt>g_j = b_j - \sum_i c_{ij} * t_i</tt>. The output is a list of <tt>POLY</tt> in a "universal family ring" <tt>UF</tt> where <tt>UF=K[x_1,..,x_n,c_{ij}]</tt>.
 
<itemize>
 
<itemize>
   <item>@param <em>OO</em> A list of terms representing an order ideal.</item>
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   <item>@param <em>OO</em> A list of terms representing an order ideal. The second element has to be of type <tt>POLY</tt>.</item>
   <item>@return A list of generic border basis polynomials w.r.t. to an order ideal OO. The polynomials will belong to the ring UF=K[x_1,..,x_n,c_{ij}].</item>
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   <item>@return A list of generic border basis polynomials w.r.t. to an order ideal <tt>OO</tt>. </item>
 
</itemize>
 
</itemize>
 
   </description>
 
   </description>
 
   <types>
 
   <types>
     <type>list</type>
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     <type>borderbasis</type>
 
   </types>
 
   </types>
 
   <key>GenericBB</key>
 
   <key>GenericBB</key>
 
   <key>BB.GenericBB</key>
 
   <key>BB.GenericBB</key>
 
   <key>borderbasis.GenericBB</key>
 
   <key>borderbasis.GenericBB</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 13:27, 29 October 2020

This article is about a function from ApCoCoA-1.

BB.GenericBB

Computes a generic border basis.

Syntax

BB.GenericBB(OO:LIST):LIST

Description

Computes the "generic" border basis w.r.t. an order ideal OO i.e. the polynomials g_j = b_j - \sum_i c_{ij} * t_i. The output is a list of POLY in a "universal family ring" UF where UF=K[x_1,..,x_n,c_{ij}].

  • @param OO A list of terms representing an order ideal. The second element has to be of type POLY.

  • @return A list of generic border basis polynomials w.r.t. to an order ideal OO.