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

From ApCoCoAWiki
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{{Version|1}}
 
<command>
 
<command>
    <title>BB.HomASgens</title>
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  <title>BB.HomASgens</title>
    <short_description>Compute the generators of the vanishing ideal of a homogeneous border basis scheme.</short_description>
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  <short_description>Computes the generators of the vanishing ideal of a homogeneous border basis scheme.</short_description>
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<syntax>
 
<syntax>
 
BB.HomASgens(K:INT,OO:LIST):LIST
 
BB.HomASgens(K:INT,OO:LIST):LIST
 
</syntax>
 
</syntax>
    <description>
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  <description>
Computes the generators of the vanishing ideal of the homogeneous border basis scheme corresponding to the lifting of the K-th element of ASneighbors(OO). The inputs are an integer K in the range 1..Len(ASneighbors(OO)) and a list OO of terms that specify an order ideal. The output is a list of polynomials in the ring <formula>BBS=K[c_{ij}]</formula>.
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This command computes the generators of the vanishing ideal of the homogeneous border basis scheme corresponding to the lifting of the <tt>K</tt>-th element of <ref>ApCoCoA-1:BB.ASneighbors|BB.ASneighbors</ref>(OO).
 
<itemize>
 
<itemize>
   <item>@param <em>K</em> The generators of the vanishing ideal of the homogeneous border basis scheme corresponding to the lifting of the K-th element of the list returned by ASneighbors(OO) will be computed.</item>
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   <item>@param <em>K</em> An integer <tt>K</tt> in the range 1..Len(<ref>ApCoCoA-1:BB.ASneighbors|BB.ASneighbors</ref>(OO)).</item>
 
   <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 generators of the vanishing ideal of the homogeneous border basis scheme corresponding to the lifting of the K-th element of the list returned by ASneighbors(OO).</item>
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   <item>@return A list of generators of the vanishing ideal. The polynomials will belong to the ring <tt>BBS=K[c_{ij}]</tt>.</item>
 
</itemize>
 
</itemize>
     </description>
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  </description>
     <see>BB.ASgens</see>
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  <types>
    <see>BB.HomNDgens</see>
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     <type>borderbasis</type>
    <see>BB.NDgens</see>
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     <type>ideal</type>
    <key>kreuzer</key>
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  </types>
    <key>bb.homasgens</key>
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  <see>ApCoCoA-1:BB.ASgens|BB.ASgens</see>
    <key>borderbasis.homasgens</key>
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  <see>ApCoCoA-1:BB.HomNDgens|BB.HomNDgens</see>
    <wiki-category>Package_borderbasis</wiki-category>
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  <see>ApCoCoA-1:BB.NDgens|BB.NDgens</see>
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 +
  <key>HomASgens</key>
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  <key>BB.HomASgens</key>
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  <key>borderbasis.HomASgens</key>
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  <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.HomASgens

Computes the generators of the vanishing ideal of a homogeneous border basis scheme.

Syntax

BB.HomASgens(K:INT,OO:LIST):LIST

Description

This command computes the generators of the vanishing ideal of the homogeneous border basis scheme corresponding to the lifting of the K-th element of BB.ASneighbors(OO).

  • @param K An integer K in the range 1..Len(BB.ASneighbors(OO)).

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

  • @return A list of generators of the vanishing ideal. The polynomials will belong to the ring BBS=K[c_{ij}].

BB.ASgens

BB.HomNDgens

BB.NDgens