ApCoCoA-1:BB.HomASgens: Difference between revisions

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<command>
<command>
   <title>BB.HomASgens</title>
   <title>BB.HomASgens</title>
   <short_description>Computes the generators of the vanishing ideal of a homogeneous border basis scheme.</short_description>
   <short_description>Computes the generators of the vanishing ideal of a homogeneous border basis scheme.</short_description>
   <syntax>BB.HomASgens(K:INT,OO:LIST):LIST</syntax>
    
<syntax>
BB.HomASgens(K:INT,OO:LIST):LIST
</syntax>
   <description>
   <description>
Computes the generators of the vanishing ideal of the homogeneous border basis scheme corresponding to the lifting of the K-th element of <ref>BB.ASneighbors</ref>(OO). The inputs are an integer K in the range 1..Len(<ref>BB.ASneighbors</ref>(OO)) and a list OO of terms that specify an order ideal. The output is a list of polynomials in the ring BBS=K[c_{ij}].
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 <ref>BB.ASneighbors</ref>(OO) will be computed.</item>
   <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 <ref>BB.ASneighbors</ref>(OO). The polynomials will belong to the ring BBS=K[c_{ij}].</item>
   <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>
   </description>
   <types>
   <types>
     <type>borderbasis</type>
     <type>borderbasis</type>
    <type>ideal</type>
   </types>
   </types>
   <see>BB.ASgens</see>
   <see>ApCoCoA-1:BB.ASgens|BB.ASgens</see>
   <see>BB.HomNDgens</see>
   <see>ApCoCoA-1:BB.HomNDgens|BB.HomNDgens</see>
   <see>BB.NDgens</see>
   <see>ApCoCoA-1:BB.NDgens|BB.NDgens</see>


   <key>HomASgens</key>
   <key>HomASgens</key>
   <key>BB.HomASgens</key>
   <key>BB.HomASgens</key>
   <key>borderbasis.HomASgens</key>
   <key>borderbasis.HomASgens</key>
   <wiki-category>Package_borderbasis</wiki-category>
   <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