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

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{{Version|1}}
 
<command>
 
<command>
    <title>borderbasis.ASgens</title>
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  <title>BB.ASgens</title>
    <short_description>generators from vanishing ideal of a border basis scheme</short_description>
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  <short_description>Computes the generators of the vanishing ideal of a border basis scheme.</short_description>
 +
 
 
<syntax>
 
<syntax>
$borderbasis.ASgens(K:INT,OO:LIST):LIST
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BB.ASgens(K:INT,OO:LIST):LIST
 
</syntax>
 
</syntax>
    <description>
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  <description>
Computes the generators of the vanishing ideal of the border basis scheme corresponding to the lifting of the K-th element of the list returned by ASneighbors(OO). The input is 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 border basis scheme corresponding to the lifting of the <tt>K</tt>-th element of the list returned by <ref>ApCoCoA-1:BB.ASneighbors|BB.ASneighbors</ref><tt>(OO)</tt>.
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<itemize>
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  <item>@param <em>K</em> An integer in the range 1..Len(<ref>ApCoCoA-1:BB.ASneighbors|BB.ASneighbors</ref>(OO)).</item>
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  <item>@param <em>OO</em> A list of terms representing an order ideal.</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>
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</itemize>
 
<example>
 
<example>
Use Q[x,y,z];
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Use QQ[x,y,z];
$borderbasis.ASgens(1, [1,x,y,z]);
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BB.ASgens(1, [1,x,y,z]);
 
[BBS :: c[1,5]c[2,1] - c[1,3]c[2,2] + c[1,4]c[3,1] - c[1,2]c[3,2] + c[1,2]c[4,1] - c[1,1]c[4,2],
 
[BBS :: c[1,5]c[2,1] - c[1,3]c[2,2] + c[1,4]c[3,1] - c[1,2]c[3,2] + c[1,2]c[4,1] - c[1,1]c[4,2],
 
BBS :: c[2,2]c[2,3] - c[2,1]c[2,5] - c[2,4]c[3,1] + c[2,2]c[3,2] - c[2,2]c[4,1] + c[2,1]c[4,2],
 
BBS :: c[2,2]c[2,3] - c[2,1]c[2,5] - c[2,4]c[3,1] + c[2,2]c[3,2] - c[2,2]c[4,1] + c[2,1]c[4,2],
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-------------------------------
 
-------------------------------
 
</example>
 
</example>
    </description>
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  </description>
     <see>borderbasis.HomASgens</see>
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  <types>
    <see>borderbasis.HomNDgens</see>
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     <type>borderbasis</type>
    <see>borderbasis.NDgens</see>
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  </types>
    <key>Kreuzer</key>
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  <see>ApCoCoA-1:BB.HomASgens|BB.HomASgens</see>
    <key>borderbasis.asgens</key>
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  <see>ApCoCoA-1:BB.HomNDgens|BB.HomNDgens</see>
    <key>borderbasisasgens</key>
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  <see>ApCoCoA-1:BB.NDgens|BB.NDgens</see>
    <wiki-category>Package_borderbasis</wiki-category>
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  <key>ASgens</key>
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  <key>BB.ASgens</key>
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  <key>borderbasis.ASgens</key>
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  <wiki-category>ApCoCoA-1:Package_borderbasis</wiki-category>
 
</command>
 
</command>

Latest revision as of 09:38, 7 October 2020

This article is about a function from ApCoCoA-1.

BB.ASgens

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

Syntax

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

Description

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

  • @param K An integer 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}].

Example

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

BB.HomASgens

BB.HomNDgens

BB.NDgens