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

From ApCoCoAWiki
(Example section update.)
(Description update.)
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<command>
 
<command>
    <title>BB.ASgens</title>
+
  <title>BB.ASgens</title>
    <short_description>Compute the generators of the vanishing ideal of a border basis scheme.</short_description>
+
  <short_description>Compute the generators of the vanishing ideal of a border basis scheme.</short_description>
<syntax>
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  <syntax>BB.ASgens(K:INT,OO:LIST):LIST</syntax>
BB.ASgens(K:INT,OO:LIST):LIST
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  <description>
</syntax>
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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 <ref>ASneighbors</ref>(OO). The inputs are an integer K in the range 1..Len(<ref>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}].
    <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 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>.
 
 
<itemize>
 
<itemize>
   <item>@param <em>K</em> 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) will be computed.</item>
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   <item>@param <em>K</em> 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 <ref>ASneighbors</ref>(OO) will be computed.</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 border basis scheme corresponding to the lifting of the K-th element of the list returned by ASneighbors(OO). The polynomials will belong to the ring BBS=K[c_{ij}].</item>
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   <item>@return A list of generators of the vanishing ideal of the border basis scheme corresponding to the lifting of the K-th element of the list returned by <ref>ASneighbors</ref>(OO). The polynomials will belong to the ring BBS=K[c_{ij}].</item>
 
</itemize>
 
</itemize>
 
<example>
 
<example>
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-------------------------------
 
-------------------------------
 
</example>
 
</example>
    </description>
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  </description>
<types>
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  <types>
<type>list</type>
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    <type>list</type>
<type>int</type>
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    <type>int</type>
<type>integer</type>
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    <type>integer</type>
</types>
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  </types>
    <see>BB.HomASgens</see>
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  <see>BB.HomASgens</see>
    <see>BB.HomNDgens</see>
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  <see>BB.HomNDgens</see>
    <see>BB.NDgens</see>
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  <see>BB.NDgens</see>
    <key>ASgens</key>
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  <key>ASgens</key>
    <key>BB.ASgens</key>
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  <key>BB.ASgens</key>
    <key>borderbasis.ASgens</key>
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  <key>borderbasis.ASgens</key>
    <wiki-category>Package_borderbasis</wiki-category>
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  <wiki-category>Package_borderbasis</wiki-category>
 
</command>
 
</command>

Revision as of 10:58, 24 April 2009

BB.ASgens

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

Syntax

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

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 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 BBS=K[c_{ij}].

  • @param K 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) will be computed.

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

  • @return A list of 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 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