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

From ApCoCoAWiki
(Short description update.)
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{{Version|1}}
 
<command>
 
<command>
    <title>BB.BorderBasis</title>
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  <title>BB.BBasisForOI</title>
    <short_description>Compute the border basis of an ideal.</short_description>
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  <short_description>Computes the border basis of an ideal w.r.t. a given order ideal.</short_description>
 +
 
 
<syntax>
 
<syntax>
BB.BorderBasis(F:LIST,OO:LIST):LIST
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BB.BBasisForOI(F:LIST,OO:LIST):LIST
 
</syntax>
 
</syntax>
    <description>
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  <description>
Computes the border basis of the ideal <formula>I=&lt;F&gt;</formula> with respect to the order ideal OO. Gives an error messages if no border basis exists. Uses the <formula>O_{\sigma}(I)</formula> border basis and the border basis transformation algorithm. The inputs are a list of polynomials F and a list OO of terms that specify an order ideal. The output is a list of polynomials.
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Computes the border basis of the ideal <tt>I = &lt;F&gt;</tt> with respect to the order ideal <tt>OO</tt>. Gives an error messages if no border basis exists. Uses the <tt>O_sigma(I)</tt> border basis and the border basis transformation algorithm. The inputs are a list of polynomials <tt>F</tt> and a list <tt>OO</tt> of terms that specify an order ideal. The output is a list of polynomials.
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<itemize>
 +
  <item>@param <em>F</em> Generators of a zero-dimensional ideal whose border basis should be computed.</item>
 +
  <item>@param <em>OO</em> A list of terms representing an order ideal.</item>
 +
  <item>@return A list of border basis polynomials.</item>
 +
</itemize>
 
<example>
 
<example>
Use Q[x,y];
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Use QQ[x,y];
BB.BorderBasis([x^2, xy + y^2], [1,x,y,y^2]);
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BB.BBasisForOI([x^2, xy + y^2], [1,x,y,y^2]);
  
 
[xy + y^2, x^2, y^3, xy^2]
 
[xy + y^2, x^2, y^3, xy^2]
 
-------------------------------
 
-------------------------------
 
</example>
 
</example>
     </description>
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  </description>
     <see>BBasis</see>
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  <types>
    <key>kreuzer</key>
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     <type>borderbasis</type>
    <key>bb.borderbasis</key>
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     <type>ideal</type>
    <key>borderbasis.borderbasis</key>
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  </types>
    <wiki-category>Package_borderbasis</wiki-category>
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  <see>ApCoCoA-1:BB.BBasis|BB.BBasis</see>
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  <see>ApCoCoA-1:BB.BBasisForMP|BB.BBasisForMP</see>
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  <key>BBasisForOI</key>
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  <key>BB.BBasisForOI</key>
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  <key>borderbasis.BBasisForOI</key>
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  <wiki-category>ApCoCoA-1:Package_borderbasis</wiki-category>
 
</command>
 
</command>

Latest revision as of 09:39, 7 October 2020

This article is about a function from ApCoCoA-1.

BB.BBasisForOI

Computes the border basis of an ideal w.r.t. a given order ideal.

Syntax

BB.BBasisForOI(F:LIST,OO:LIST):LIST

Description

Computes the border basis of the ideal I = <F> with respect to the order ideal OO. Gives an error messages if no border basis exists. Uses the O_sigma(I) border basis and the border basis transformation algorithm. The inputs are a list of polynomials F and a list OO of terms that specify an order ideal. The output is a list of polynomials.

  • @param F Generators of a zero-dimensional ideal whose border basis should be computed.

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

  • @return A list of border basis polynomials.

Example

Use QQ[x,y];
BB.BBasisForOI([x^2, xy + y^2], [1,x,y,y^2]);

[xy + y^2, x^2, y^3, xy^2]
-------------------------------

BB.BBasis

BB.BBasisForMP