ApCoCoA-1:BB.BBasis: Difference between revisions
From ApCoCoAWiki
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<command> | |||
<title>BBasis</title> | |||
<short_description>Compute the border basis of a zero-dimensional ideal.</short_description> | |||
<syntax> | <syntax>BBasis(I:IDEAL):LIST of POLY</syntax> | ||
BBasis(I:IDEAL):LIST of POLY | <description> | ||
</syntax> | |||
<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | <em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | ||
<par/> | <par/> | ||
Let < | Let <tt>sigma</tt> be a degree compatible term ordering. The function <tt>BBasis</tt> calls the ApCoCoAServer to compute the O_sigma(I)-border basis of the zero-dimensional input ideal <tt>I</tt> and returns it as a list of polynomials. | ||
<par/> | |||
The return value will be the computed border basis. | The return value will be the computed border basis. | ||
<itemize> | <itemize> | ||
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------------------------------- | ------------------------------- | ||
</example> | </example> | ||
</description> | |||
<see>GBasis5, and more</see> | |||
<see>BB.BBasisForOI</see> | |||
<types> | |||
<type>apcocoaserver</type> | |||
</types> | |||
<key>BBasis</key> | |||
<key>BB.BBasis</key> | |||
<key>borderbasis.BBasis</key> | |||
<key>border basis</key> | |||
<wiki-category>Package_borderbasis</wiki-category> | |||
</command> | |||
Revision as of 10:56, 24 April 2009
BBasis
Compute the border basis of a zero-dimensional ideal.
Syntax
BBasis(I:IDEAL):LIST of POLY
Description
Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.
Let sigma be a degree compatible term ordering. The function BBasis calls the ApCoCoAServer to compute the O_sigma(I)-border basis of the zero-dimensional input ideal I and returns it as a list of polynomials.
The return value will be the computed border basis.
@param I A zero-dimensional ideal of which to compute a border basis.
@return A list of border basis polynomials.
Example
Use QQ[x, y], DegLex; I := Ideal([x^2, xy + y^2]); BB := BBasis(I); BB; ------------------------------- [xy + y^2, x^2, y^3, xy^2] -------------------------------
