ApCoCoA-1:BB.BBasisForOI: Difference between revisions
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{{Version|1}} | |||
<command> | <command> | ||
<title>BB.BBasisForOI</title> | |||
<short_description>Computes the border basis of an ideal w.r.t. a given order ideal.</short_description> | |||
<syntax> | <syntax> | ||
BB.BBasisForOI(F:LIST,OO:LIST):LIST | |||
</syntax> | </syntax> | ||
<description> | |||
Computes the border basis of the ideal < | Computes the border basis of the ideal <tt>I = <F></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. | ||
<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 | 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] | [xy + y^2, x^2, y^3, xy^2] | ||
------------------------------- | ------------------------------- | ||
</example> | </example> | ||
</ | </description> | ||
<see>BBasis</see> | <types> | ||
<type>borderbasis</type> | |||
<type>ideal</type> | |||
</types> | |||
<see>ApCoCoA-1:BB.BBasis|BB.BBasis</see> | |||
<see>ApCoCoA-1:BB.BBasisForMP|BB.BBasisForMP</see> | |||
<key>BBasisForOI</key> | |||
<key>BB.BBasisForOI</key> | |||
<key>borderbasis.BBasisForOI</key> | |||
<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] -------------------------------
