Difference between revisions of "ApCoCoA-1:BB.BBasisForOI"
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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 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 | + | 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> |
| − | <key> | + | <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> | ||
| + | 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] | ||
| + | ------------------------------- | ||
| + | </example> | ||
| + | </description> | ||
| + | <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] -------------------------------
