Difference between revisions of "ApCoCoA-1:BB.BBasisForOI"
From ApCoCoAWiki
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<description> | <description> | ||
Computes the border basis of the ideal <formula>I=<F></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. | Computes the border basis of the ideal <formula>I=<F></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. | ||
| + | <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]; | Use Q[x,y]; | ||
Revision as of 13:44, 22 April 2009
BB.BorderBasis
Compute the border basis of an ideal.
Syntax
BB.BorderBasis(F:LIST,OO:LIST):LIST
Description
Computes the border basis of the ideal <formula>I=<F></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.
@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 Q[x,y]; BB.BorderBasis([x^2, xy + y^2], [1,x,y,y^2]); [xy + y^2, x^2, y^3, xy^2] -------------------------------
