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

From ApCoCoAWiki

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− | 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. | + | 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> | <itemize> | ||

<item>@param <em>F</em> Generators of a zero-dimensional ideal whose border basis should be computed.</item> | <item>@param <em>F</em> Generators of a zero-dimensional ideal whose border basis should be computed.</item> |

## Revision as of 14:43, 8 July 2009

## 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] -------------------------------