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

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