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

## 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.

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