# ApCoCoA-1:BB.BBasis

From ApCoCoAWiki

## BBasis

Compute the border basis of a zero-dimensional ideal.

### Syntax

BBasis(I:IDEAL):LIST of POLY

### Description

*Please note:* The function(s) explained on this page is/are using the *ApCoCoAServer*. You will have to start the ApCoCoAServer in order to use it/them.

Let <formula>\sigma</formula> be a degree compatible term ordering. The function `BBasis` calls the ApCoCoAServer to compute the <formula>\mathcal{O}_\sigma(I)</formula>-border basis of the zero-dimensional input ideal `I` and returns it as a list of polynomials.

The return value will be the computed border basis.

@param

*I*A zero-dimensional ideal of which to compute a border basis.@return A list of border basis polynomials.

#### Example

Use Q[x, y], DegLex; I := Ideal([x^2, xy + y^2]); BB := BBasis(I); BB; ------------------------------- [xy + y^2, x^2, y^3, xy^2] -------------------------------