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

## 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 QQ[x, y], DegLex;
I := Ideal([x^2, xy + y^2]);
BB := BBasis(I);
BB;

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[xy + y^2, x^2, y^3, xy^2]
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