# ApCoCoA-1:BB.BBasisForOI

From ApCoCoAWiki

## BB.BBasisForOI

Compute 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] -------------------------------