# ApCoCoA-1:BB.BBasisForMP

## BB.BBasisForMP

Computes the border basis of an ideal generated by marked polynomials.

### Syntax

BB.BBasisForMP(F:LIST of LIST):LIST of LIST

### Description

Computes the border basis of the zero-dimensional ideal `I = <F>` with respect to the set of marked polynomials `F`. The input is a list of tuples `[P, T]` where `P` is a polynomial and `T` must be a term of the support of `P` such that `deg(P) = deg(T)`. The output is a list of tuples `[P, T]` denoting a border basis of `I` where `P` is a polynomial and `T` is the term of the support of `P` such that `deg(P) = deg(T)` and `T` is a border term. An error will indicate if the given term marking does not lead to a successful computation.

@param

*F*List of tuples`[P, T]`where`P`is a polynomial and`T`must be a term of the support of`P`such that`deg(P) = deg(T)`. The polynomials`P`must generate a zero-dimensional ideal.@return A list of tuples

`[P, T]`denoting a border basis of`I`where`P`is a polynomial and`T`is the term of the support of`P`such that`deg(P) = deg(T)`and`T`is a border term.

#### Example

Use QQ[x,y]; BB.BBasisForMP([ [,], [,] ]); -------------------------------