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

## BB.MultMat

Computes the i-th multiplication matrix associated to a border basis.

### Syntax

```BB.MultMat(I:INT, OO:LIST, BB:LIST):MAT
```

### Description

Computes the I-th multiplication matrix associated to the given input OO-border basis BB of the ideal generated by the polynomials of BB where I is an index number in the range 1..NumIndets().

The output is a matrix.

• @param I Index of indeterminate.

• @param OO A list of terms representing an order ideal.

• @param BB A list of terms representing the OO-border basis of the ideal generated by the polynomials of BB.

• @return The I-th multiplication matrix.

#### Example

```Use QQ[x,y];

BB.MultMat(1,
[1, y, y^2, y^3, x, xy, x^2, x^2y],
[xy^2, x^3 + xy, y^4, xy^3, x^2y^2, x^3y]);

-------------------------------
Mat([
[0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0],
[1, 0, 0, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0, -1, 0],
[0, 0, 0, 0, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 1, 0, 0]
])
-------------------------------
```