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# matrix(Arrangement) -- make a matrix from the defining equations

- Function: matrix
- Usage:
    `matrix A`
- Inputs:
  - A, a hyperplane arrangement,
- Optional inputs:
  - Degree => ..., default value null, this optional input is ignored by this function
- Outputs:
  - a matrix, having one row, whose entries are the defining equations

## Description

A hyperplane arrangement is defined by a list of affine-linear equations. This methods creates a matrix, over the underlying ring of the hyperplane arrangement, whose entries are the defining equations.

A few reflection arrangements yield the following matrices.

    i1 : A = typeA 3

    o1 = {x  - x , x  - x , x  - x , x  - x , x  - x , x  - x }
           1    2   1    3   1    4   2    3   2    4   3    4

    o1 : Hyperplane Arrangement

    i2 : R = ring A

    o2 = R

    o2 : PolynomialRing

    i3 : matrix A

    o3 = | x_1-x_2 x_1-x_3 x_1-x_4 x_2-x_3 x_2-x_4 x_3-x_4 |

                 1      6
    o3 : Matrix R  <-- R

    i4 : matrix typeB 2

    o4 = | x_1 x_1-x_2 x_1+x_2 x_2 |

                            1                 4
    o4 : Matrix (QQ[x ..x ])  <-- (QQ[x ..x ])
                     1   2             1   2

    i5 : matrix typeD 4

    o5 = | x_1-x_2 x_1+x_2 x_1-x_3 x_1+x_3 x_1-x_4 x_1+x_4 x_2-x_3 x_2+x_3
         ------------------------------------------------------------------------
         x_2-x_4 x_2+x_4 x_3-x_4 x_3+x_4 |

                            1                 12
    o5 : Matrix (QQ[x ..x ])  <-- (QQ[x ..x ])
                     1   4             1   4

The trivial arrangement has no equations.

    i6 : trivial = arrangement({},R)

    o6 = {}

    o6 : Hyperplane Arrangement

    i7 : matrix trivial

    o7 = 0

                 1
    o7 : Matrix R  <-- 0

    i8 : assert(matrix trivial == 0)

## See also

- arrangement(List) -- make a hyperplane arrangement
- ring(Arrangement) -- get the underlying ring of a hyperplane arrangement

## Ways to use this method:

- matrix(Arrangement) -- make a matrix from the defining equations

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/HyperplaneArrangements.m2:1473:0.