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rank(CentralArrangement) -- compute the rank of a central hyperplane arrangement

Description

The center of a hyperplane arrangement is the intersection of its defining affine-linear equations. The rank of a hyperplane arrangement is the codimension of its center.

We illustrate this method with some basic examples.

i1 : R = QQ[x,y,z];
 
i2 : B = arrangement("braid", R)

o2 = {x, y, z, x - y, x - z, y - z}

o2 : Hyperplane Arrangement 
i3 : rank B

o3 = 3
 
i4 : assert(rank B === rank matroid B)
 
i5 : rank typeA 4

o5 = 4
 
i6 : M = arrangement("MacLane")

o6 = {x , x , x , x  - x , x  - x , x  - 6420x , x  - 6420x  - x , x  - 6420x  + 6419x }
       1   2   3   1    2   1    3   2        3   1        2    3   1        2        3

o6 : Hyperplane Arrangement 
i7 : rank M

o7 = 3

The trivial arrangement has no equations.

i8 : trivial = arrangement(map(R^(numgens R),R^0,0),R)

o8 = {}

o8 : Hyperplane Arrangement 
i9 : rank trivial

o9 = 0
 
i10 : assert(rank trivial === 0)

See also

Ways to use this method:

The source of this document is in /__w/M2/M2/macaulay2-1.26.05+ds/M2/Macaulay2/packages/HyperplaneArrangements.m2:1572:0.