Arrangement == Arrangement -- whether two hyperplane arrangements are equal

Synopsis

Operator: ==
Usage:

A == B
Inputs:
- A, a hyperplane arrangement,
- B, a hyperplane arrangement,
Outputs:
- a Boolean value, that is true if the underlying rings are equal and the lists of hyperplanes are the same

Two hyperplane arrangements are equal their underlying rings are identical and their defining linear forms are listed in the same order.

Although the following two arrangements have the same hyperplanes, they are not equal because the linear forms are different.

i1 : R = QQ[x, y];

i2 : A = arrangement{x, y, x+y}

o2 = {x, y, x + y}

o2 : Hyperplane Arrangement

i3 : assert(A == A)

i4 : B = arrangement{2*x, y, x+y}

o4 = {2x, y, x + y}

o4 : Hyperplane Arrangement

i5 : A == B

o5 = false

i6 : assert not (A == B)

i7 : assert( A != B )

The order in which the hyperplanes are listed is also important.

i8 : A' = arrangement{y, x, x+y}

o8 = {y, x, x + y}

o8 : Hyperplane Arrangement

i9 : A == A'

o9 = false

i10 : assert( A != A' )