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

## Synopsis

• Operator: ==
• Usage:
A == B
• Inputs:
• Outputs:
• , that is true if the underlying rings are equal and the lists of hyperplanes are the same

## Description

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' )