Union and Intersection in PowerShell?

I have an array of objects of the following structure:

structure Disk
{
  int UID;
  String Computer;
}

A computer may have a bunch of shared disks, and a disk may be shared among computers.

I want to find out all the disks common to all the computers. For example, I have computer A, B, and C; Disks 1, 2, and 3. The disk array is {1,A}, {1,B}, {2,A},{2,B},{2,C},{3,A}. The result that I want should be the disk 2, because it appears on A, B, and C.

Is there a effective way to achieve this?

With multiple foreach loops it's achievable, but definitely I want a better way. I'm thinking about operations like intersection, but didn't find this in PowerShell.

Assuming $arr is the array, you can do like this:

$computers = $arr | select -expand computer -unique
$arr | group uid | ?{$_.count -eq $computers.count} | select name

In general, I would approach union and intersection in Powershell like this:

$a = (1,2,3,4)
$b = (1,3,4,5)
$a + $b | select -uniq    #union
$a | ?{$b -contains $_}   #intersection

But for what you are asking, the above solution works well and not really about union and intersection in the standard definition of the terms.

Update:

I have written pslinq which provides Union-List and Intersect-List that help to achieve set union and intersection with Powershell.

You can also do

$a = (1,2,3,4)
$b = (1,3,4,5)
Compare-Object $a $b -PassThru -IncludeEqual                   # union
Compare-Object $a $b -PassThru -IncludeEqual -ExcludeDifferent # intersection

Doesn't work if $a is null though.

For set subtraction (a - b):

$a | ?{-not ($b -contains $_)}

While this won't work in the earliest versions, in more recent versions you can just call the .NET LINQ extension functions directly, e.g.

[system.linq.enumerable]::union([object[]](1,2,3),[object[]](2,3,4))

(Without the cast to some enumerable type, PowerShell throws a "cannot find overload" error.)

This definitely works in PowerShell V4 and V5 and definitely doesn't in V2. I don't have a system at hand with V3.