import string

class Rectangle$($object$)$:

def $\_\_$init$\_\_($self$,*$intervals$,$ name$=$None$)$: $[29]$ # Whooho!! Let's try with another example. Now $T$ is inside R$.$

$.$

$"""$A rectangle is initialized with a list, whose elements are

either Interval, or a pair of numbers.

It would be perhaps cleaner to accept only list of intervals,

but specifying rectangles via a list of pairs, with each pair

defining an interval, makes for a concise shorthand that will be

useful in tests.

Every rectangle has a name, used to depict it$.$

If no name is provided, we invent a random one."""

self.intervals $=[]$

for i in intervals:

self.intervals.append$($i if type$($i$)==$ Interval else Interval$(*$i$))$

# I want each rectangle to have a name.

if name is None:

self.name $=\text{'}\text{'}.$join$($

random.choices$($string$.$ascii$\_$letters $+$ string.digits, k$=8))$

else:

self.name $=$ name

def $\_\_$repr$\_\_($self$)$:

$"""$Function used to print a rectangle."""

s $=$ "Rectangle $"+$ self.name $+"$: $"$

s $+=$ repr$([($i$.$x$0,$ i$.$x$1)$ for i in self.intervals$])$

return s

def clone$($self$,$ name$=$None$)$:

$"""$Returns a clone of itself, with a given name."""

name $=$ name or self.name $+"\text{'}"$

return Rectangle$(*$self$.$intervals, name$=$name$)$

def $\_\_$len$\_\_($self$)$:

$"""$Returns the number of dimensions of the rectangle

$($not the length of the edges$).$ This is used with

$\_\_$getitem$\_\_$ below, to get the interval along a dimension."""

return len$($self$.$intervals$)$

def $\_\_$getitem$\_\_($self$,$ n$)$:

$"""$Returns the interval along the n$-$th dimension"""

return self.intervals$[$n$]$

def $\_\_$setitem$\_\_($self$,$ n$,$ i$)$:

$"""$Sets the interval along the n$-$th dimension to be i$"""$

self.intervals$[$n$]=$ i

def $\_\_$eq$\_\_($self$,$ other$)$:

if not isinstance$($other$,$ Rectangle$)$:

return False

# We rely on interval equality here.

return self.intervals $==$ other.intervals

@property

def ndims$($self$)$:

$"""$Returns the number of dimensions of the interval."""

return len$($self$.$intervals$)$

@property

def volume$($self$)$:

return np$.$prod$([$i$.$length for i in self.intervals$])$