isGraded -- determines if a poset is graded

Synopsis

Usage:

i = isGraded P
Inputs:
- P, an instance of the type Poset,
Outputs:
- i, a Boolean value, whether the maximal chains of $P$ are the same length

The poset $P$ is graded if all of its maximalChains are the same length.

Clearly, the $n$ chain and the $n$ booleanLattice are graded.

i1 : n = 5;

i2 : isGraded chain n

o2 = true

i3 : isGraded booleanLattice n

o3 = true

However, the pentagon lattice is not graded.

i4 : P = poset {{1,2}, {1,3}, {3,4}, {2,5}, {4, 5}};

i5 : isGraded P

o5 = false