isAtomic -- determines if a lattice is atomic

Synopsis

Usage:

i = isAtomic P
Inputs:
- P, an instance of the type Poset, a lattice
Outputs:
- i, a Boolean value, whether $P$ is atomic

Description

The lattice $P$ is atomic if every non-minimal vertex of $P$ is the join of atoms of $P$. Equivalently, $P$ is atomic if every non-minimal, non-atom vertex of $P$ covers at least two vertices.

The diamond poset is atomic. Also $n$ booleanLattices are atomic.

i1 : P = poset {{1, 2}, {1, 3}, {1, 4}, {2, 5}, {3, 5}, {4, 5}};

i2 : isLattice P

o2 = true

i3 : isAtomic P

o3 = true

i4 : isAtomic booleanLattice 4

o4 = true

The following lattice is non-atomic. Also, $n$ chains are non-atomic, for $n \geq 3$.

i5 : Q = poset {{1, 2}, {1, 3}, {2, 4}, {2, 5}, {3, 4}, {4, 6}, {5, 6}};

i6 : isLattice Q

o6 = true

i7 : isAtomic Q

o7 = false

i8 : isAtomic chain 5

o8 = false

Ways to use isAtomic :

isAtomic(Poset)

For the programmer

The object isAtomic is a method function.

isAtomic -- determines if a lattice is atomic

Synopsis

Description

See also

Ways to use isAtomic :

For the programmer