isDistributive -- determines if a lattice is distributive

Synopsis

Usage:

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

Description

The lattice $P$ is distributive if the meet operation distributes over the join operation. Equivalently, $P$ is distributive if the join operation distributes over the meet operation.

The $n$ booleanLattice is distributive.

i1 : isDistributive booleanLattice 3

o1 = true

The pentagon lattice and diamond lattice are prototypical non-distributive lattices.

i2 : P = poset {{1,2}, {1,3}, {3,4}, {2,5}, {4, 5}};

i3 : isLattice P

o3 = true

i4 : isDistributive P

o4 = false

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

i6 : isLattice D

o6 = true

i7 : isDistributive D

o7 = false

Ways to use isDistributive :

isDistributive(Poset)

For the programmer

The object isDistributive is a method function.

isDistributive -- determines if a lattice is distributive

Synopsis

Description

See also

Ways to use isDistributive :

For the programmer