areIsomorphic -- determines if two posets are isomorphic

Synopsis

Usage:

r = areIsomorphic(P, Q)

r = P == Q
Inputs:
- P, an instance of the type Poset,
- Q, an instance of the type Poset,
Outputs:
- r, a Boolean value, whether $P$ and $Q$ are isomorphic as posets

Description

Two posets are isomorphic if there is a partial order preserving bijection between the ground sets of the posets which preserves the specified ground set partitions.

i1 : C = chain 5;

i2 : P = poset {{a,b},{b,c},{c,d},{d,e}};

i3 : areIsomorphic(C, P)

o3 = true

The product of $n$ chains of length $2$ is isomorphic to the boolean lattice on $n$ elements. These are also isomorphic to the divisor lattice on the product of $n$ distinct primes.

i4 : B = booleanLattice 4;

i5 : B == product(4, i -> chain 2)

o5 = true

i6 : B == divisorPoset (2*3*5*7)

o6 = true

i7 : B == divisorPoset (2^2*3*5)

o7 = false

Ways to use areIsomorphic :

areIsomorphic(Poset,Poset)

For the programmer

The object areIsomorphic is a method function.

areIsomorphic -- determines if two posets are isomorphic

Synopsis

Description

See also

Ways to use areIsomorphic :

For the programmer