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# isomorphism(Poset,Poset) -- computes an isomorphism between isomorphic posets

- Function: isomorphism
- Usage:
    `pi' = isomorphism(P, Q)`
- Inputs:
  - P, an instance of the type Poset,
  - Q, an instance of the type Poset,
- Optional inputs:
  - Homogeneous => ..., default value true,
  - Strategy (missing documentation) => ..., default value null,
  - Strict => ..., default value false,
  - Tries => ..., default value null,
  - Verbose => ..., default value false,
- Outputs:
  - pi', a hash table, which specifies a partial order preserving bijection from the ground set of $P$ to the ground set of $Q$

## 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 : isomorphism(divisorPoset (2*3*5), booleanLattice 3)

    o1 = HashTable{1 => 000 }
                   2 => 001
                   3 => 010
                   5 => 100
                   6 => 011
                   10 => 101
                   15 => 110
                   30 => 111

    o1 : HashTable

This method was inspired by John Stembridge's Maple package available at http://www.math.lsa.umich.edu/~jrs/maple.html#posets.

## See also

- areIsomorphic -- determines if two posets are isomorphic
- removeIsomorphicPosets -- returns a sub-list of non-isomorphic posets

## Ways to use this method:

- isomorphism(Poset,Poset) -- computes an isomorphism between isomorphic posets

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Posets.m2:3195:0.