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transitiveClosure -- computes the transitive closure of a set of relations

Usage:

M = transitiveClosure(G, R)
Inputs:
- G, a list, the ground set
- R, a list, pairs {$a,b$} which indicate that $a \leq b$
Outputs:
- M, a matrix, with entries $(i,j)$ equal to 1 if $G_j \leq G_i$ and 0 otherwise

Description

This method uses the descendants method from the Graphs package to compute the RelationMatrix from the relations $R$.

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

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

i3 : transitiveClosure(G, R)

o3 = | 1 1 1 1 1 |
     | 0 1 0 1 1 |
     | 0 0 1 1 1 |
     | 0 0 0 1 1 |
     | 0 0 0 0 1 |

              5       5
o3 : Matrix ZZ  <-- ZZ

See also

poset -- creates a new Poset object

Ways to use transitiveClosure:

transitiveClosure(List,List)

For the programmer

The object transitiveClosure is a method function.

The source of this document is in Posets.m2:2151:0.