Relations -- a set of relations in the poset that generates all other relations

Synopsis

Usage:
R = P.Relations
Inputs:
- P, an object of class Poset
Outputs:
- R, a list, list of pairs of elements in P where (a,b) means a is less than or equal to b

Description

Since any poset is in fact a HashTable this symbol denotes the data in the HashTable which will describe all of the relations between elements in P.

i1 : P = poset ({a,b,c,d,e,f},{(a,d),(d,f),(b,d),(b,e),(c,e),(e,f)});

i2 : P.Relations --note there is not a one to one correspondence between these and entries in the RelationMatrix

o2 = {(a, d), (d, f), (b, d), (b, e), (c, e), (e, f)}

o2 : List

i3 : P.RelationMatrix

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

                6          6
o3 : Matrix RR    <--- RR
              53         53

Caveat

Typically, the relations are the data entered in by the user and by no means account for every relation. The RelationMatrix is usually computed from this set and thus is a better descriptor of the relations in P.

For the programmer

The object Relations is a symbol.

Relations -- a set of relations in the poset that generates all other relations

Synopsis

Description

Caveat

See also

For the programmer