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allRelations -- computes all relations of a poset

Usage:

R = allRelations P

R = allRelations(P, NoLoops)
Inputs:
- P, an instance of the type Poset,
- NoLoops, a Boolean value, whether loops, i.e., relations of the form $\{a,a\}$, should be returned
Outputs:
- R, a list, containing all relations between elements of $P$

Description

This method returns all relations of a poset, though loops may be suppressed with the input NoLoops.

i1 : P = divisorPoset 12;

i2 : allRelations P

o2 = {{1, 1}, {1, 2}, {1, 3}, {1, 4}, {1, 6}, {1, 12}, {2, 2}, {2, 4}, {2,
     ------------------------------------------------------------------------
     6}, {2, 12}, {3, 3}, {3, 6}, {3, 12}, {4, 4}, {4, 12}, {6, 6}, {6, 12},
     ------------------------------------------------------------------------
     {12, 12}}

o2 : List

i3 : allRelations(P, true)

o3 = {{1, 2}, {1, 3}, {1, 4}, {1, 6}, {1, 12}, {2, 4}, {2, 6}, {2, 12}, {3,
     ------------------------------------------------------------------------
     6}, {3, 12}, {4, 12}, {6, 12}}

o3 : List

See also

compare -- compares two elements in a poset
coveringRelations -- computes the minimal list of generating relations of a poset

Ways to use allRelations:

allRelations(Poset)
allRelations(Poset,Boolean)

For the programmer

The object allRelations is a method function.

The source of this document is in Posets.m2:4646:0.