RelationMatrix -- the matrix expressing all of the relations between elements in a Poset

Synopsis

Usage:
M = P.RelationMatrix
Inputs:
- P, an object of class Poset
Outputs:
- M, a matrix, where the ijth entry indicates whether or not the jth element in the set is less than or equal to the ith element

Description

Since any poset is in fact a HashTable this symbol denotes the data in the HashTable containing all possible relations between elements.

i1 : S = QQ[a,b,c,d];

i2 : M = monomialIdeal (b^2, b*c, c^2);

o2 : MonomialIdeal of S

i3 : L = lcmLattice (M);

i4 : L.GroundSet

          2          2   2   2    2 2
o4 = {1, c , b*c, b*c , b , b c, b c }

o4 : List

i5 : L.RelationMatrix

o5 = | 1 1 1 1 1 1 1 |
     | 0 1 0 1 0 0 1 |
     | 0 0 1 1 0 1 1 |
     | 0 0 0 1 0 0 1 |
     | 0 0 0 0 1 1 1 |
     | 0 0 0 0 0 1 1 |
     | 0 0 0 0 0 0 1 |

              7        7
o5 : Matrix ZZ  <--- ZZ

For the programmer

The object RelationMatrix is a symbol.

RelationMatrix -- the matrix expressing all of the relations between elements in a Poset

Synopsis

Description

See also

For the programmer