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Posets :: RelationMatrix

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

Synopsis

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

See also

For the programmer

The object RelationMatrix is a symbol.