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Posets :: divisorPoset

divisorPoset -- returns the poset of all divisors of a given monomial

Synopsis

Description

This command computes the poset of all divisors of a given monomial. For two monomials, u and v with u strictly dividing v, we have u < v in this poset.
i1 : S = QQ[a,b,c,d];
i2 : P = divisorPoset(a*b^2*d^3)

o2 = Poset{cache => CacheTable{}                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       }
                                2   3             2     3   2   2    2 2   2 3             2     3                   2       3     2     2      2 2     2 3
           GroundSet => {1, d, d , d , b, b*d, b*d , b*d , b , b d, b d , b d , a, a*d, a*d , a*d , a*b, a*b*d, a*b*d , a*b*d , a*b , a*b d, a*b d , a*b d }
           RelationMatrix => | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 |
                             | 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 |
                             | 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 |
                             | 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 |
                             | 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 |
                             | 0 0 0 0 0 1 1 1 0 1 1 1 0 0 0 0 0 1 1 1 0 1 1 1 |
                             | 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 1 1 0 0 1 1 |
                             | 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 |
                             | 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 |
                             | 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 |
                             | 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 |
                             | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 |
                             | 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 |
                             | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 0 1 1 1 |
                             | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 1 |
                             | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 |
                             | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 |
                             | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 |
                             | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 |
                             | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 |
                             | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 |
                             | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 |
                             | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 |
                             | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 |
                                              2        3                            2          3        2        2         2 2        2 3                            2          3                                  2            3          2          2           2 2          2 3                2        3                    2          3        2         2 2        2 3                    2          3                        2            3          2           2 2          2 3     2   2     2   3     2     2     2     3     2   2 2     2   2 3     2     2     2     3     2       2     2       3     2     2 2     2     2 3     3   3     3     3     3   2 3     3     3     3       3     3     2 3                            2          3        2        2         2 2        2 3                                  2            3          2          2           2 2          2 3                        2            3          2           2 2          2 3                            2              3            2             2 2            2 3       2     2       2     3       2   2 2       2   2 3       2       2       2       3       2     2 2       2     2 3       3     3       3   2 3       3       3       3     2 3     2   2     2   2      2   2 2     2   2 3     2     2     2     2      2     2 2     2     2 3     2    2      2    2 2     2    2 3     2      2      2      2 2     2      2 3     2 2   2 2     2 2   2 3     2 2     2 2     2 2     2 3     2 3   2 3     2 3     2 3                            2          3                                  2            3          2          2           2 2          2 3                        2            3                            2              3            2             2 2            2 3       2     2       2     3       2       2       2       3       2     2 2       2     2 3       3     3       3       3       3     2 3                                        2              3            2            2             2 2            2 3                                2                3              2               2 2              2 3         2       2         2       3         2     2 2         2     2 3         3       3         3     2 3       2     2       2     2        2     2 2       2     2 3       2      2        2      2 2       2      2 3       2 2     2 2       2 2     2 3       2 3     2 3
           Relations => {(1, 1), (1, d), (1, d ), (1, d ), (1, b), (1, b*d), (1, b*d ), (1, b*d ), (1, b ), (1, b d), (1, b d ), (1, b d ), (1, a), (1, a*d), (1, a*d ), (1, a*d ), (1, a*b), (1, a*b*d), (1, a*b*d ), (1, a*b*d ), (1, a*b ), (1, a*b d), (1, a*b d ), (1, a*b d ), (d, d), (d, d ), (d, d ), (d, b*d), (d, b*d ), (d, b*d ), (d, b d), (d, b d ), (d, b d ), (d, a*d), (d, a*d ), (d, a*d ), (d, a*b*d), (d, a*b*d ), (d, a*b*d ), (d, a*b d), (d, a*b d ), (d, a*b d ), (d , d ), (d , d ), (d , b*d ), (d , b*d ), (d , b d ), (d , b d ), (d , a*d ), (d , a*d ), (d , a*b*d ), (d , a*b*d ), (d , a*b d ), (d , a*b d ), (d , d ), (d , b*d ), (d , b d ), (d , a*d ), (d , a*b*d ), (d , a*b d ), (b, b), (b, b*d), (b, b*d ), (b, b*d ), (b, b ), (b, b d), (b, b d ), (b, b d ), (b, a*b), (b, a*b*d), (b, a*b*d ), (b, a*b*d ), (b, a*b ), (b, a*b d), (b, a*b d ), (b, a*b d ), (b*d, b*d), (b*d, b*d ), (b*d, b*d ), (b*d, b d), (b*d, b d ), (b*d, b d ), (b*d, a*b*d), (b*d, a*b*d ), (b*d, a*b*d ), (b*d, a*b d), (b*d, a*b d ), (b*d, a*b d ), (b*d , b*d ), (b*d , b*d ), (b*d , b d ), (b*d , b d ), (b*d , a*b*d ), (b*d , a*b*d ), (b*d , a*b d ), (b*d , a*b d ), (b*d , b*d ), (b*d , b d ), (b*d , a*b*d ), (b*d , a*b d ), (b , b ), (b , b d), (b , b d ), (b , b d ), (b , a*b ), (b , a*b d), (b , a*b d ), (b , a*b d ), (b d, b d), (b d, b d ), (b d, b d ), (b d, a*b d), (b d, a*b d ), (b d, a*b d ), (b d , b d ), (b d , b d ), (b d , a*b d ), (b d , a*b d ), (b d , b d ), (b d , a*b d ), (a, a), (a, a*d), (a, a*d ), (a, a*d ), (a, a*b), (a, a*b*d), (a, a*b*d ), (a, a*b*d ), (a, a*b ), (a, a*b d), (a, a*b d ), (a, a*b d ), (a*d, a*d), (a*d, a*d ), (a*d, a*d ), (a*d, a*b*d), (a*d, a*b*d ), (a*d, a*b*d ), (a*d, a*b d), (a*d, a*b d ), (a*d, a*b d ), (a*d , a*d ), (a*d , a*d ), (a*d , a*b*d ), (a*d , a*b*d ), (a*d , a*b d ), (a*d , a*b d ), (a*d , a*d ), (a*d , a*b*d ), (a*d , a*b d ), (a*b, a*b), (a*b, a*b*d), (a*b, a*b*d ), (a*b, a*b*d ), (a*b, a*b ), (a*b, a*b d), (a*b, a*b d ), (a*b, a*b d ), (a*b*d, a*b*d), (a*b*d, a*b*d ), (a*b*d, a*b*d ), (a*b*d, a*b d), (a*b*d, a*b d ), (a*b*d, a*b d ), (a*b*d , a*b*d ), (a*b*d , a*b*d ), (a*b*d , a*b d ), (a*b*d , a*b d ), (a*b*d , a*b*d ), (a*b*d , a*b d ), (a*b , a*b ), (a*b , a*b d), (a*b , a*b d ), (a*b , a*b d ), (a*b d, a*b d), (a*b d, a*b d ), (a*b d, a*b d ), (a*b d , a*b d ), (a*b d , a*b d ), (a*b d , a*b d )}

o2 : Poset

Ways to use divisorPoset :