Posets¶

Posets

EXAMPLES:

sage: from msinvar.posets import Poset
sage: P=Poset([[1,2],[1,3]]); P
Poset with vertices
{1, 2, 3}
and relations
[[1, 2], [1, 3]]
sage: list(P.succ(1))
[1, 2, 3]
sage: list(P.ideals())
[{1, 2, 3}, {1, 2}, {1, 3}, {1}, set()]

class msinvar.posets.Poset(rel, vert=None)[source]¶

Bases: object

Poset class.

EXAMPLES:

sage: from msinvar.posets import Poset
sage: P=Poset([[1,2],[1,3]]); P
Poset with vertices
{1, 2, 3}
and relations
[[1, 2], [1, 3]]
sage: list(P.succ(1))
[1, 2, 3]
sage: list(P.ideals())
[{1, 2, 3}, {1, 2}, {1, 3}, {1}, set()]

upper_closure(vert)[source]¶

lower_closure(vert)[source]¶

succ(i)[source]¶

pred(i)[source]¶

ideals(size=100)[source]¶: List if ideals in a poset having <=``size`` elements.