HasseDiagrams

Hasse diagrams are drawings of posets (partially ordered sets).

Basic Usage

To create a Hasse diagram for a Poset and draw it on the screen, do this:

julia> using Posets, HasseDiagrams

julia> p = subset_lattice(3)
{8, 19} Int64 poset

julia> h = HasseDiagram(p)
Hasse diagram of a {8, 19} Int64 poset

julia> draw(h)

Note that h contains a copy of p, so subsequent changes to p are not reflected in h.

Creating a Layout

When a Hasse diagram is created, it is given a default layout. Hasse diagrams can be given an alternative layout with the function set_xy!. There are two forms:

• set_xy!(h, method) uses the function method to compute the layout. The function acts on the posets held inside h. The list of available layout methods is in the next section.
• set_xy!(h, xy) uses the dictionary xy to site the vertices. Vertex v is placed at xy[v]. If v is not a key of xy, then its location is unchanged.

Scaling

The function scale!(p,μ) multiplies all coordinates in the embedding by μ. It is likely more useful just to multiply the x- or y-coordinates; to do so, use scalex! or scaley!, respecitvely.

Layout Methods

• basic_layout places vertices vertically based on their rank and, within each rank, the horizontal placement is evenly spaced.
• dim2_layout is a decent layout function that is applicable to posets whose dimension is at most two. Reasonbly quick. If the poset has dimension greater than two, a reasonable alternative is presented.
• layered_layout is a Sugiyaqma style layout from the LayeredLayouts module. Can be slow.
• force_layout is an experimental layout method in which edges of the cover graph act like springs, all vertices repel each other, and levels are determined by dual_ranking.

Layout Examples

Results for a randomly generated two-dimensional poset:

Properties

Font size

• Use set_font_size!(h, sz) to set labels to be sz points. Use 0 to hide labels. Default is FONT_SIZE = 10.
• Use get_font_size(h) to determine the current font size for h.

Node radius

• Use set_radius!(h, r) to set the size of the circles that represent the elements of the poset. Default is RADIUS = 12.
• Use get_radius(h) to determine the current radius.

Fill color

• Use set_fill_color!(h, c) to set the fill color for the circles to c. Default is FILL_COLOR = :white. All circles are filled with the same color.
• Use get_fill_color(h) to determine the current color.

Example

Here is an example for drawing (small) subset lattices with sensible labels. Here is the function to produce the picture:

using Posets, HasseDiagrams, SimpleDrawing, ShowSet

function draw_bool(k)
    p = subset_lattice(k)
    h = HasseDiagram(p)
    labs = Dict{Int,String}()
    for v in 1:nv(p)
        labs[v] = string(subset_decode(v))
    end
    set_labels!(h, labs)
    set_font_size!(h, 8)
    set_radius!(h, 30)
    set_fill_color!(h, :lightblue)
    set_xy!(h, layered_layout)
    draw(h)
    expand_canvas()  # from SimpleDrawing
end

Here is the result of draw_bool(4):

Extra Control: Drawing Objects

Much greater control of the appearance of a HasseDiagram can be achieved using the make_objects function. The input to make_objects is a HasseDiagram and the output is a list of Segment and Point objects from SimpleDrawingObjects. This list begins with Segment objects representing the edges of the HasseDiagram following by Point objects representing the vertices. This allows the user to specify various attributes for the objects. For example, this would enable changing the colors of selected vertices (as opposed to using set_fill_color! which sets all vertices to the same color).

Note that modifying the objects in the output of make_objects(h) does not modify h or its attributes. It simply gives a list of objects that can be individually modified.