hasse.Hasse

class rewalt.hasse.Hasse(ogp)

Bases: object

Class for “oriented Hasse diagrams” of oriented graded posets.

The oriented Hasse diagram is stored as a NetworkX directed graph whose nodes are the elements of the oriented graded poset.

The orientation information is encoded by having edges corresponding to input faces point from the face, and edges corresponding to output faces point towards the face. To recover the underlying poset’s Hasse diagram, it suffices to reverse the edges that point from an element of higher dimension.

Objects of the class can also store labels for nodes of the Hasse diagram, for example the images of the corresponding elements through a map or a diagram.

The class also has a method draw() that outputs a visualisation of the Hasse diagram. This works with any drawing.DrawBackend; currently available are

  • a Matplotlib backend, and

  • a TikZ backend.

Parameters

ogp (ogposets.OgPoset | ogposets.OgMap | diagrams.Diagram) – The oriented graded poset, or a map of oriented graded posets, or a diagram.

Notes

If given a map of oriented graded posets (or shapes), produces the Hasse diagram of its source, with nodes labelled with the images of elements through the map.

If given a diagram, produces the Hasse diagram of its shape, with nodes labelled with the images of elements through the diagram.

Methods

draw(**params)

Outputs a visualisation of the Hasse diagram, using a backend.

place_nodes()

Places the nodes of the Hasse diagram on the unit square canvas, and returns their coordinates.

Attributes

diagram

Returns the oriented Hasse diagram as a NetworkX graph.

labels

Returns the labels of nodes of the Hasse diagram, in the same format as ogposets.OgMap.mapping().

nodes

Returns the set of nodes of the Hasse diagram, that is, the graded set of elements of the oriented graded poset it encodes.
property nodes

Returns the set of nodes of the Hasse diagram, that is, the graded set of elements of the oriented graded poset it encodes.

Returns

nodes – The set of nodes of the Hasse diagram.

Return type

ogposets.GrSet

property diagram

Returns the oriented Hasse diagram as a NetworkX graph.

Returns

diagram – The oriented Hasse diagram.

Return type

networkx.DiGraph

property labels

Returns the labels of nodes of the Hasse diagram, in the same format as ogposets.OgMap.mapping().

Returns

labels – The labels of the Hasse diagram.

Return type

list[list]

place_nodes()

Places the nodes of the Hasse diagram on the unit square canvas, and returns their coordinates.

The nodes are placed on different heights according to the dimension of the element their correspond to. Elements of the same dimension are then placed at different widths in order of position.

The coordinates are returned as a dictionary whose keys are the elements corresponding to nodes of the diagram.

Returns

coordinates – The coordinates assigned to nodes.

Return type

dict[tuple[float]]

draw(**params)

Outputs a visualisation of the Hasse diagram, using a backend.

Currently supported are a Matplotlib backend and a TikZ backend; in both cases it is possible to show the output (as a pop-up window for Matplotlib, or as code for TikZ) or save to file.

Various customisation options are available, including different orientations and colours.

Keyword Arguments

  • tikz (bool) – Whether to output TikZ code (default is False).

  • show (bool) – Whether to show the output (default is True).

  • path (str) – Path where to save the output (default is None).

  • orientation (str) – Orientation of the Hasse diagram: one of 'bt' (bottom-to-top), 'lr' (left-to-right), 'tb' (top-to-bottom), 'rl' (right-to-left) (default is 'bt').

  • bgcolor (multiple types) – The background colour (default is 'white').

  • fgcolor (multiple types) – The foreground colour, given by default to nodes and labels (default is 'black').

  • labels (bool) – Whether to display node labels (default is True).

  • inputcolor (multiple types) – The colour of edges corresponding to input faces (default is 'magenta').

  • outputcolor (multiple types) – The colour of edges corresponding to output faces (default is 'blue').

  • xscale (float) – (TikZ only) Scale factor to apply to x axis in output (default is based on the dimension and maximal number of elements in one dimension).

  • yscale (float) – (TikZ only) Scale factor to apply to y axis in output (default is based on the dimension and maximal number of elements in one dimension).