P≷OSET Editor

partially (re)ordered set editor v1.0

Import
n =

Edit
Cardinality:
Canvas size:
up to
Permutation:
Links:
Removed links:

Export

LaTeX macros

To use the diagram in a LaTeX document (in math or text mode), load the package 'causets' with \usepackage{causets} and use one of the following macros.

Matrices

Help

Steps to create a diagram of a poset

  1. Generate a predefined poset with the desired cardinality — or add/remove elements to/from some imported poset to get the desired number of elements.
  2. Auto-link the elements with the button ⟐ if the imported poset was higher dimensional (otherwise the button is disabled).
  3. Rearrange the elements until (almost) all of the automatic links coincide with the links of the desired diagram.
  4. Shuffle the elements to see if there is another similar configuration where all links are already matched by the auto-links.
  5. Remove unwanted links. This is only necessary if the dimension of the poset is more than 2 — or if it is a causal set that cannot be embedded in (1+1)-dimensional Minkowski spacetime.
  6. Lastly if required, add new links to your diagram. Again this step is not necessary for 2-dimensional posets.
All these actions can be done with the toolbar and by using a mouse/touchpad or keyboard.

Import options

You can import or generate a diagram from any of the following input types. Note that the number of elements of a diagram is limited.

predefined type
Select a predefined type and the cardinality (or order). The numeric input for n is bounded from above, but a larger value could be entered via keyboard.
permutation (for a 2D-order)
Enter a permutation of consecutive integers as a comma-separated list.
permutation and list of removed links
Additionally to a permutation, enter a comma-separated list of link pairs in the format 'number/number' to be excluded when drawing the automatic links from the permutation.
permutation and list of links
The permutation is only used to position the elements. A comma-separated list of link pairs (in the format 'number/number') is used to draw links between the elements.
LaTeX macro
Paste a LaTeX macro \pcauset, \rcauset, or \causet followed by (an optional argument enclosed in square brackets [] and) one or two arguments for the permutation and links enclosed in braces {}.

Toolbar functions

Above the canvas:

⌶
Copy the poset back to the input and revise manually.
↶
Undo the last actions if it was one of the following: generate, move/remove/add element, remove/add link.
↷
Redo the last actions if it was one of the following: generate, move/remove/add element, remove/add link.
⇄
Mirror the diagram horizontally, which yields an equivalent diagram.
⇅
Mirror the diagram vertically, which yields a diagram of the opposite poset.
⎐
Increase all element labels by 1.
⎏
Decrease all element labels by 1.
✕
Delete the selected element.
⩒
Link/unlink the selected elements.
⟐
Reset all links to the automatic links (the links of the underlying 2D-order).
Below the canvas:
Labels
Show/hide the element labels.
Cross
Show/hide the selection cross.
Grid
Show/hide the element grid.
Canvas size
Set the relative canvas size as percentage of the page width. Use 'fill' to size the canvas to the maximal value.
up to
Set the maximal canvas size. Use 'unbounded' to resize the canvas to the relative size. If 'fill' and 'unbounded' is selected, the canvas is sized to 100% of the page width.
⏍
Copy the value of a text field to the clipboard.

Mouse and touchscreen functions

Click on an element (highlighted with a red mark on hover) to select it. If another element is already selected, clicking on a succeeding element that can be linked (connected by an edge) in the diagram, the (possible) link will be selected.
Click along the row/column going in 45 degree angles away from the selected element to move it there.
Click on an empty area to unselect.
Double click on an element to replace it by a 2-antichain.
Double click on an element while holding the shift key to replace it by a 2-chain.

Keyboard functions

W
Select the next element in north-west direction.
A
Select the next element in south-east direction.
S
Select the next element in south-west direction.
D
Select the next element in north-east direction.
⇧ W
Move the selected element in north-west direction.
⇧ A
Move the selected element in south-east direction.
⇧ S
Move the selected element in south-west direction.
⇧ D
Move the selected element in north-east direction.
Del
Delete the selected element.
.
Add a new element to the right of the diagram and select it.

About

The purpose of this editor is the visualisation of finite partially ordered sets (posets) with Hasse diagrams. Its development started from a research project and it uses the same principle as the LaTeX package causets. This editor shall serve as a tool to help drawing diagrams with the package, while the package offers many more options to draw, style and modify Hasse diagrams. More information are given in the package manual.

Disclaimer

This web tool has been tested, but I do not take responsibility for incorrectly represented data.

Report a problem or make a suggestion: Please send me a comprehensive problem description and information of your browser (name and version) if you encounter an error. I also welcome any suggestions to improve the tool. My contact details are on my main page.