P≷OSET Editor
partially (re)ordered set editor v1.0
This editor uses JavaScript. Please activated it.
Import
Edit
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
Note that most posets do not have a unique diagram. The best
diagrams are obtained by having as few manually added links and "removed
links" as possible. For example, if the poset is 2-dimensional, there exists
a diagram with no "removed links". All posets with up to 5 elements and all
but 3 posets with 6 elements are 2-dimensional.
Steps to create a diagram of a poset
-
Generate a predefined poset with the desired cardinality — or
add/remove elements to/from some imported poset to get the desired
number of elements.
-
Auto-link the elements with the button ⟐ if the imported poset
was higher dimensional (otherwise the button is disabled).
-
Rearrange the elements until (almost) all of the automatic links
coincide with the links of the desired diagram.
-
Shuffle the elements to see if there is another similar configuration
where all links are already matched by the auto-links.
-
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.
-
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 {}
.
order matrix
Paste a causal matrix, where each row is a comma-separated list of
values 0 and 1, and the rows are separeted by a line break.
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.
© Copyright 2024, Christoph Minz.
PrOSET editor version v1.0 (revision 2024-08-10).
Styled with Bootstrap.
Hosted by GitHub Pages.
Go to the page impressum.