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Script to draw quivers from matrix representations
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qvdraw

README.md

qvdraw utils

This repo provides a number of tools and utilities for drawing quivers, exchange graphs and other cluster objects. The main tools included are:

  • qvdraw - A bash script to draw a picture representation of a quiver.

  • qv2tex - A program to compute exchange graphs and output a LaTeX file which uses Tikz to draw the graph

  • qv*2gml - A program to convert various objects into a gml representation.

qvdraw

Draws quivers from the matrix representation.

Usage

qvdraw [-nh] [-o "opts"] [filename]
Input

filename should be the name of a file which contains a number of matrix representations of quivers (see Matrix format). If the files contains anything else then it could cause errors.

If no filename is specified then the script assumes the input will be stdin. This allows other programs to pipe into qvdraw.

  • -n supresses the direction of arrows. If this option is not specified then all arrows are directed, if -n is specified then the edges in the quiver will not be directed.

  • -h show usage.

  • -o "options" passes any options to the gml2pic program. Examples include -width pixels and -pic filetype. See the gml2pic usage docs to see all options.

Output

For each line in filename, a picture of the quiver will be created in the current working directory. These will always be named 1.png, 2.png etc. There is currently no detection of whether files with these names already exists, so any such files will be overwritten.

Structure

qvdraw is a bash script which uses three programs:

  • qv2gml
  • gmlayout
  • gml2pic

The first two are included in this repo, while gml2pic can be found on the OGDF website.

qv2tex

qv2tex outputs LaTeX code to generate pictures of various cluster objects.

Usage
qv2tex -lr [-n number] [-q|m|g|e|c quiver]
Takes a qv matrix and outputs the TeX to draw the quiver.
   -q Draw a single quiver
   -m Draw the move graph of a quiver
   -g Draw the quiver graph of a quiver
   -e Draw the exchange graph of a quiver with cluster (x1 ... )
   -c Draw the quasi-Cartan companion exchange graph
   -l Draw the labelled exchange/quiver graph
   -n Limit the number of seeds computed to given number
   -r Don't compute mutations which do not lead to green sequences

The main options are -q, -m, -g, -e, -c which specify what type of graph the program should output. Each of these options should be followied by a matrix representing a quiver, as described in Matrix format:

  • -q Outputs a single quiver, provided as a matrix.
  • -m Draws the minimal mutation-infinite move graph of the MMI quiver.
  • -g Draws the quiver exchange graph of the provided quiver.
  • -e Draws the exchange graph, with initial quiver given by (x1, ...). This graph will be the slowest to compute, especially as the number of vertices increases, as the symbolic manipulation is not very fast.
  • -c Draws the quiver exchange graph, but each quiver is decorated with the fully-compatible quasi-Cartan companion. The graph will stop at a vertex if the mutated quasi-Cartan is no longer fully-compatible.

The -l option can be added to the -g and -e options to specify that the graph should be the labelled version, where each vertex is a labelled quiver or seed and not considered up to permutations.

The -n option can be used to specify a maximum number of vertices to compute. This allows the user to draw a section of an infinite graph, or stop after a certain time if the computations are taking too long.

The -r option is not fully implemented, but tries to construct exchange graphs which contain only those mutations which could apear in a maximal green sequence. Currently this only prevents mutations at the source of a multiple arrow.

Matrix format

The matrix format expected is consistent with that used in the libqv library. This allows any output from qv* programs to be used as input to qvdraw.

{ { a b c } { d e f } { g h i } }
  • The matrix starts and ends with curly braces. { matrix }
  • Each row of the matrix is contained in curly braces. { row entries }
  • Each entry must be separated by a space.

If the input is not in this form, the chances are the program will throw an exception.

Build

Run make to compile all utilities.

The qvdraw script requires the three programs specified above and so either keep the programs in the same folder, or ensure they are included in your path.

Dependencies

qv2gml and gmlayout require the following libraries and their headers to be installed and accessible by the compiler:

qv2tex also requires:

The Makefile can be modified to include the install locations of these libraries, by changing the INCLUDES and LFLAGS variables.

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