description | A very basic tool to visualize cluster algebras with ncurses |
owner | sgilles@math.umd.edu |
last change | Wed, 1 Jun 2016 15:27:18 +0000 (1 11:27 -0400) |
URL | git://repo.or.cz/cluster-algebra-visualize.git |
| https://repo.or.cz/cluster-algebra-visualize.git |
push URL | ssh://repo.or.cz/cluster-algebra-visualize.git |
| https://repo.or.cz/cluster-algebra-visualize.git (learn more) |
bundle info | cluster-algebra-visualize.git downloadable bundles |
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README
This is a very basic tool to visualize cluster algebras, as described
by e.g. Marsh in [1]. I'll not go over the theory here.
The easiest way to see how this works is to run
./cluster-algebra-visualize 7_a.txt
which shows one pair of faces of a n=7 simplex fitted with the quiver
described in [2]. To perform the flip described in [2], we can mutate
as follows:
m 10 4 0 2 a 1a
m 11 5 1 9 19 23 f 3 b 1b
m 12 6 8 18 4 0 2 a 22 e c 1c
m 13 7 17 5 1 9 f 3 b 21 d 1d
m 14 16 6 8 0 2 e c 20 1e
m 15 7 1 3 d 1f
And the result is, as predicted, the quiver which would be attached to
the opposite pair of faces (7_b.txt).
Caveats:
o No good error handling at all.
o The display is a haphazard mixture of unicode and ASCII (you'll
see what that means). I completely blame the current state of
monospaced unicode-aware fonts at the moment, which render unicode
arrows as double-width in contradiction to wcwidth(3). Unicode
arrows are therefore unsuitable for extensive use in a TUI at the
moment.
o Arrows with multiplicity greater than 1 are not obvious: they are
simply drawn in reverse. There is no way to see what the
multiplicity is.
o Arrows which overlap other arrows are not drawn intelligently. It
may be difficult to find out where an arrow starts or ends.
o Points are labelled in hexadecimal, so when more than 16 points
are onscreen, during point selection the labels might overwrite
other data.
o To delete an arrow, add another arrow going the other way.
o I wrote this over the course of a weekend and never really
expected anyone else to use it. This documentation is mostly for
my own sake.
References:
[1] Robert Marsh, Lecture notes on cluster algebras, European
Mathematical Society, Zürich, 2013.
[2] Vladimir Fock and Alexander Goncharov, Moduli spaces of local
systems and higher Teichmüller theory, Publications Mathématiques
de l’Institut des Hautes Études Scientifiques 103, no. 1, 1–211,
DOI 10.1007/s10240-006-0039-4. Preprint at
<http://arxiv.org/abs/math/0311149v4>