cluster-algebra 0.1.2

calculator for cluster algebras

cluster algebra calculator

This library provides a calculator for cluster algebras. Especially it is useful for calculating algebraic relations and visualizing quivers

requirements

• python >= 3.8
• sympy
• pandas

Installation

pip install cluster_algebra

Usage

from cluster_algebra import *

q = Quiver(vertices=range(14), 
	clusters=[(1, 13), (2, 13), (2, 12), (2, 11), (2, 10), (3, 10), (4, 10), (5, 10), (5, 9), (6, 9), (6, 8)], 
	laminations=[
	# [(0, 8)], 
	# [(4, 12)]
], is_principal=True)

Create a quiver (with vertices from 0 to 13) and make triangulations as clusters. When adding laminations, you can use indices (first 0 means the frozen edge 0-1, second 8 means frozen edge 8-9). If is_principal is True, same number of principal laminations will be added before than you added manually.

After creating a quiver instance, you can

• flip some variables,

q.flip(edge=(3, 10))
# or
q.flip(index=3)

• get exchange matrix,

q.get_exchange_matrix()

• express target variable,

from IPython.display import display, Math

q2 = q.express_target()

for rel in q2.relations:
    display(Math(rel._repr_latex_()))

for rel in q2.expressions:
    display(Math(rel._repr_latex_()))

• plotting polygon with Plotter

from math import pi

p = Plotter()

p.plot_quiver(q, rotation=pi, lamination_label_pos=0.7)