Python Knot package: pythonknot

Python Knot is a Python package for creating and manipulating knots and links. It is based on the KnotTheory package for Mathematica.

1.Installation

only support python 3.8 or later pip install pythonknot

2.Features

1. Create and manipulate knots and links.
2. Compute invariants of knots and links.
3. Visualize knots and links.

3.Usage

import pythonknot.alexander_poly as alexander_poly
print(dir(alexander_poly))

positions = alexander_poly.read_xyz("test/traj_knot31_L300_close.txt")
print(positions.shape)
# calculate the knot type for ring polymer
knottype = alexander_poly.calculate_knot_type(positions, "ring")
print(len(knottype))    

# calculate the knot type for open polymer
knottype = alexander_poly.calculate_knot_type(positions, "open")


## calculate the knot size for ring polymer
knottype, knotsize = alexander_poly.calculate_knot_size(positions[1:100], "ring")

print(knottype)
print(knotsize)

# open chain 
positions = alexander_poly.read_xyz("test/traj_knot31_L300_open.txt")
print(positions.shape)
knottype, knotsize = alexander_poly.calculate_knot_size(positions, "open")
print(knottype)
print(knotsize)

3.1 HOMFLY polynomial

# read traj
import pythonknot.alexander_poly as alexander_poly
positions = alexander_poly.read_xyz("traj_knot31_L300_close.txt")
print(positions.shape)

import pythonknot.homfly as homfly
crossing_number, homflr_poly = homfly.homfly_str(positions[0])  # position should be N_atom*3 array

3.2 pdb parser

load pdb trajectory, return the position of the atoms in the pdb file

import pythonknot.pdb_parser as pdb_parser

import pythonknot.pdb_parser as pdb_parser

mypdb = pdb_parser.PDBParser()
mypdb.load('output.pdb')

traj = mypdb.get_all_frame_coordinates()    # with shape (N_frame, N_atom, 3)
print(traj.shape)

Development

KMT algorithm, simplify the configuration of the polymer chain, return the simplified chain and the knot type of the chain

#position should be a 2D array, the first dimension is the number of beads, the second dimension is the x, y, z coordinates
simplified_knot = alexander_poly.KMT_chain(positions, "open")

# if you have ring polymer, you can use the following code
simplified_knot = alexander_poly.KMT_chain(positions, "ring")

Extented gauss notation,

# default for open chain
gauss_notation = alexander_poly.gauss_notation(simplified_knot)

# if you have ring polymer, you can use the following code, add the first point to the end of the chain
simplified_knot = np.vstack((simplified_knot, simplified_knot[0]))
gauss_notation = alexander_poly.gauss_notation(simplified_knot)

TODO list

add other method of open chain knot type calculation, KMT after adding the tail add write_xyz function to save the xyz file, modify with append mode