# Welcome to Topoly¶

Topoly is a **Python** package that collects programs useful for
**polymer topology** analysis. We wanted to make it simple in use, but powerful
at the same time.

We provide twofold tutorial for our package. In the first part all functions are briefly presented with explanation of idea how do they work. The second part is topoly_tutorial package with examples of Topoly package usage.

## What you can do with Topoly?¶

Find knots, links, lassos, theta-curves, handcuffs and their type.

Calculate knot/link invariants:

Polynomials: Alexander, Jones, Conway, HOMFLY, Yamada, Kauffman, BLM/Ho,

Brackets: Kauffman, APS,

Other: writhe, Gaussian linking number.

Find minimal surface of a loop.

Simplify polymer structure preserving its topology.

Generate random polygon structures: walks, loops, lassos, handcuffs.

Generate knot map (like in KnotProt).

Calculate sum (U) and product (#) of knots.

Visualize structures.

## Page contents¶

- Getting started
- Topoly requirements
- Package structure
- Tutorial
- Accepted structures
- Knot, link, theta-curve and handcuff type identification (invariants calculation)
- Calculating invariants of conjoined structures
- Gaussian Linking Number calculation (GLN)
- Lasso type identification (minimal surface calculation)
- Random polygons generation
- Visualization
- Finding loops, theta-curves and handcuffs in structure
- Matrix functions
- Data manipulation

- Dictionary
- Documentation
- Knot, link, theta-curve and handcuff type indentification (invariants calculation)
- Calculating invariants of conjoined structures
- Lasso type indentification (minimal surface calculation)
- Finding loops, theta-curves and handcuffs in structure
- Random polygons generation
- Knot map manipulating functions
- Visualization
- Data manipulation
- Parameters for various functions (topoly.params)

- Topoly License
- How to cite Topoly

# Indices and tables¶

# Contact¶

All questions and remarks should be addressed to Joanna Sułkowska (jsulkowska AT cent.uw.edu.pl)