First version of README.md, input file with HOMFLYPT polynomials added

README.md

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+# A Sage script to verify periodicity
+
+This repository contains a SageMath script used for computations in [Finite orthogonal groups and periodicity of links](https://arxiv.org/abs/1810.03881v1).
+
+
+
+-----
+
+
+The following criteria for knots periodicity were implemented:
+
+- Przytycki's criterion for HOMFLYPT polynomials,
+- Murasugi's criterion,
+- Naik's homological criterion,
+- criterion introduced in Theorem 1.4. in above mentioned paper (called in the script and the following description *Borodzik's criterion*).
+
+
+
+-----
+
+
+
+For a given list of knots [encoded in PD-code](http://katlas.org/wiki/Planar_Diagrams) (an input file is required) the script generates output with results for each criterion.
+
+
+-----
+
+
+We tested all knots up to 15 crossings and for periods 3, 5, 7, 9, 11, 13.
+
+## Running the script
+
+
+### Prerequisites
+
+- [SageMath 8.1](http://www.sagemath.org).
+
+- For Przytycki's criterion the module [libhomfly](https://github.com/miguelmarco/libhomfly/blob/master/README.md) is needed to calculate HOMFLYPT polynomial. There is also possibility to read saved polynomials from a file (file `homflypt.input` in the repository contains HOMFLYPTY polynomials for some knots).
+
+
+
+### Input data
+
+Files with PD-codes for all knots up to 15 crossing are available in the repository (`knots_11_15.txt` and `knots_3_10.txt`) and should be saved in the same folder as the script or a path in the `class MySettings` should be adjusted. Similarly, if other input files will be used, settings have to be changed. A correction in parsing or reading functions may be also necessary (`check_11_to_15()`, `check_up_to_10()`, `parse_pd_code()`, `parse_knot_name()`).
+
+
+### Running in terminal
+
+The script should be run in terminal: `sage periodicity.sage`.
+
+### Results
+
+All results will be saved in a file `results.out`. A line, for example `12a100,3,1,1,1,0,1`, should be read as follow. A knot 12a100 in tests for a period equal 3 (second position) gives results saved in five numbers: `1,1,1,0,1`, which correspond to criteria: Murasugi's, Naik's - part 1, Naik's - part 2, Borodzik's, Przytycki's. Only `0` means that results excluded periodicity. As computations of first 4 numbers depend on previous results, ones zero occurs, the following criteria will be skipped. The Przytycki's criterion is calculated independently of the others. `-1` means that criterion doesn't exclude periodicity, but the criterion wasn't applicable or that the testing algorithm met an empty list of arguments to be verified.
+
+
+
+
+## Authors
+
+* **Maria Marchwicka**
+* **Wojciech Politarczyk**
+
+## License
+
+This project is licensed under the GNU General Public License - see the [LICENSE.md](LICENSE.md) file for details.