From 3e0dbddabde769e0020c426807048757c10f8fbf Mon Sep 17 00:00:00 2001 From: Maria Marchwicka Date: Wed, 10 Oct 2018 15:35:12 +0200 Subject: [PATCH] meaning of -1 in output file --- README.md | 14 +++----------- 1 file changed, 3 insertions(+), 11 deletions(-) diff --git a/README.md b/README.md index e968542..4b1df16 100644 --- a/README.md +++ b/README.md @@ -2,27 +2,19 @@ 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*). - - +- Naik's homological criterion (in two steps - called in the script and the following description as Naik's 1 and Naik's 2), +- criterion introduced in Theorem 1.4. in above mentioned paper (called *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. - ----- @@ -50,7 +42,7 @@ 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. +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 1, Naik's 2, Borodzik's, Przytycki's. `0` means that results excluded periodicity. As computations of the 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 a criterion doesn't exclude periodicity, but it wasn't applicable (like Przytycki's criterion) or that the testing algorithm met an empty list of arguments to be verified (Naik's 2 and Borodzik's criteria). Przytycki's criterion in general is not applicable for non-prime periods, but the corresponding result is set to be `-1` also if no HOMFLYPT polynomial could be found (nigher in an input file nor by using `libhomfly` module).