jmhbrown/quantum-a-polynomial

quantum-A-polynomial

These notebooks were written for SageMath 9.5 and Python 3.

It uses SnapPy to provide triangulations of knot complements. this can be installed with the following terminal command:

sage -pip install --upgrade --user snappy

Usage

Use sage wrapper.sage to run the computations from the command line. More usage details can be had using sage wrapper.sage -h.

See example_input.json for an example on how to configure the runs.

To launch the notebooks run the command jupyter-notebook in the root directory of this project.

This project uses the Intitialization cells extension, so that some cells run automatically when you open the notebook. If the initialization cells are not indicated (in the upper right corner of each cell) when you open the notebook, you might need to change the default view in View > Cell Toolbar > Initialization Cell. To re-run initialization cells, click the little calculator icon in the header.

quantum-a-polynomial's Issues

Check that the relations matrix is being used correctly, i.e. that I'm dividing the q-power by 2 whenever I'm using the matrix to convert between normal form and products.

Wrong Signs

I'm getting the wrong signs and sometimes worse. Here are things to try:

• Compare triangulations that have different outputs based on whether qrt2 is sent to +1 or -1
• Look at ratios of long edges instead of the automatically constructed extra generators.
• #2

Ideal Elimination:

• Figure out if restricting from laurent polynomials to just polynomials causes trouble with variable elimination.
• Try the elimination step by hand.