Planalg

This is a Mathematica package for working with planar algebras and categories.

To use: either

• open Planalg/Planalg.wl in Mathematica and click Run All Code

or either

• copy the Planalg directory to $UserBaseDirectory/Applications

• or add the following line to your $UserBaseDirectory/Kernel/init.m file:

    PrependTo[$Path, "a directory that contains the Planalg directory"]

Then, evaluate <<Planalg` in Mathematica to load the application.

Example

Calculate the determinant of the Gram matrix for the chromatic algebra on three strands:

basis = FlowMakeBasis[Q, 3, 3, Virtual -> False];
gram = MakeGramian[basis];
Det[gram] // Factor

Calculate using an unnormalized trace

TableForm@
 Table[Gramian[FlowMakeBasis[Q, n, 0, Virtual -> True], 
         Trace -> (PTr[#, Normalized -> False] &)] // Det // Factor,
       {n, 2, 6}]