HEISENBERG PATH GRAPHER
Created in collaboration with Anschel Schaffer-Cohen.

This program graphs lifts of planar paths in the continuous Heisenberg group $H(\mathbb{R})$.
Paths must be written in the generators (i.e. of the form $a^{n_1} b^{n_2} a^{n_3} \ldots$), and may be entered in one of two forms:

• As a string in the generators $\{a, b, A,B\}^*$ in quotes, ex: "abAB". 
• As a bracketed set of bracketed syllables with the generator in single quotes ex: [['a',1], ['b', 1], ['A', 1], ['B', 1]]
  

strings in the generators is useful for considering words in the discrete Heisenberg group $H(\mathbb{Z}) < H(\mathbb{R})$ whereas bracketed-syllables is helpful for paths that do not move along the lattice.  In addition to graphing the lift, the program will output the endpoint and path length in the Carnot-Carathéodory metric given by the $L^1$ norm.