A tool for computing the combinatorics of marked cycle curves over dynamical moduli spaces.

Installing and Running

0. Ensure that you have Rust installed. You can install Rust via e.g. Rustup: curl --proto '=https' --tlsv1.2 -sSf https://sh.rustup.rs | sh

1. Compile the repository: cargo build --release && cd target/release

2. Run the binary, e.g. ./marked-cycles --crit-period 2 --marked-period 6

Options

The following command line arguments can be passed to marked-cycles:

• -m, --marked-period <MARKED_PERIOD>: Period of the marked cycle (0 to skip) [default: 0]
• -c, --crit-period <CRIT_PERIOD>: Period of the critical cycle. Must be 1 or 2. --crit-period 1 will produce a cell structure over the family $f_c(z) = z^2+c$, while --crit-period 2 will produce a cover over the family $f_c(z) = \frac{z^2+c}{z^2-1}$. Default: 1.
• -t, --table-max-period <TABLE_MAX_PERIOD>: If a nonzero value n is specified, this prints a data table describing the combinatorics of the curve over crit-period of each period from 2 through n. [default: 0]
• -d, --dynatomic: Compute cell structure for dynatomic curve instead of marked cycle curve
• -b, --binary: Display cell ids in binary.
• -indent <INDENT>: How far to indent the cell descriptions [default: 4]
• -h, --help: Print help

These options are also available via ./marked-cycles --help.