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ext-rs

ext

ext-rs is a collection of libraries for doing homological algebra over Fp. The main and original purpose is to compute Ext of a Steenrod module, but the library is written to be sufficiently generic to deal with more general applications.

The library also comes with a number of "example" binaries that use the library for various purposes. These can be used directly to perform specific computations, or act as actual examples for how to use the library.

Since ext-rs is based on Rust, one must install Rust before using this library.

Quickstart

Installing sseq

  1. Install Git (if not already installed)

    • On Windows: Install Git for Windows
    • On macOS: git will be installed automatically when you type a git command in the terminal
    • On Linux: use your package manager

  2. Install Rust (if not already installed) Install Rust via rustup: download the installer here. Run the installer and accept the defaults.

  3. Clone the repository

    • Open a new terminal. (On windows: hit Windows + r, type cmd, and hit enter to get a command prompt.)
    • Type git clone --depth 1 https://github.com/SpectralSequences/sseq and hit enter.

  4. Navigate to the project folder
    In your terminal type cd sseq/ext and hit enter.

  5. Now you're ready to run the example in the "First usage" section.

    Troubleshooting:

    • If you get a command not found error when running a cargo command, make sure you're using a new terminal window (not the one you used to install rust).
    • If it says that Cargo.toml is not found, then you may have skipped Step 4.

First usage: how to compute the Adams E2 term

To produce an svg chart of the stable Adams spectral sequence E2 term for a given module, run:

cargo run --example chart

On your first run, you can just accept the defaults (the 2-primary sphere in a modest range of degrees) by pressing enter. Other preset Steenrod modules can be found in the ext/steenrod_modules/ directory; enter their name (e.g. C2) in the first prompt. If the module you want is not in this list, read the file ext/MODULE-SPEC.md in this repository which explains how to construct your own.

More essential end-user documentation, such as command-line options that will speed up runtimes, can be found at https://spectralsequences.github.io/sseq/docs/ext/.

Notable functionality

In addition to the standard Ext, more runnable code can be found in ext/examples. All of the "examples" can be run in a similar way as chart. In particular, we highlight the following notable functionality:

  • Ext over the odd-primary Steenrod algebra (start by using the module S_3 for the 3-primary sphere in the chart example above)
  • Adams d2's via the secondary Steenrod algebra (see the secondary example)
  • Massey products (see the massey example)
  • Unstable Adams E2 term for spheres (see the unstable_chart example)

Library documentation

Documentation for both the examples and the library itself is hosted at https://spectralsequences.github.io/sseq/docs/ext/.

If documentation for a specific version of the library is sought, it can be generated by running

make docs

after which the documentation is placed at target/doc/. The link above opens the file target/doc/ext/index.html.

Development

Linting

Lint scripts can be run with

make lint

This runs clippy and rustfmt.

Tests

There are multiple types of tests

Unit tests, doc tests and integration tests

These can be run by

make test

Example benchmarks

In the examples/benchmarks/ folder, we have some benchmarks to test the examples against. In each file, the first row specifies the argument to run (the arguments after cargo run --example), and the rest of the file is what the output should be.

These can be run by

make benchmarks
make benchmarks-concurrent

Running

make fix-benchmarks

updates the outputs in all benchmark files to match the current program output. This is useful for adding new benchmarks.

These can be run for individual benchmarks by e.g.

make examples/benchmarks/resolve-S_2
make examples/benchmarks/resolve-S_2-concurrent
make examples/benchmarks/resolve-S_2-fixed