XAct.jl

Project Profile for AI Agents (LLM TL;DR)

Name: XAct.jl (Repository: XAct.jl)
Primary language: Julia
Purpose: Symbolic tensor algebra and curvature calculus for general relativity
Python package: xact-py (import as xact)
Verification: Oracle-based parity tests via sxact
License: GNU General Public License v3.0 (GPL-3.0)

XAct.jl is the native Julia port of the Wolfram xAct suite. Start here if you want the project overview, the newcomer path, and the map of names used across the repository, Julia package, Python package, and verification tooling.

Start with the canonical newcomer path

Choose one path and follow it in order:

Installation — set up Julia, Python, or the verification stack
Getting Started — run the first working Julia or Python examples
Typed Expressions (TExpr) — learn the recommended expression API
Basics tutorial or notebooks — continue with guided practice

Use the page that matches your goal

Goal	Go to
Install the project	Installation
Run the first working examples	Getting Started
Learn the typed expression API	Typed Expressions (TExpr)
Work through a guided Julia tutorial	Basics tutorial
Migrate existing Wolfram workflows	Wolfram Migration Guide
Look up Wolfram-to-Julia mappings	Wolfram Translation Reference
Understand the package and module names	Naming and product map
Inspect API details	Reference

Understand the project naming

Name	Kind	Meaning
`XAct.jl`	Repository	The Git repository you clone and browse
`XAct.jl` / `XAct`	Julia package and module	The native Julia tensor algebra engine
`xact-py`	Python package	The distribution published to PyPI
`xact`	Python import	The Python API imported in user code
`sxact`	Verification framework	The Python tooling for oracle-based parity tests

Know what the project contains

The project has two user-facing layers:

XAct.jl — the Julia computational engine for canonicalization, contraction, covariant derivatives, perturbation theory, coordinate components, and invariants.
xact-py / xact — the Python wrapper around the Julia core.

It also has one project-facing support layer:

sxact — the verification framework used to compare results against Wolfram Engine snapshots.

Try the Julia fast track

If you already have Julia installed, this is the shortest successful session:

using XAct

reset_state!()
def_manifold!(:M, 4, [:a, :b, :c, :d])
def_tensor!(:T, ["-a", "-b"], :M; symmetry_str="Symmetric[{-a,-b}]")

@indices M a b c d
T_h = tensor(:T)

ToCanonical(T_h[-b,-a] - T_h[-a,-b])

The typed API validates index usage before evaluation. For the full typed-expression model, continue to Typed Expressions (TExpr).

Continue based on where you are coming from

New to the project: start with Installation, then Getting Started
Already using Wolfram xAct: use the Wolfram Migration Guide
Looking for API facts: go to the Julia API or Python API
Evaluating implementation status: read the Feature Matrix

Troubleshooting the first page mismatch

Situation	Best page
“I need commands, not overview.”	Installation or Getting Started
“I need Wolfram mappings, not onboarding.”	Wolfram Translation Reference
“I need the typed API details.”	Typed Expressions (TExpr)
“I need package naming clarified.”	Naming and product map

Project note

Most of the codebase was developed with AI assistance and then checked by humans and by oracle-backed verification. The mathematical trust story depends on both implementation review and parity testing.