The Principia Machina/Tools/Dedalus

Dedalus: Spectral Solvers for Equations Entered Symbolically

Added to the survey on 2026-10-06 by the Research Toolkit's research pass. The scores below are that pass's assessment from the evidence cited under References, on the survey's four axes and scale; they are not the original survey's (2026-09-26), and no rule of the Principia Machina reads them. See the additions on the front page.

Overview & Architectural Fit

Dedalus solves partial differential equations by spectral methods. Equations and boundary conditions are entered symbolically, close to how they are written on paper; the solution is expanded as $u(x,t)=\sum _n{\hat{u}}_n(t){\varphi }_n(x)$ on Cartesian domains, disks, annuli, spheres and shells, in parallel with MPI. It solves initial-value, boundary-value and eigenvalue problems.

Mathematical Evaluation for TPM

• Lagrangian / Action (2/10): Takes equations, not actions.
• Field / PDE (9/10): Spectrally accurate, with flexible entry of equations.
• Relativity (2/10): Not a relativity code; at most linear equations on a fixed background.
• Quantum / Data (3/10): Can integrate Schrödinger or Gross-Pitaevskii equations; nothing learns from data.

Integration Pipeline

1. Take the Euler-Lagrange field equations derived with SymPy or xAct.
2. Solve them as an initial-value problem.
3. Monitor the Noether charges (energy, momentum, angular momentum): at spectral accuracy, any drift beyond the time-stepping error is a sharp sign of a fault in the derivation or the discretization.
4. Solve the eigenvalue problem $\lambda Mx=Lx$ of the second variation, for the linear stability of an extremum of the action.

Status, Licence and Limits

• Status: Active. Version 3.0.5, 31 January 2026 (PyPI).
• Licence: GPL-3.0.
• Home: https://dedalus-project.org
• Limits: Domains are limited to geometries a spectral basis can represent. Shocks and non-smooth solutions fit poorly. The GPL may matter for redistribution.

On the Principia Machina

A tool runs only where the sponsor installed and bound it, and what it returns is untrusted input, vetted before use; its numbers are never values of the site's calculator, TPC. A value it computes lands as a RESULT with QUANTITY, VALUE, UNIT and AT, its initial and boundary values as SITUATION records; the regime of a numerical result, and whether such a value may be presented, are open questions of the specification. See Agent/Tools and the operator's guide.

References

• DEDALUS2020 – Burns K.J., Vasil G.M., Oishi J.S., Lecoanet D., Brown B.P. (2020). Dedalus: A flexible framework for numerical simulations with spectral methods. Phys. Rev. Research 2, 023068. doi:10.1103/PhysRevResearch.2.023068.