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reduce-relie-lie-symmetries

@hinsley/DiffSymAgent
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Use when working with ReLie in REDUCE (including inside Docker) to compute Lie group symmetries of differential equations, handle conditional/contact/variational/approximate symmetries or equivalence transformations, or interpret ReLie outputs and Lie algebra utilities.

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SKILL.md

name reduce-relie-lie-symmetries
description Use when working with ReLie in REDUCE (including inside Docker) to compute Lie group symmetries of differential equations, handle conditional/contact/variational/approximate symmetries or equivalence transformations, or interpret ReLie outputs and Lie algebra utilities.

ReLie symmetry workflows in REDUCE

Quick start (point symmetries)

  • Load ReLie: in "resources/relie-src/relie.red"$ (or load_package relie$ if precompiled).
  • Set the minimal globals: jetorder, xvar, uvar, diffeqs, leadders.
  • Run the standard pipeline: relie(4)$.
  • Extract generators: reliegen(1,{})$, then inspect symmetries, generators, splitsymmetries.

Docker readiness (when running in containers)

  • Confirm the CLI and daemon: docker --version then docker info.
  • If the daemon is down, start Docker Desktop (macOS: open -a Docker) and wait for docker info to succeed.
  • If you use Colima instead of Docker Desktop, start it with colima start and re-check docker info.
  • If you see permission denied ... docker.sock, rerun with elevated permissions or fix socket access (Codex sandboxing may require escalation).

Keep these invariants in mind

  • Treat ReLie state as global; always (re)declare variables before relieinit().
  • diffeqs and leadders must have the same length and be solvable for the chosen leading derivatives.
  • Mixed-derivative names must follow the xvar order.

Always explain results in natural language

After any computation, translate the output into plain language:

  • State what was computed (e.g., point/conditional/contact/variational/approximate/equivalence symmetries) and the PDE or system.
  • Report how many solution-sets are in symmetries and how many generators you extracted.
  • Interpret each generator as a transformation (translations, scalings, Galilean boosts, shifts in u, etc.).
  • If arbitrary functions appear in symmetries, explain that this indicates an infinite-dimensional symmetry (often due to linearity or gauge freedom).
  • Note any unsolved conditions or non-vanishing constraints and what they mean for validity.
  • Say what the symmetries are useful for: similarity reduction to ODEs, invariant solutions, conservation laws (Noether), and classification of PDE families.

Use resources/relie_result_interpretation.md for a compact template and common patterns.

Use the reference guide for details

  • For conditional/contact/variational/approximate/equivalence workflows, Lie algebra utilities, and troubleshooting, open resources/ReLie_whitepaper_synopsis.md.
  • For the Docker run command and minimal bootstrap, use the reduce-relie-basics skill.

Debugging pattern

  • If reliesolve() fails, run staged calls (relieinit, relieinv, reliedet, reliesolve) and inspect invcond and deteqs.
  • Enable CRACK verbosity with onprintcrack() when you need step-by-step solving.