name: reduce-crack-basics description: Use when solving overdetermined algebraic/ODE/PDE systems with the CRACK package in REDUCE, especially for Lie symmetry determining equations; covers crack() usage, dependency declarations, batch vs interactive control, and interpreting solutions and case splits.

CRACK workflows in REDUCE

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.

Quick start (batch mode)

% Declare dependencies for all unknown functions

depend f, x, y;
depend g, x;

% Call crack with equations, inequalities, unknowns, extra vars
crack({eq1, eq2}, {}, {f, g}, {});

Before you call CRACK

• Always declare functional dependence with depend for every unknown function.
• Unknown functions must appear polynomially in the equations.
• Keep parametric functions out of the {fun1,...} list; declare their dependencies and include any extra independent variables in the 4th argument.
• If you need interactive control, set off batch_mode; before calling crack.

Batch vs interactive control

• Batch mode runs modules in proc_list automatically.
• Interactive mode lets you inspect, choose equations, and run modules step by step.
• A hybrid approach is to insert stop batch into proc_list so you can switch to interactive once safe steps are done.

Always explain results in natural language

After any CRACK run, summarize the output clearly:

• State what CRACK was solving (e.g., determining equations for Lie symmetries).
• Report the number of solutions returned and whether there were case splits.
• For each solution, list:
  • remaining conditions,
  • solved assignments for functions,
  • remaining free functions/constants,
  • nonzero assumptions.
• Explain what free functions mean (underdetermined/infinite-dimensional families).
• If CRACK returns {} or contradictions, say that no solutions exist under the given assumptions.
• Connect to PDE theory: these solutions typically determine infinitesimals of symmetry generators, which enable similarity reduction, invariant solutions, and conservation-law derivations.

Use the reference guide for details

Open resources/crack_manual_synopsis.md for:

• the full interactive command set,
• module numbers and behavior,
• strategy notes and troubleshooting,
• global flags and tuning parameters.

When CRACK is used inside ReLie

ReLie calls CRACK inside reliesolve(). If ReLie stalls or returns partial solutions:

• enable CRACK verbosity in ReLie (onprintcrack()),
• run the staged pipeline (relieinit, relieinv, reliedet) and inspect the determining equations,
• then solve interactively with CRACK if needed.