Co Scientist Symbolic Mathematics

Symbolic mathematics

Symbolic mathematics skill. SymPy-based symbolic computation, equation solving, calculus, linear algebra, and mathematical proof assistance.

Use This Skill When

• SymPy-based symbolic computation.
• Equation solving.
• Calculus.
• Linear algebra.
• Mathematical proof assistance.

Required Inputs

• Research objective, decision target, or hypothesis.
• Available data, source constraints, and domain assumptions.
• Required outputs, success metrics, and deadline or reproducibility constraints.

Workflow

1. Confirm scope, assumptions, and the exact artifact set to save.
2. Apply the narrowest domain method that answers the request with defensible evidence.
3. Save code, tables, figures, and intermediate outputs to files instead of chat-only output.
4. State limitations, uncertainty, and any validation or sensitivity checks performed.
5. Append skill selection, handoff I/O, and file writes to logs/process-log.jsonl.

Deliverables

• report.md: concise method, results, interpretation, and file inventory in the user's language.
• results/: structured outputs, metrics, model artifacts, or extracted findings.
• figures/: English-only charts, diagrams, or panels when visual output is needed.
• data/: processed or derived datasets when transformation occurs.

Quality Gates

• The selected method matches the scientific question and stated assumptions.
• Outputs are reproducible, saved to files, and traceable from inputs to conclusions.
• Missing data, uncertainty, bias, and hard limits are made explicit.
• report.md and logs/process-log.jsonl reference the generated artifacts.
• No essential result remains chat-only.

If any gate fails: identify the specific failing check, fix the issue, and re-validate before proceeding.

Gotchas

• Computational resource requirements should be estimated before execution. Large analyses may exceed memory or time
• Intermediate results must be checkpointed to files. Long-running analyses should be resumable
• Parameter sensitivity analysis should be performed for key parameters before finalizing results

Validation Loop

1. Execute analysis and generate outputs
2. Check:
   • Method selection matches the research question and stated assumptions
   • All outputs are saved to files (no chat-only results)
   • Limitations and uncertainty are explicitly stated
   • logs/process-log.jsonl is updated with execution trace
3. If any check fails:
   • Identify the failing gate
   • Fix the specific issue
   • Re-run validation
4. Proceed only after all gates pass