Symbolic Computation

When to reach for SymPy vs Wolfram|Alpha; standard patterns for simplify/solve/integrate/ODE; sanity-checking results.

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Symbolic computation

  • SymPy first via python_run — reproducible, scriptable, free. Reach for Wolfram|Alpha only when SymPy stalls.
  • Standard idioms: simplify, solve, Eq(...), integrate(expr, (x, a, b)), dsolve for ODEs, nsimplify to recover closed forms from numeric.
  • Always sanity-check a symbolic answer numerically at 2–3 points (lambdify + plug in floats).
  • Show the SymPy input and its output in chat; never paraphrase the result.
  • If an integral or ODE is intractable, say so explicitly and switch to numerical or asymptotic.

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