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name: symbolic-computation description: "When to reach for SymPy vs Wolfram|Alpha; standard patterns for simplify/solve/integrate/ODE; sanity-checking results."

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.