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Problem-solving strategies for root finding in numerical methods
Passed 23 of 23 test cases with the skill, and 15 of 23 without it.
and 5 more in the full report
8 fixed15 passed either way0 still failing0 broke
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One of 8 test cases the skill fixed. Same model, same prompt, with and without the skill.
What exact command line string using `sympy_compute.py` under `runtime.harness` solves the equation x**2 - 4 = 0 for variable x?
| Checked | Without skill | With skill |
|---|---|---|
| Passes quadratic polynomial x**2 - 4 to scripts/sympy_compute.py | Missed | Passed |
The instructions your model reads when the skill loads.
Use this skill when working on root-finding problems in numerical methods.
Characterize the Problem
Method Selection
| Situation | Method | Implementation |
|---|---|---|
| Bracketed, no derivatives | Bisection, Brent | scipy.optimize.brentq |
| Derivatives available | Newton-Raphson | scipy.optimize.newton |
| No derivatives | Secant method | scipy.optimize.newton (no fprime) |
| System of equations | scipy.optimize.fsolve | Requires Jacobian ideally |
Implement Root Finding
scipy.optimize.brentq(f, a, b) - guaranteed convergence if bracketedscipy.optimize.newton(f, x0, fprime=df) - quadratic convergence near rootscipy.optimize.fsolve(F, x0)Handle Multiple Roots
sympy_compute.py solve "f(x)" --var x for symbolic solutionsVerify Solutions
z3_solve.py prove "f(root) == 0"test cases passed, vs 15 / 23 without
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