nsforge-verification-suite

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驗證工具組合。觸發詞：驗證, verify, check, 維度, dimension。

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[Academic Research]

When & Why to Use This Skill

The nsforge-verification-suite is a specialized Claude skill designed for rigorous mathematical and physical formula validation. It provides a robust set of tools for symbolic equality checks, calculus verification (derivatives and integrals), equation solution testing, and dimensional analysis. This skill is essential for ensuring technical accuracy, preventing calculation errors, and maintaining consistency in scientific and engineering workflows.

Use Cases

  • Academic Research: Validating complex symbolic derivations and mathematical proofs to ensure logical consistency and algebraic correctness.
  • Physics and Engineering: Performing dimensional analysis on physical equations (e.g., mechanics, thermodynamics, or pharmacokinetics) to verify unit consistency and identify formula errors.
  • Calculus Verification: Automatically checking the correctness of derivatives and integrals for complex functions, providing immediate feedback on mathematical operations.
  • Educational Support: Assisting students and educators in verifying solutions to algebraic equations and providing human-readable dimension analysis results for better understanding.
namensforge-verification-suite
description驗證工具組合。觸發詞：驗證, verify, check, 維度, dimension。

驗證工具 Skill

⚠️ 驗證後必須向用戶展示結果！

  • 驗證成功/失敗都要清楚告知用戶
  • 維度分析結果要用人類可讀格式展示

工具速查

驗證類型 工具 參數
符號等價 symbolic_equal(expr1, expr2) 兩表達式
導數驗證 verify_derivative(original, claimed, var) 原式、宣稱導數、變數
積分驗證 verify_integral(original, claimed, var) 被積函數、宣稱積分、變數
解驗證 verify_solution(equation, solution, var) 方程、解、變數
維度分析 check_dimensions(expr, units_map) 表達式、單位映射

調用範例

# 符號等價
symbolic_equal("(x+1)**2", "x**2 + 2*x + 1")  # → True

# 導數驗證：d/dx[ln(x²)] = 2/x ?
verify_derivative("ln(x**2)", "2/x", "x")  # → correct: True

# 積分驗證：∫sin(x)dx = -cos(x) ?
verify_integral("sin(x)", "-cos(x)", "x")  # → correct: True

# 解驗證：x=2 是 x²-4=0 的解？
verify_solution("x**2 - 4", "2", "x")  # → correct: True

# 維度分析
check_dimensions("m * a", {"m": "kg", "a": "m/s**2"})
# → dimension: [mass]*[length]/[time]**2 = Force

常用單位映射

# 力學
{"F": "N", "m": "kg", "a": "m/s**2", "v": "m/s", "t": "s"}

# 藥動學
{"C": "mg/L", "V": "L", "k": "1/h", "t": "h", "D": "mg"}

# 熱力學
{"T": "K", "E": "J", "R": "J/(mol*K)", "n": "mol"}

驗證順序建議

  1. 維度分析 - 維度錯，結果必錯
  2. 符號驗證 - 代數正確性
  3. 數值抽樣 - 特殊情況