| name | nsforge-quick-calculate |
| description | 快速計算(無需會話)。觸發詞:計算, 簡化, 求解, 微分, 積分, 極限, 級數, 不等式, 機率。 |
快速計算 Skill
⚠️ 每次計算後必須向用戶展示結果!
- 在推導中使用
derivation_show() 顯示當前狀態
- 單獨計算用
print_latex_expression() (SymPy-MCP)
工具分工
| 我想要... | MCP | 工具 |
|---|
| 簡化/展開/分解 | SymPy | simplify_expression, expand_expression, factor_expression |
| 展開表達式 | NSForge | expand_expression(expr, deep?, modulus?) 🆕 |
| 因式分解 | NSForge | factor_expression(expr, modulus?) 🆕 |
| 收集同類項 | NSForge | collect_expression(expr, symbols) 🆕 |
| 三角化簡 | NSForge | trigsimp_expression(expr, method?) 🆕 |
| 冪次化簡 | NSForge | powsimp_expression(expr, deep?) 🆕 |
| 根式化簡 | NSForge | radsimp_expression(expr) 🆕 |
| 組合函數化簡 | NSForge | combsimp_expression(expr) 🆕 |
| 部分分式 | NSForge | apart_expression(expr, var) 🆕🔥🔥 |
| 約分 | NSForge | cancel_expression(expr) 🆕 |
| 合併分式 | NSForge | together_expression(expr, deep?) 🆕 |
| 微分/積分 | SymPy | differentiate_expression, integrate_expression |
| 解方程 | SymPy | solve_algebraically, solve_linear_system |
| ODE/PDE | SymPy | dsolve_ode, pdsolve_pde |
| 矩陣 | SymPy | matrix_* 系列 |
| 單位換算 | SymPy | convert_to_units |
| Laplace 變換 | NSForge | laplace_transform_expression(expr, t, s) 🆕🔥🔥 |
| 反 Laplace | NSForge | inverse_laplace_transform_expression(expr, s, t) 🆕🔥🔥 |
| Fourier 變換 | NSForge | fourier_transform_expression(expr, x, k) 🆕🔥 |
| 反 Fourier | NSForge | inverse_fourier_transform_expression(expr, k, x) 🆕🔥 |
| 極限 | NSForge | calculate_limit(expr, var, point, direction?) |
| 級數展開 | NSForge | calculate_series(expr, var, point?, order?) |
| 求和 Σ | NSForge | calculate_summation(expr, index, lower, upper) |
| 不等式 | NSForge | solve_inequality(ineq, var, domain?) |
| 不等式系統 | NSForge | solve_inequality_system(ineqs, var) |
| 定義分佈 | NSForge | define_distribution(type, params, name?) |
| 統計量 | NSForge | distribution_stats(type, params, stats?) |
| 機率計算 | NSForge | distribution_probability(type, params, condition) |
| 假設查詢 | NSForge | query_assumptions(expr, query, assumptions?) |
| 假設簡化 | NSForge | refine_expression(expr, assumptions) |
| 數值計算 | NSForge | evaluate_numeric(expr, values, precision?) |
| 等價檢查 | NSForge | symbolic_equal(expr1, expr2) |
SymPy-MCP 調用模式
intro("x", ["real"], [])
expr = introduce_expression("x**2 - 1")
result = simplify_expression(expr)
print_latex_expression(result)
❌ 禁止:計算後不顯示結果就繼續下一步
✅ 正確:每次計算後都用 print_latex_expression 或 derivation_show() 展示
NSForge 獨特工具範例
expand_expression("(x+1)**2")
factor_expression("x**2 - 1")
collect_expression("x*y + x**2*y + y", "y")
trigsimp_expression("sin(x)**2 + cos(x)**2")
powsimp_expression("x**2 * x**3")
radsimp_expression("1/(sqrt(3) + sqrt(2))")
combsimp_expression("factorial(n)/factorial(n-2)")
apart_expression("1/((s+1)*(s+2))", "s")
cancel_expression("(x**2-1)/(x-1)")
together_expression("1/x + 1/y")
laplace_transform_expression("exp(-k*t)", "t", "s")
laplace_transform_expression("Heaviside(t)", "t", "s")
inverse_laplace_transform_expression("1/(s+k)", "s", "t")
fourier_transform_expression("exp(-x**2)", "x", "k")
inverse_fourier_transform_expression("1/(1+k**2)", "k", "x")
calculate_limit("sin(x)/x", "x", "0")
calculate_limit("1/x", "x", "0", direction="+")
calculate_series("exp(x)", "x", "0", order=4)
calculate_summation("k", "k", "1", "n")
solve_inequality("x**2 - 4 < 0", "x")
solve_inequality_system(["x > 0", "x < 5"], "x")
distribution_stats("normal", {"mean": "mu", "std": "sigma"})
distribution_probability("exponential", {"rate": "1"}, "X < 2")
query_assumptions("x**2", "positive", {"x": ["real", "nonzero"]})
refine_expression("sqrt(x**2)", {"x": ["positive"]})
🔥🔥 完整 Laplace 工作流(多隔室 PK)
apart_expression("Dose/(V1*(s + lambda1)*(s + lambda2))", "s")
→ {"result": "A/(s + lambda1) + B/(s + lambda2)"}
inverse_laplace_transform_expression("A/(s + lambda1) + B/(s + lambda2)", "s", "t")
→ {"result": "A*exp(-lambda1*t) + B*exp(-lambda2*t)"}
需要推導追蹤?
切換到 nsforge-derivation-workflow skill。