What is nsforge-derivation-workflow?

This Claude skill enables a structured, step-by-step mathematical derivation workflow by integrating symbolic computation with persistent knowledge management. It bridges the gap between complex calculation and formal documentation, ensuring every logical step is verified via SymPy, displayed in LaTeX, and recorded with contextual notes for rigorous scientific and engineering modeling.

When should I use nsforge-derivation-workflow?

nsforge-derivation-workflow is useful in the following scenarios: • Scientific Modeling: Deriving complex equations (e.g., biochemical kinetics or physical laws) while documenting specific assumptions and environmental constraints for each step. • Engineering Formula Composition: Building multi-variable engineering models through symbolic substitution and simplification with a clear audit trail of the derivation process. • Academic Proof Development: Generating verified, step-by-step mathematical proofs where each transition is mathematically validated and ready for export into research papers. • Educational Tutoring: Guiding students through rigorous mathematical logic by showing intermediate results and allowing 'what-if' explorations through the rollback and CRUD features.

name	nsforge-derivation-workflow
description	步進式推導工作流。觸發詞：推導, derive, 組合公式, 建立模型。

推導工作流 Skill

核心原則

SymPy-MCP 做計算，NSForge 記錄知識！ 每步都要顯示給用戶看！ 使用：

derivation_show() (NSForge) - 顯示當前推導狀態

print_latex_expression() (SymPy-MCP) - 顯示計算結果

⚠️ 黃金法則：永遠向用戶展示公式！

❌ 錯誤：執行計算後直接下一步
✅ 正確：執行計算 → derivation_show() 或 print_latex_expression() → 等用戶確認 → 下一步

工作流程

Phase 1: derivation_start(name, description)
    ↓
Phase 2: 循環 {
    SymPy-MCP: intro_many → introduce_expression → 計算 → print_latex_expression
    NSForge:   derivation_record_step(expression, description, notes?)
    NSForge:   derivation_show()  ← 🆕 顯示當前狀態！
    NSForge:   derivation_add_note(note, note_type?)  # 可選
}
    ↓
Phase 3: derivation_complete(description, assumptions?, limitations?, references?)
         derivation_show()  ← 🆕 顯示最終結果！

工具速查

階段	MCP	工具	用途
開始	NSForge	`derivation_start(name, description)`	建立會話
計算	SymPy	`intro_many`, `introduce_expression`, `substitute_expression`...	符號計算
顯示	SymPy	`print_latex_expression`	⚠️ 必須！
記錄	NSForge	`derivation_record_step(expr, desc, notes?, source?)`	記錄步驟+知識
🆕 顯示	NSForge	`derivation_show(format?, show_steps?)`	⚠️ 必須！顯示當前狀態
說明	NSForge	`derivation_add_note(note, note_type?)`	純文字洞見
完成	NSForge	`derivation_complete(...)`	存檔+元資料

note_type: assumption, limitation, observation, correction, clinical, physical

🆕 步驟 CRUD 操作

操作	工具	用途
📖 Read	`derivation_get_step(step_number)`	查看單一步驟詳情
✏️ Update	`derivation_update_step(step_number, notes?, assumptions?, ...)`	更新步驟元資料
🗑️ Delete	`derivation_delete_step(step_number)`	刪除最後一步
⏪ Rollback	`derivation_rollback(to_step)`	⚡ 回滾到指定步驟
📝 Insert	`derivation_insert_note(after_step, note, note_type?)`	在指定位置插入說明

Handoff：NSForge 做不到時

⚠️ Phase 2 後更新：Laplace/Fourier 變換已實作，無需 Handoff！

當需要 ODE/PDE、矩陣運算、聯立方程組：

# 1. 導出
result = derivation_export_for_sympy()
# → 返回 intro_many_command, current_expression

# 2. SymPy-MCP 計算
intro_many([...])
dsolve_ode(...) / solve_linear_system(...)
print_latex_expression(...)

# 3. 導入回 NSForge
derivation_import_from_sympy(
    expression="...",
    operation_performed="Solved ODE",
    sympy_tool_used="dsolve_ode",
    notes="...",
    assumptions_used=[...],
    limitations=[...]
)

調用範例

# Phase 1
derivation_start("temp_mm", "Temperature-corrected Michaelis-Menten")

# Phase 2a: SymPy 計算
intro_many([{"name": "V_max", "assumptions": ["positive"]}, ...])
mm = introduce_expression("V_max * C / (K_m + C)")
print_latex_expression(mm)

# Phase 2b: NSForge 記錄
derivation_record_step(
    expression="V_max * C / (K_m + C)",
    description="Base Michaelis-Menten",
    notes="假設溫度恆定"
)

# Phase 2c: 加入洞見
derivation_add_note("酵素在 >42°C 會變性", note_type="limitation")

# Phase 3
derivation_complete(
    description="...",
    assumptions=["Michaelis-Menten kinetics"],
    limitations=["Valid for 32-42°C"],
    tags=["enzyme", "temperature"]
)

🆕 步驟 CRUD 範例

# 📖 Read: 查看第 11 步詳情
derivation_get_step(11)
→ {"step": {"description": "...", "notes": "...", "output_latex": "..."}}

# ✏️ Update: 更新第 11 步的說明
derivation_update_step(
    step_number=11,
    notes="此假設在高溫時不成立",
    limitations=["Valid only for T < 42°C"]
)

# ⏪ Rollback: 發現第 11 步開始走錯，回滾到第 10 步
derivation_rollback(to_step=10)
→ {"deleted_count": 6, "deleted_steps": [11, 12, ...], "current_expression": "..."}
# 現在可以從第 10 步重新開始推導！

# 📝 Insert: 在步驟 5 和 6 之間插入說明
derivation_insert_note(
    after_step=5,
    note="此處假設達穩態",
    note_type="assumption"
)

nsforge-derivation-workflow

When & Why to Use This Skill

Use Cases