Buckets:
tahamajs/Sysmem2_in_AI / ComputerAssignments /CA5_geometric_reasoning /src /tools /geometry_tools.py
| """ | |
| Geometry Tools for LangChain Agents | |
| ابزارهای هندسه برای عوامل LangChain | |
| This module provides specialized tools for geometric problem solving | |
| that can be used by LangChain agents. | |
| """ | |
| import os | |
| import json | |
| import logging | |
| import numpy as np | |
| import matplotlib.pyplot as plt | |
| import matplotlib.patches as patches | |
| from typing import Dict, List, Any, Optional, Tuple | |
| from datetime import datetime | |
| import sympy as sp | |
| from sympy import symbols, solve, simplify, expand, factor | |
| from sympy.geometry import Point, Line, Circle, Triangle, Polygon | |
| from sympy.geometry.util import intersection | |
| from langchain.tools import BaseTool | |
| from langchain.llms.base import BaseLLM | |
| logger = logging.getLogger(__name__) | |
| class GeometryTools: | |
| """ | |
| Collection of geometry tools for LangChain agents | |
| مجموعه ابزارهای هندسه برای عوامل LangChain | |
| """ | |
| def __init__(self, config: Dict[str, Any], llm: BaseLLM): | |
| """ | |
| Initialize geometry tools | |
| Args: | |
| config: Tools configuration | |
| llm: Language model for advanced reasoning | |
| """ | |
| self.config = config | |
| self.llm = llm | |
| # Load theorem database | |
| self.theorem_db = self._load_theorem_database() | |
| logger.info("Geometry Tools initialized") | |
| def _load_theorem_database(self) -> Dict[str, Any]: | |
| """Load theorem database from file""" | |
| try: | |
| db_path = ( | |
| self.config.get("theorem_lookup", {}) | |
| .get("parameters", {}) | |
| .get("database_path", "data/theorems/theorems.json") | |
| ) | |
| if os.path.exists(db_path): | |
| with open(db_path, "r", encoding="utf-8") as f: | |
| return json.load(f) | |
| else: | |
| # Create sample theorem database | |
| return self._create_sample_theorem_db() | |
| except Exception as e: | |
| logger.error(f"Error loading theorem database: {e}") | |
| return self._create_sample_theorem_db() | |
| def _create_sample_theorem_db(self) -> Dict[str, Any]: | |
| """Create a sample theorem database""" | |
| return { | |
| "pythagorean": { | |
| "name": "قضیه فیثاغورث", | |
| "description": "در مثلث قائم‌الزاویه، مربع وتر برابر است با مجموع مربعات دو ضلع دیگر", | |
| "formula": "a² + b² = c²", | |
| "category": "مثلث", | |
| "difficulty": "پایه", | |
| }, | |
| "thales": { | |
| "name": "قضیه تالس", | |
| "description": "اگر خطی موازی با یکی از اضلاع مثلث رسم شود، مثلث‌های مشابه ایجاد می‌کند", | |
| "formula": "AB/AC = AD/AE", | |
| "category": "مثلث", | |
| "difficulty": "متوسط", | |
| }, | |
| "circle_angle": { | |
| "name": "قضیه زاویه مرکزی و محیطی", | |
| "description": "زاویه مرکزی دو برابر زاویه محیطی است که روی همان کمان قرار دارد", | |
| "formula": "∠AOB = 2∠ACB", | |
| "category": "دایره", | |
| "difficulty": "متوسط", | |
| }, | |
| "tangent": { | |
| "name": "قضیه مماس", | |
| "description": "خط مماس بر دایره عمود بر شعاع در نقطه تماس است", | |
| "formula": "OT ⊥ PT", | |
| "category": "دایره", | |
| "difficulty": "پایه", | |
| }, | |
| "chord": { | |
| "name": "قضیه وتر", | |
| "description": "اگر دو وتر در دایره همدیگر را قطع کنند، حاصل ضرب قطعات یکی برابر حاصل ضرب قطعات دیگری است", | |
| "formula": "AE × EB = CE × ED", | |
| "category": "دایره", | |
| "difficulty": "متوسط", | |
| }, | |
| } | |
| def coordinate_geometry_solver(self, problem_description: str) -> str: | |
| """ | |
| Solve geometric problems using coordinate geometry | |
| Args: | |
| problem_description: Description of the geometric problem | |
| Returns: | |
| Solution using coordinate geometry | |
| """ | |
| try: | |
| # Use LLM to analyze the problem and extract coordinates | |
| analysis_prompt = f""" | |
| مسئله هندسی زیر را تحلیل کنید و مختصات نقاط را استخراج کنید: | |
| {problem_description} | |
| لطفاً: | |
| 1. نوع مسئله را تشخیص دهید | |
| 2. مختصات نقاط را مشخص کنید | |
| 3. فرمول‌های مورد نیاز را شناسایی کنید | |
| 4. راه‌حل را با استفاده از هندسه تحلیلی ارائه دهید | |
| """ | |
| analysis = self.llm(analysis_prompt) | |
| # Try to solve using SymPy for symbolic computation | |
| try: | |
| # Define symbolic variables | |
| x, y = symbols("x y") | |
| # This is a simplified example - in practice, you'd parse the problem | |
| # and create appropriate equations | |
| solution = f""" | |
| تحلیل مسئله: | |
| {analysis} | |
| راه‌حل با هندسه تحلیلی: | |
| 1. مختصات نقاط را تعریف می‌کنیم | |
| 2. معادلات مربوطه را تشکیل می‌دهیم | |
| 3. سیستم معادلات را حل می‌کنیم | |
| 4. نتیجه نهایی را محاسبه می‌کنیم | |
| توجه: این یک راه‌حل نمونه است. برای مسائل پیچیده‌تر، | |
| نیاز به تحلیل دقیق‌تر مسئله و تشکیل معادلات مناسب است. | |
| """ | |
| except Exception as e: | |
| solution = f""" | |
| تحلیل مسئله: | |
| {analysis} | |
| خطا در محاسبات سمبلیک: {str(e)} | |
| لطفاً مسئله را با جزئیات بیشتری ارائه دهید. | |
| """ | |
| logger.info("Coordinate geometry solution generated") | |
| return solution | |
| except Exception as e: | |
| logger.error(f"Error in coordinate geometry solver: {e}") | |
| return f"خطا در حل مسئله با هندسه تحلیلی: {str(e)}" | |
| def synthetic_geometry_solver(self, problem_description: str) -> str: | |
| """ | |
| Solve geometric problems using synthetic geometry | |
| Args: | |
| problem_description: Description of the geometric problem | |
| Returns: | |
| Solution using synthetic geometry | |
| """ | |
| try: | |
| # Use LLM to analyze the problem | |
| analysis_prompt = f""" | |
| مسئله هندسی زیر را با استفاده از هندسه ترکیبی حل کنید: | |
| {problem_description} | |
| لطفاً: | |
| 1. قضایای مرتبط را شناسایی کنید | |
| 2. مراحل اثبات را به ترتیب ارائه دهید | |
| 3. از نمادهای هندسی مناسب استفاده کنید | |
| 4. نتیجه نهایی را مشخص کنید | |
| """ | |
| solution = self.llm(analysis_prompt) | |
| # Add theorem references | |
| relevant_theorems = self._find_relevant_theorems(problem_description) | |
| if relevant_theorems: | |
| solution += "\n\nقضایای مرتبط:\n" | |
| for theorem in relevant_theorems: | |
| solution += f"- {theorem['name']}: {theorem['description']}\n" | |
| logger.info("Synthetic geometry solution generated") | |
| return solution | |
| except Exception as e: | |
| logger.error(f"Error in synthetic geometry solver: {e}") | |
| return f"خطا در حل مسئله با هندسه ترکیبی: {str(e)}" | |
| def theorem_lookup(self, query: str) -> str: | |
| """ | |
| Look up relevant theorems based on query | |
| Args: | |
| query: Search query for theorems | |
| Returns: | |
| Relevant theorems information | |
| """ | |
| try: | |
| relevant_theorems = self._find_relevant_theorems(query) | |
| if not relevant_theorems: | |
| return "هیچ قضیه مرتبطی یافت نشد. لطفاً کلمات کلیدی دیگری امتحان کنید." | |
| result = "قضایای مرتبط:\n\n" | |
| for theorem in relevant_theorems: | |
| result += f"📐 {theorem['name']}\n" | |
| result += f" توضیح: {theorem['description']}\n" | |
| result += f" فرمول: {theorem.get('formula', 'N/A')}\n" | |
| result += f" دسته‌بندی: {theorem['category']}\n" | |
| result += f" سطح: {theorem['difficulty']}\n\n" | |
| logger.info(f"Found {len(relevant_theorems)} relevant theorems") | |
| return result | |
| except Exception as e: | |
| logger.error(f"Error in theorem lookup: {e}") | |
| return f"خطا در جستجوی قضایا: {str(e)}" | |
| def _find_relevant_theorems(self, query: str) -> List[Dict[str, Any]]: | |
| """ | |
| Find relevant theorems based on query | |
| Args: | |
| query: Search query | |
| Returns: | |
| List of relevant theorems | |
| """ | |
| try: | |
| relevant_theorems = [] | |
| query_lower = query.lower() | |
| # Simple keyword matching | |
| keywords = { | |
| "مثلث": ["pythagorean", "thales"], | |
| "دایره": ["circle_angle", "tangent", "chord"], | |
| "فیثاغورث": ["pythagorean"], | |
| "تالس": ["thales"], | |
| "مماس": ["tangent"], | |
| "وتر": ["chord"], | |
| "زاویه": ["circle_angle"], | |
| } | |
| for keyword, theorem_keys in keywords.items(): | |
| if keyword in query_lower: | |
| for theorem_key in theorem_keys: | |
| if theorem_key in self.theorem_db: | |
| relevant_theorems.append(self.theorem_db[theorem_key]) | |
| return relevant_theorems | |
| except Exception as e: | |
| logger.error(f"Error finding relevant theorems: {e}") | |
| return [] | |
| def proof_verification(self, proof_statement: str) -> str: | |
| """ | |
| Verify mathematical proofs | |
| Args: | |
| proof_statement: The proof to verify | |
| Returns: | |
| Verification result | |
| """ | |
| try: | |
| verification_prompt = f""" | |
| اثبات زیر را بررسی کنید و صحت آن را تأیید کنید: | |
| {proof_statement} | |
| لطفاً: | |
| 1. هر مرحله از اثبات را بررسی کنید | |
| 2. منطق ریاضی را تأیید کنید | |
| 3. خطاهای احتمالی را شناسایی کنید | |
| 4. نتیجه نهایی را مشخص کنید | |
| """ | |
| verification = self.llm(verification_prompt) | |
| logger.info("Proof verification completed") | |
| return verification | |
| except Exception as e: | |
| logger.error(f"Error in proof verification: {e}") | |
| return f"خطا در تأیید اثبات: {str(e)}" | |
| def diagram_generation(self, description: str) -> str: | |
| """ | |
| Generate geometric diagrams | |
| Args: | |
| description: Description of the geometric figure | |
| Returns: | |
| Information about the generated diagram | |
| """ | |
| try: | |
| # Use LLM to analyze the description and create diagram specifications | |
| analysis_prompt = f""" | |
| بر اساس توضیحات زیر، مشخصات نمودار هندسی را تعیین کنید: | |
| {description} | |
| لطفاً: | |
| 1. نوع شکل هندسی را مشخص کنید | |
| 2. نقاط، خطوط و زاویه‌ها را شناسایی کنید | |
| 3. ابعاد و مختصات را تعیین کنید | |
| 4. راهنمای رسم نمودار را ارائه دهید | |
| """ | |
| diagram_specs = self.llm(analysis_prompt) | |
| # Create a simple diagram using matplotlib | |
| try: | |
| fig, ax = plt.subplots(1, 1, figsize=(10, 8)) | |
| # This is a simplified example - in practice, you'd parse the description | |
| # and create appropriate geometric elements | |
| # Draw a sample triangle | |
| triangle = patches.Polygon( | |
| [(1, 1), (4, 1), (2.5, 3)], | |
| closed=True, | |
| fill=False, | |
| edgecolor="blue", | |
| linewidth=2, | |
| ) | |
| ax.add_patch(triangle) | |
| # Add labels | |
| ax.text(1, 0.8, "A", fontsize=12, ha="center") | |
| ax.text(4, 0.8, "B", fontsize=12, ha="center") | |
| ax.text(2.5, 3.2, "C", fontsize=12, ha="center") | |
| ax.set_xlim(0, 5) | |
| ax.set_ylim(0, 4) | |
| ax.set_aspect("equal") | |
| ax.grid(True, alpha=0.3) | |
| ax.set_title("نمودار هندسی نمونه", fontsize=14) | |
| # Save the diagram | |
| diagram_path = f"visualizations/diagram_{datetime.now().strftime('%Y%m%d_%H%M%S')}.png" | |
| os.makedirs(os.path.dirname(diagram_path), exist_ok=True) | |
| plt.savefig(diagram_path, dpi=300, bbox_inches="tight") | |
| plt.close() | |
| result = f""" | |
| نمودار هندسی ایجاد شد: | |
| {diagram_specs} | |
| فایل نمودار در مسیر زیر ذخیره شد: | |
| {diagram_path} | |
| """ | |
| except Exception as e: | |
| result = f""" | |
| تحلیل نمودار: | |
| {diagram_specs} | |
| خطا در ایجاد نمودار: {str(e)} | |
| """ | |
| logger.info("Diagram generation completed") | |
| return result | |
| except Exception as e: | |
| logger.error(f"Error in diagram generation: {e}") | |
| return f"خطا در ایجاد نمودار: {str(e)}" | |
| def get_tool_info(self) -> Dict[str, Any]: | |
| """ | |
| Get information about available tools | |
| Returns: | |
| Dictionary containing tool information | |
| """ | |
| return { | |
| "tools": [ | |
| { | |
| "name": "coordinate_geometry_solver", | |
| "description": "حل مسائل هندسی با استفاده از هندسه تحلیلی", | |
| "parameters": ["problem_description"], | |
| }, | |
| { | |
| "name": "synthetic_geometry_solver", | |
| "description": "حل مسائل هندسی با استفاده از هندسه ترکیبی", | |
| "parameters": ["problem_description"], | |
| }, | |
| { | |
| "name": "theorem_lookup", | |
| "description": "جستجوی قضایای مرتبط", | |
| "parameters": ["query"], | |
| }, | |
| { | |
| "name": "proof_verification", | |
| "description": "تأیید صحت اثبات‌های ریاضی", | |
| "parameters": ["proof_statement"], | |
| }, | |
| { | |
| "name": "diagram_generation", | |
| "description": "ایجاد نمودارهای هندسی", | |
| "parameters": ["description"], | |
| }, | |
| ], | |
| "theorem_database_size": len(self.theorem_db), | |
| "available_theorems": list(self.theorem_db.keys()), | |
| } | |
| def add_theorem(self, theorem_data: Dict[str, Any]): | |
| """ | |
| Add a new theorem to the database | |
| Args: | |
| theorem_data: Dictionary containing theorem information | |
| """ | |
| try: | |
| theorem_id = theorem_data.get("id", f"theorem_{len(self.theorem_db) + 1}") | |
| self.theorem_db[theorem_id] = theorem_data | |
| logger.info(f"Theorem '{theorem_id}' added to database") | |
| except Exception as e: | |
| logger.error(f"Error adding theorem: {e}") | |
| def save_theorem_database(self, file_path: str = None): | |
| """ | |
| Save theorem database to file | |
| Args: | |
| file_path: Path to save the database | |
| """ | |
| try: | |
| if file_path is None: | |
| file_path = ( | |
| self.config.get("theorem_lookup", {}) | |
| .get("parameters", {}) | |
| .get("database_path", "data/theorems/theorems.json") | |
| ) | |
| os.makedirs(os.path.dirname(file_path), exist_ok=True) | |
| with open(file_path, "w", encoding="utf-8") as f: | |
| json.dump(self.theorem_db, f, ensure_ascii=False, indent=2) | |
| logger.info(f"Theorem database saved to {file_path}") | |
| except Exception as e: | |
| logger.error(f"Error saving theorem database: {e}") | |
Xet Storage Details
- Size:
- 17.8 kB
- Xet hash:
- 6c2477553c7423de7c3878a8a5ff4f50d20efcd232dd33b293ebba43a986549a
·
Xet efficiently stores files, intelligently splitting them into unique chunks and accelerating uploads and downloads. More info.