sympy

1# SymPy - Symbolic Mathematics in Python
2 
3## Overview
4 
5SymPy is a Python library for symbolic mathematics that enables exact computation using mathematical symbols rather than numerical approximations. This skill provides comprehensive guidance for performing symbolic algebra, calculus, linear algebra, equation solving, physics calculations, and code generation using SymPy.
6 
7## When to Use This Skill
8 
9Use this skill when:
10- Solving equations symbolically (algebraic, differential, systems of equations)
11- Performing calculus operations (derivatives, integrals, limits, series)
12- Manipulating and simplifying algebraic expressions
13- Working with matrices and linear algebra symbolically
14- Doing physics calculations (mechanics, quantum mechanics, vector analysis)
15- Number theory computations (primes, factorization, modular arithmetic)
16- Geometric calculations (2D/3D geometry, analytic geometry)
17- Converting mathematical expressions to executable code (Python, C, Fortran)
18- Generating LaTeX or other formatted mathematical output
19- Needing exact mathematical results (e.g., `sqrt(2)` not `1.414...`)
20 
21## Core Capabilities
22 
23### 1. Symbolic Computation Basics
24 
25**Creating symbols and expressions:**
26```python
27from sympy import symbols, Symbol
28x, y, z = symbols('x y z')
29expr = x**2 + 2*x + 1
30 
31# With assumptions
32x = symbols('x', real=True, positive=True)
33n = symbols('n', integer=True)
34```
35 
36**Simplification and manipulation:**
37```python
38from sympy import simplify, expand, factor, cancel
39…