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Master Symbolic Mathematics with the SymPy AI Agent Skill

Master symbolic math with SymPy.

Solve equations, perform calculus, and handle 2D/3D geometry without numerical errors like 1.414. Download the skill today.

  • Symbolic Math
  • Python
  • Calculus
  • Algebra
  • Scientific Computing

About This Skill

Leverage SymPy for exact mathematical results. This skill covers 10+ core use cases including calculus, algebra, and physics, ensuring you never settle for approximations like 1.414 when you need the precision of sqrt(2).

Quick Start

  1. 1Install SymPy via pip install sympy
  2. 2Import symbols and define mathematical variables
  3. 3Apply functions like simplify, solve, or integrate to your expressions
Example Command
from sympy import symbols, solve; x = symbols('x'); solve(x**2 - 1, x)

Core Capabilities

Symbolic Computation Basics

Create symbols and expressions with specific assumptions for real, positive, or integer values to ensure mathematical rigor.

Equation Solving

Solve algebraic, differential, and systems of equations symbolically to obtain exact analytical solutions.

Calculus Operations

Perform complex derivatives, integrals, limits, and series expansions with high precision and symbolic accuracy.

Linear Algebra

Manipulate matrices and perform linear algebra operations using symbolic variables rather than fixed numerical values.

Usage Examples

Input

simplify(sin(x)**2 + cos(x)**2)

Output

1

Before

(x + 1)**2

After

x**2 + 2*x + 1

Input

factor(x**2 - 1)

Output

(x - 1)*(x + 1)

SKILL.md

---
name: sympy
description: "SymPy is a Python library for symbolic mathematics that enables exact computation using mathematical symbols rather than numerical approximations."
license: https://github.com/sympy/sympy/blob/master/LICENSE
metadata:
    skill-author: K-Dense Inc.
risk: unknown
source: "https://github.com/sympy/sympy"
---

# SymPy - Symbolic Mathematics in Python

## Overview

SymPy 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.

## When to Use This Skill

Use this skill when:
- Solving equations symbolically (algebraic, differential, systems of equations)
- Performing calculus operations (derivatives, integrals, limits, series)
- Manipulating and simplifying algebraic expressions
- Working with matrices and linear algebra symbolically
- Doing physics calculations (mechanics, quantum mechanics, vector analysis)
- Number theory computations (primes, factorization, modular arithmetic)
- Geometric calculations (2D/3D geometry, analytic geometry)
- Converting mathematical expressions to executable code (Python, C, Fortran)
- Generating LaTeX or other formatted mathematical output
- Needing exact mathematical results (e.g., `sqrt(2)` not `1.414...`)

## Core Capabilities

### 1. Symbolic Computation Basics

**Creating symbols and expressions:**
```python
from sympy import symbols, Symbol
x, y, z = symbols('x y z')
expr = x**2 + 2*x + 1

# With assumptions
x = symbols('x', real=True, positive=True)
n = symbols('n', integer=True)
```

**Simplification and manipulation:**
```python
from sympy import simplify, expand, factor, cancel
simplify(sin(x)**2 + cos(x)**2)  # Returns 1
expand((x + 1)**3)  # x**3 + 3*x**2 + 3*x + 1
factor(x**2 - 1)    # (x - 1)*(x + 1)
```

**For detailed basics:** See `ref

Frequently Asked Questions

FAQ

Is SymPy compatible with other Python libraries?
Yes, SymPy integrates seamlessly with NumPy and Matplotlib, and it can convert symbolic expressions into executable code for C, Fortran, and Python.
Who is the target audience for this SymPy skill?
This skill is designed for software developers, data scientists, and researchers who require exact mathematical symbolic manipulation rather than numerical approximations.
How does SymPy differ from alternatives like NumPy?
While NumPy uses numerical approximations (e.g., 1.414 for sqrt(2)), SymPy performs exact symbolic computation, keeping the expression as sqrt(2) to avoid rounding errors.
Does this skill support multiple programming languages?
SymPy is a Python-native library, but this skill provides guidance on generating mathematical output for LaTeX and source code for C and Fortran.
What results can I expect from using this skill?
You can expect to automate complex algebraic simplifications, solve differential equations, and generate precise mathematical documentation or code from symbolic expressions.

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Trigger Phrases

Use these phrases to activate this skill in your AI coding assistant:

Solve symbolic equationsSimplify algebraic expressionsPerform symbolic calculusGenerate LaTeX from PythonSymbolic linear algebra