sympy

name	sympy
description	Use this skill when working with symbolic mathematics in Python. This skill should be used for symbolic computation tasks including solving equations algebraically, performing calculus operations (derivatives, integrals, limits), manipulating algebraic expressions, working with matrices symbolically, physics calculations, number theory problems, geometry computations, and generating executable code from mathematical expressions. Apply this skill when the user needs exact symbolic results rather than numerical approximations, or when working with mathematical formulas that contain variables and parameters.
license	https://github.com/sympy/sympy/blob/master/LICENSE
metadata	{"skill-author":"K-Dense Inc."}
verified	false
lastVerifiedAt	"2026-02-19T05:29:09.098Z"
source	builtin
trust_score	100
provenance_sha	29078f63676402f7

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:

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:

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)