# sympy

> Symbolic mathematics in Python — use for algebraic equation solving, calculus operations (derivatives, integrals, limits), matrix manipulation, physics calculations, and generating executable code from mathematical expressions when exact symbolic results are needed.

**Use case**: Symbolic algebra, calculus, and exact mathematical computation

**Canonical URL**: https://agentcookbooks.com/skills/sympy/

**Topics**: claude-code, skills, science, data-science

**Trigger phrases**: "solve this equation symbolically", "take the derivative of", "compute this integral", "simplify this expression", "sympy calculation"

**Source**: [K-Dense AI](https://github.com/K-Dense-AI/scientific-agent-skills/tree/main/scientific-skills/sympy)

**License**: MIT

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## What it does

`sympy` is a Claude Code skill from K-Dense AI's [scientific-agent-skills repo](https://github.com/K-Dense-AI/scientific-agent-skills). It turns Claude into a SymPy expert for symbolic computation — solving equations algebraically, computing derivatives and integrals exactly, expanding and factoring expressions, working with matrices symbolically, number theory, geometry, and generating `lambdify` code that converts symbolic expressions into fast numerical functions.

A session produces verified symbolic results: exact closed-form answers rather than numerical approximations, with optional code generation to evaluate the expression numerically at specific values.

## When to use it

Reach for it when:

- You need an exact symbolic answer — a formula, not a floating-point number
- You're deriving gradients or Jacobians for optimization problems and want the exact expression before numerical evaluation
- You're checking whether a complex algebraic expression simplifies to a known form

When *not* to reach for it:

- Pure numerical computation where floating-point precision is acceptable — numpy/scipy are faster
- Statistical modeling or data analysis — this is a pure mathematics tool

## Install

Copy the `SKILL.md` from K-Dense AI's [sympy folder](https://github.com/K-Dense-AI/scientific-agent-skills/tree/main/scientific-skills/sympy) into `.claude/skills/sympy/` in your project.

Trigger phrases: "solve this equation symbolically", "take the derivative of", "compute this integral", "simplify this expression".

## What a session looks like

A typical session has three phases:

1. **Expression setup.** Describe the mathematical problem — equation to solve, expression to differentiate or integrate, or matrix to analyze. Claude sets up the SymPy symbolic variables and expressions.
2. **Symbolic computation.** The requested operation runs: `sympy.solve()`, `sympy.diff()`, `sympy.integrate()`, `sympy.simplify()`, or the appropriate algebra or calculus function. Claude shows intermediate steps for complex derivations.
3. **Code and verification.** The result is returned in both human-readable LaTeX and executable SymPy code. For expressions that will be evaluated numerically, Claude generates a `lambdify` wrapper for fast numerical evaluation.

## Receipts

**Where it works well:**
- Gradient derivation for custom loss functions — SymPy produces the exact gradient expression that can then be verified against automatic differentiation results
- Definite integral evaluation for probability density functions — SymPy handles many integrals that require Mathematica or hours of hand calculation otherwise

**Where it backfires:**
- Very complex integrals that have no closed form — SymPy returns the input unevaluated rather than notifying you that numerical integration is the right approach
- Performance: symbolic simplification can be slow for large expressions; Claude doesn't always warn about this upfront

**Pattern that works:** always call `sympy.simplify()` or `sympy.trigsimp()` on the result — SymPy often returns correct but unsimplified expressions that look more complex than they are.

## Source and attribution

Originally authored by [K-Dense Inc.](https://github.com/K-Dense-AI). The canonical SKILL.md lives in the [`sympy` folder](https://github.com/K-Dense-AI/scientific-agent-skills/tree/main/scientific-skills/sympy) of their public scientific-agent-skills repository.

License: MIT. Install, adapt, and redistribute with attribution preserved.

This page documents the skill from a practitioner's perspective. For the formal spec and any updates, defer to the source repo.