name	math
description	Unified math capabilities - computation, solving, and explanation. I route to the right tool.
triggers	calculate, compute, solve, integrate, derivative, eigenvalue, matrix, simplify, factor, limit, series, differential equation, unit convert, explain, what is, how does
allowed-tools	Bash, Read, Write
priority	high

/math - Unified Math Capabilities

One entry point for all computation and explanation. I route to the right tool based on your request.

For formal proofs, use /prove instead.

Quick Examples

You Say	I Use
"Solve x² - 4 = 0"	SymPy solve
"Integrate sin(x) from 0 to π"	SymPy integrate
"Eigenvalues of [[1,2],[3,4]]"	SymPy eigenvalues
"Is x² + 1 > 0 for all x?"	Z3 prove
"Convert 5 miles to km"	Pint
"Explain what a functor is"	Category theory skill

Computation Scripts

SymPy (Symbolic Math)

uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/math/sympy_compute.py" <command> <args>

Command	Description	Example
`solve`	Solve equations	`solve "x**2 - 4" --var x`
`integrate`	Definite/indefinite integral	`integrate "sin(x)" --var x --lower 0 --upper pi`
`diff`	Derivative	`diff "x**3" --var x`
`simplify`	Simplify expression	`simplify "sin(x)2 + cos(x)2"`
`limit`	Compute limit	`limit "sin(x)/x" --var x --point 0`
`series`	Taylor expansion	`series "exp(x)" --var x --point 0 --n 5`
`dsolve`	Solve ODE	`dsolve "f''(x) + f(x)" --func f --var x`
`laplace`	Laplace transform	`laplace "sin(t)" --var t`

Matrix Operations:

Command	Description
`det`	Determinant
`eigenvalues`	Eigenvalues
`eigenvectors`	Eigenvectors with multiplicities
`inverse`	Matrix inverse
`transpose`	Transpose
`rref`	Row echelon form
`rank`	Matrix rank
`nullspace`	Null space basis
`linsolve`	Linear system Ax=b
`charpoly`	Characteristic polynomial

Number Theory:

Command	Description
`factor`	Factor polynomial
`factorint`	Prime factorization
`isprime`	Primality test
`gcd`	Greatest common divisor
`lcm`	Least common multiple
`modinverse`	Modular inverse

Combinatorics:

Command	Description
`binomial`	C(n,k)
`factorial`	n!
`permutation`	P(n,k)
`partition`	Integer partitions p(n)
`catalan`	Catalan numbers
`bell`	Bell numbers

Z3 (Constraint Solving)

uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/math/z3_solve.py" <command> <args>

Command	Use Case
`sat`	Is this satisfiable?
`prove`	Is this always true?
`optimize`	Find min/max subject to constraints

Pint (Units)

uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/math/pint_compute.py" convert <value> <from_unit> <to_unit>

Example: convert 5 miles kilometers

Math Router (Auto-Route)

uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/math/math_router.py" route "<natural language request>"

Returns the exact command to run. Use when unsure which script.

Topic Skills (For Explanation)

When the request is "explain X" or "what is X", I reference these:

Topic	Skill Location	Key Concepts
Abstract Algebra	`math/abstract-algebra/`	Groups, rings, fields, homomorphisms
Category Theory	`math/category-theory/`	Functors, natural transformations, limits
Complex Analysis	`math/complex-analysis/`	Analytic functions, residues, contour integrals
Functional Analysis	`math/functional-analysis/`	Banach spaces, operators, spectra
Linear Algebra	`math/linear-algebra/`	Matrices, eigenspaces, decompositions
Mathematical Logic	`math/mathematical-logic/`	Propositional, predicate, proof theory
Measure Theory	`math/measure-theory/`	Lebesgue, σ-algebras, integration
Real Analysis	`math/real-analysis/`	Limits, continuity, convergence
Topology	`math/topology/`	Open sets, compactness, connectedness
ODEs/PDEs	`math/odes-pdes/`	Differential equations, boundary problems
Optimization	`math/optimization/`	Convex, LP, gradient methods
Numerical Methods	`math/numerical-methods/`	Approximation, error analysis
Graph/Number Theory	`math/graph-number-theory/`	Graphs, primes, modular arithmetic
Information Theory	`math/information-theory/`	Entropy, coding, channels

Routing Logic

I decide based on your request:

"solve/calculate/compute" → SymPy (exact symbolic)
"is X always true?" → Z3 (constraint proving)
"convert units" → Pint
"explain/what is" → Topic skill for context
"prove formally" → Redirect to /prove

Examples

Solve Equation

User: Solve x² - 5x + 6 = 0
Claude: uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/math/sympy_compute.py" solve "x**2 - 5*x + 6" --var x
Result: x = 2 or x = 3

Compute Eigenvalues

User: Find eigenvalues of [[2, 1], [1, 2]]
Claude: uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/math/sympy_compute.py" eigenvalues "[[2,1],[1,2]]"
Result: {1: 1, 3: 1}  (eigenvalue 1 with multiplicity 1, eigenvalue 3 with multiplicity 1)

Prove Inequality

User: Is x² + y² ≥ 2xy always true?
Claude: uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/math/z3_solve.py" prove "x**2 + y**2 >= 2*x*y"
Result: PROVED (equivalent to (x-y)² ≥ 0)

Convert Units

User: How many kilometers in 26.2 miles?
Claude: uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/math/pint_compute.py" convert 26.2 miles kilometers
Result: 42.16 km

When to Use /prove Instead

Use /prove when you need:

Machine-verified formal proof (Lean 4)
Category theory proofs (functors, Yoneda, etc.)
Publication-quality verification
Abstract algebra proofs

/math is for computation. /prove is for verification.

math

Install Skill

SKILL.md