math

SKILL.md

/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/cc_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/cc_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/cc_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/cc_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/cc_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/cc_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/cc_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/cc_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.