/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 "x2 + y2 >= 2xy" 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.