math

/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.

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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 |

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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 |

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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 |

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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

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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.

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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 |

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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

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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

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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.