/math-unified

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.

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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 `/prov