rubicanjr/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.