{"id":"math-unified","name":"math","summary":"統合数学能力 - 計算、解法、説明。正しいツールにルーティングします。","body":"# /math - Unified Math Capabilities\n\n**One entry point for all computation and explanation.** I route to the right tool based on your request.\n\nFor formal proofs, use `/prove` instead.\n\n---\n\n## Quick Examples\n\n| You Say | I Use |\n|---------|-------|\n| \"Solve x² - 4 = 0\" | SymPy solve |\n| \"Integrate sin(x) from 0 to π\" | SymPy integrate |\n| \"Eigenvalues of [[1,2],[3,4]]\" | SymPy eigenvalues |\n| \"Is x² + 1 > 0 for all x?\" | Z3 prove |\n| \"Convert 5 miles to km\" | Pint |\n| \"Explain what a functor is\" | Category theory skill |\n\n---\n\n## Computation Scripts\n\n### SymPy (Symbolic Math)\n```bash\nuv run python \"$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/sympy_compute.py\" <command> <args>\n```\n\n| Command | Description | Example |\n|---------|-------------|---------|\n| `solve` | Solve equations | `solve \"x**2 - 4\" --var x` |\n| `integrate` | Definite/indefinite integral | `integrate \"sin(x)\" --var x --lower 0 --upper pi` |\n| `diff` | Derivative | `diff \"x**3\" --var x` |\n| `simplify` | Simplify expression | `simplify \"sin(x)**2 + cos(x)**2\"` |\n| `limit` | Compute limit | `limit \"sin(x)/x\" --var x --point 0` |\n| `series` | Taylor expansion | `series \"exp(x)\" --var x --point 0 --n 5` |\n| `dsolve` | Solve ODE | `dsolve \"f''(x) + f(x)\" --func f --var x` |\n| `laplace` | Laplace transform | `laplace \"sin(t)\" --var t` |\n\n**Matrix Operations:**\n| Command | Description |\n|---------|-------------|\n| `det` | Determinant |\n| `eigenvalues` | Eigenvalues |\n| `eigenvectors` | Eigenvectors with multiplicities |\n| `inverse` | Matrix inverse |\n| `transpose` | Transpose |\n| `rref` | Row echelon form |\n| `rank` | Matrix rank |\n| `nullspace` | Null space basis |\n| `linsolve` | Linear system Ax=b |\n| `charpoly` | Characteristic polynomial |\n\n**Number Theory:**\n| Command | Description |\n|---------|-------------|\n| `factor` | Factor polynomial |\n| `factorint` | Prime factorization |\n| `isprime` | Primality test |\n| `gcd` | Greatest common divisor |\n| `lcm` | Least common multiple |\n| `modinverse` | Modular inverse |\n\n**Combinatorics:**\n| Command | Description |\n|---------|-------------|\n| `binomial` | C(n,k) |\n| `factorial` | n! |\n| `permutation` | P(n,k) |\n| `partition` | Integer partitions p(n) |\n| `catalan` | Catalan numbers |\n| `bell` | Bell numbers |\n\n---\n\n### Z3 (Constraint Solving)\n```bash\nuv run python \"$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/z3_solve.py\" <command> <args>\n```\n\n| Command | Use Case |\n|---------|----------|\n| `sat` | Is this satisfiable? |\n| `prove` | Is this always true? |\n| `optimize` | Find min/max subject to constraints |\n\n---\n\n### Pint (Units)\n```bash\nuv run python \"$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/pint_compute.py\" convert <value> <from_unit> <to_unit>\n```\n\nExample: `convert 5 miles kilometers`\n\n---\n\n### Math Router (Auto-Route)\n```bash\nuv run python \"$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/math_router.py\" route \"<natural language request>\"\n```\n\nReturns the exact command to run. Use when unsure which script.\n\n---\n\n## Topic Skills (For Explanation)\n\nWhen the request is \"explain X\" or \"what is X\", I reference these:\n\n| Topic | Skill Location | Key Concepts |\n|-------|----------------|--------------|\n| **Abstract Algebra** | `math/abstract-algebra/` | Groups, rings, fields, homomorphisms |\n| **Category Theory** | `math/category-theory/` | Functors, natural transformations, limits |\n| **Complex Analysis** | `math/complex-analysis/` | Analytic functions, residues, contour integrals |\n| **Functional Analysis** | `math/functional-analysis/` | Banach spaces, operators, spectra |\n| **Linear Algebra** | `math/linear-algebra/` | Matrices, eigenspaces, decompositions |\n| **Mathematical Logic** | `math/mathematical-logic/` | Propositional, predicate, proof theory |\n| **Measure Theory** | `math/measure-theory/` | Lebesgue, σ-algebras, integration |\n| **Real Analysis** | `math/real-analysis/` | Limits, continuity, convergence |\n| **Topology** | `math/topology/` | Open sets, compactness, connectedness |\n| **ODEs/PDEs** | `math/odes-pdes/` | Differential equations, boundary problems |\n| **Optimization** | `math/optimization/` | Convex, LP, gradient methods |\n| **Numerical Methods** | `math/numerical-methods/` | Approximation, error analysis |\n| **Graph/Number Theory** | `math/graph-number-theory/` | Graphs, primes, modular arithmetic |\n| **Information Theory** | `math/information-theory/` | Entropy, coding, channels |\n\n---\n\n## Routing Logic\n\nI decide based on your request:\n\n```\n\"solve/calculate/compute\" → SymPy (exact symbolic)\n\"is X always true?\" → Z3 (constraint proving)\n\"convert units\" → Pint\n\"explain/what is\" → Topic skill for context\n\"prove formally\" → Redirect to /prove\n```\n\n---\n\n## Examples\n\n### Solve Equation\n```\nUser: Solve x² - 5x + 6 = 0\nClaude: uv run python \"$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/sympy_compute.py\" solve \"x**2 - 5*x + 6\" --var x\nResult: x = 2 or x = 3\n```\n\n### Compute Eigenvalues\n```\nUser: Find eigenvalues of [[2, 1], [1, 2]]\nClaude: uv run python \"$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/sympy_compute.py\" eigenvalues \"[[2,1],[1,2]]\"\nResult: {1: 1, 3: 1}  (eigenvalue 1 with multiplicity 1, eigenvalue 3 with multiplicity 1)\n```\n\n### Prove Inequality\n```\nUser: Is x² + y² ≥ 2xy always true?\nClaude: uv run python \"$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/z3_solve.py\" prove \"x**2 + y**2 >= 2*x*y\"\nResult: PROVED (equivalent to (x-y)² ≥ 0)\n```\n\n### Convert Units\n```\nUser: How many kilometers in 26.2 miles?\nClaude: uv run python \"$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/pint_compute.py\" convert 26.2 miles kilometers\nResult: 42.16 km\n```\n\n---\n\n## When to Use /prove Instead\n\nUse `/prove` when you need:\n- Machine-verified formal proof (Lean 4)\n- Category theory proofs (functors, Yoneda, etc.)\n- Publication-quality verification\n- Abstract algebra proofs\n\n`/math` is for computation. `/prove` is for verification.","author":"@parcadei","ownerProfile":null,"authorContacts":null,"sourceUrl":"https://github.com/parcadei/Continuous-Claude-v3/tree/main/.claude/skills/math-unified","license":"MIT","category":"coding","lang":"en","tokens":1717,"stars":0,"calls30d":1,"claimed":false,"visibility":"public","origin":"crawler","version":"0.1.0","createdAt":"2026-08-22","updatedAt":"2026-08-22","files":[],"requires":{"mcp":[],"tools":["Bash","Read","Write"]},"safety":{"flags":[],"scannedAt":"2026-08-22","hasScripts":false,"networkEndpoints":[]}}