--- id: sm-math name: "math" url: https://skills.yangsir.net/skill/sm-math author: parcadei domain: science tags: ["mathematics", "numerical-computation", "problem-solving", "scientific-computing"] install_count: 574 rating: 4.20 (22 reviews) github: https://github.com/parcadei/continuous-claude-v3 --- # math > 提供统一的数学计算和解释能力，根据用户请求路由到合适的工具，支持各种数学任务。 **Stats**: 574 installs · 4.2/5 (22 reviews) ## Before / After 对比 ### 统一数学计算能力，高效解决各类问题。 ## Readme # 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. ## 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 "$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/sympy_compute.py" ``` Command Description Example `solve` Solve equations `solve "x**2 - 4" --var x` `integrate` Definite/indefinite integral `integrate "sin(x)" --var x --lower 0 --upper pi` `diff` Derivative `diff "x**3" --var x` `simplify` Simplify expression `simplify "sin(x)**2 + cos(x)**2"` `limit` Compute limit `limit "sin(x)/x" --var x --point 0` `series` Taylor expansion `series "exp(x)" --var x --point 0 --n 5` `dsolve` Solve ODE `dsolve "f''(x) + f(x)" --func f --var x` `laplace` Laplace transform `laplace "sin(t)" --var t` **Matrix Operations:** Command Description `det` Determinant `eigenvalues` Eigenvalues `eigenvectors` Eigenvectors with multiplicities `inverse` Matrix inverse `transpose` Transpose `rref` Row echelon form `rank` Matrix rank `nullspace` Null space basis `linsolve` Linear system Ax=b `charpoly` Characteristic polynomial **Number Theory:** Command Description `factor` Factor polynomial `factorint` Prime factorization `isprime` Primality test `gcd` Greatest common divisor `lcm` Least common multiple `modinverse` Modular inverse **Combinatorics:** Command Description `binomial` C(n,k) `factorial` n! `permutation` P(n,k) `partition` Integer partitions p(n) `catalan` Catalan numbers `bell` Bell numbers ### Z3 (Constraint Solving) ``` uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/z3_solve.py" ``` Command Use Case `sat` Is this satisfiable? `prove` Is this always true? `optimize` Find min/max subject to constraints ### Pint (Units) ``` uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/pint_compute.py" convert ``` Example: `convert 5 miles kilometers` ### Math Router (Auto-Route) ``` uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/math_router.py" route "" ``` 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 "$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/z3_solve.py" prove "x**2 + y**2 >= 2*x*y" Result: PROVED (equivalent to (x-y)² ≥ 0) ``` ### Convert Units ``` User: How many kilometers in 26.2 miles? Claude: uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/pint_compute.py" convert 26.2 miles kilometers Result: 42.16 km ``` ## 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. 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