foryourhealth111-pixel/math
bundled/skills/math/SKILL.md
Unified math capabilities - computation, solving, and explanation. I route to the right tool.
$ install --global
skillsauthnpx skillsauth add foryourhealth111-pixel/vco-skills-codex mathInstall this skill globally with one command. Works with Claude Code, Cursor, and Windsurf.
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SKILL.md
- 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.
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 "$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/sympy_compute.py" <command> <args>
| Command | Description | Example |
|---------|-------------|---------|
| solve | Solve equations | solve "x**2 - 4" --var x |
| integrate | Definite/indefinite integral | integrate "sin(x)" --var x --lower 0 --upper pi |
| diff | Derivative | diff "x**3" --var x |
| simplify | Simplify expression | simplify "sin(x)**2 + cos(x)**2" |
| limit | Compute limit | limit "sin(x)/x" --var x --point 0 |
| series | Taylor expansion | series "exp(x)" --var x --point 0 --n 5 |
| dsolve | Solve ODE | dsolve "f''(x) + f(x)" --func f --var x |
| laplace | Laplace transform | laplace "sin(t)" --var t |
Matrix Operations:
| Command | Description |
|---------|-------------|
| det | Determinant |
| eigenvalues | Eigenvalues |
| eigenvectors | Eigenvectors with multiplicities |
| inverse | Matrix inverse |
| transpose | Transpose |
| rref | Row echelon form |
| rank | Matrix rank |
| nullspace | Null space basis |
| linsolve | Linear system Ax=b |
| charpoly | Characteristic polynomial |
Number Theory:
| Command | Description |
|---------|-------------|
| factor | Factor polynomial |
| factorint | Prime factorization |
| isprime | Primality test |
| gcd | Greatest common divisor |
| lcm | Least common multiple |
| modinverse | Modular inverse |
Combinatorics:
| Command | Description |
|---------|-------------|
| binomial | C(n,k) |
| factorial | n! |
| permutation | P(n,k) |
| partition | Integer partitions p(n) |
| catalan | Catalan numbers |
| bell | Bell numbers |
Z3 (Constraint Solving)
uv run python "$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 |
Pint (Units)
uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/pint_compute.py" convert <value> <from_unit> <to_unit>
Example: convert 5 miles kilometers
Math Router (Auto-Route)
uv run python "$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.
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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