SKILL.md
/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 /proveExamples
Solve Equation
User: Solve x² - 5x + 6 = 0
Claude: uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/sympy_compute.py" solve "x**2 - 5*x + 6" --var x
Result: x = 2 or x = 3Compute Eigenvalues
User: Find eigenvalues of [[2, 1], [1, 2]]
Claude: uv run python "$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 kmWhen 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.