/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.