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Original

English
🇨🇳

Translation

Chinese

/math - Unified Math Capabilities

/math - 统一数学能力

One entry point for all computation and explanation. I route to the right tool based on your request.
For formal proofs, use 
/prove
instead.
所有计算与讲解的统一入口。我会根据你的请求匹配合适的工具。
如需形式化证明，请使用 
/prove
。

Quick Examples

快速示例

You SayI 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
你输入我使用
"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"范畴论技能

Computation Scripts

计算脚本

SymPy (Symbolic Math)

SymPy（符号数学）

bash
uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/sympy_compute.py" <command> <args>
CommandDescriptionExample
solve
Solve equations
solve "x**2 - 4" --var x
integrate
Definite/indefinite integral
integrate "sin(x)" --var x --lower 0 --upper pi
diff
Derivative
diff "x**3" --var x
simplify
Simplify expression
simplify "sin(x)**2 + cos(x)**2"
limit
Compute limit
limit "sin(x)/x" --var x --point 0
series
Taylor expansion
series "exp(x)" --var x --point 0 --n 5
dsolve
Solve ODE
dsolve "f''(x) + f(x)" --func f --var x
laplace
Laplace transform
laplace "sin(t)" --var t
Matrix Operations:
CommandDescription
det
Determinant
eigenvalues
Eigenvalues
eigenvectors
Eigenvectors with multiplicities
inverse
Matrix inverse
transpose
Transpose
rref
Row echelon form
rank
Matrix rank
nullspace
Null space basis
linsolve
Linear system Ax=b
charpoly
Characteristic polynomial
Number Theory:
CommandDescription
factor
Factor polynomial
factorint
Prime factorization
isprime
Primality test
gcd
Greatest common divisor
lcm
Least common multiple
modinverse
Modular inverse
Combinatorics:
CommandDescription
binomial
C(n,k)
factorial
n!
permutation
P(n,k)
partition
Integer partitions p(n)
catalan
Catalan numbers
bell
Bell numbers
bash
uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/sympy_compute.py" <command> <args>
命令描述示例
solve
求解方程
solve "x**2 - 4" --var x
integrate
定积分/不定积分
integrate "sin(x)" --var x --lower 0 --upper pi
diff
求导
diff "x**3" --var x
simplify
化简表达式
simplify "sin(x)**2 + cos(x)**2"
limit
计算极限
limit "sin(x)/x" --var x --point 0
series
泰勒展开
series "exp(x)" --var x --point 0 --n 5
dsolve
求解常微分方程
dsolve "f''(x) + f(x)" --func f --var x
laplace
拉普拉斯变换
laplace "sin(t)" --var t
矩阵运算：
命令描述
det
行列式
eigenvalues
特征值
eigenvectors
特征向量（含重数）
inverse
矩阵逆
transpose
转置
rref
行最简形
rank
矩阵秩
nullspace
零空间基
linsolve
线性方程组Ax=b求解
charpoly
特征多项式
数论：
命令描述
factor
多项式因式分解
factorint
素因数分解
isprime
素性测试
gcd
最大公约数
lcm
最小公倍数
modinverse
模逆元
组合数学：
命令描述
binomial
组合数C(n,k)
factorial
阶乘n!
permutation
排列数P(n,k)
partition
整数分拆p(n)
catalan
卡特兰数
bell
贝尔数

Z3 (Constraint Solving)

Z3（约束求解）

bash
uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/z3_solve.py" <command> <args>
CommandUse Case
sat
Is this satisfiable?
prove
Is this always true?
optimize
Find min/max subject to constraints
bash
uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/z3_solve.py" <command> <args>
命令使用场景
sat
判断是否可满足
prove
判断是否恒成立
optimize
带约束的极值求解

Pint (Units)

Pint（单位转换）

bash
uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/pint_compute.py" convert <value> <from_unit> <to_unit>
Example: 
convert 5 miles kilometers
bash
uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/pint_compute.py" convert <value> <from_unit> <to_unit>
示例：
convert 5 miles kilometers

Math Router (Auto-Route)

数学路由工具（自动匹配）

bash
uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/math_router.py" route "<natural language request>"
Returns the exact command to run. Use when unsure which script.
bash
uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/math_router.py" route "<natural language request>"
返回要执行的具体命令。当你不确定使用哪个脚本时使用此工具。

Topic Skills (For Explanation)

主题技能（用于讲解）

When the request is "explain X" or "what is X", I reference these:
TopicSkill LocationKey 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
当请求为“解释X”或“什么是X”时，我会参考以下内容：
主题技能位置核心概念
抽象代数
math/abstract-algebra/
群、环、域、同态
范畴论
math/category-theory/
函子、自然变换、极限
复分析
math/complex-analysis/
解析函数、留数、围道积分
泛函分析
math/functional-analysis/
巴拿赫空间、算子、谱
线性代数
math/linear-algebra/
矩阵、特征空间、分解
数理逻辑
math/mathematical-logic/
命题逻辑、谓词逻辑、证明论
测度论
math/measure-theory/
勒贝格测度、σ-代数、积分
实分析
math/real-analysis/
极限、连续性、收敛性
拓扑学
math/topology/
开集、紧性、连通性
常微分方程/偏微分方程
math/odes-pdes/
微分方程、边值问题
优化理论
math/optimization/
凸优化、线性规划、梯度方法
数值方法
math/numerical-methods/
近似计算、误差分析
图论/数论
math/graph-number-theory/
图、素数、模算术
信息论
math/information-theory/
熵、编码、信道

Routing Logic

路由逻辑

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
我会根据你的请求做出判断：
"solve/calculate/compute" → SymPy（精确符号计算）
"is X always true?" → Z3（约束证明）
"convert units" → Pint
"explain/what is" → 主题技能（提供上下文）
"prove formally" → 重定向到 /prove

Examples

示例

Solve Equation

求解方程

User: Solve x² - 5x + 6 = 0
Claude: uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/sympy_compute.py" solve "x**2 - 5*x + 6" --var x
Result: x = 2 or x = 3
用户：Solve x² - 5x + 6 = 0
Claude: uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/sympy_compute.py" solve "x**2 - 5*x + 6" --var x
结果：x = 2 或 x = 3

Compute Eigenvalues

计算特征值

User: Find eigenvalues of [[2, 1], [1, 2]]
Claude: uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/sympy_compute.py" eigenvalues "[[2,1],[1,2]]"
Result: {1: 1, 3: 1}  (eigenvalue 1 with multiplicity 1, eigenvalue 3 with multiplicity 1)
用户：Find eigenvalues of [[2, 1], [1, 2]]
Claude: uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/sympy_compute.py" eigenvalues "[[2,1],[1,2]]"
结果：{1: 1, 3: 1} （特征值1的重数为1，特征值3的重数为1）

Prove Inequality

证明不等式

User: Is x² + y² ≥ 2xy always true?
Claude: uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/z3_solve.py" prove "x**2 + y**2 >= 2*x*y"
Result: PROVED (equivalent to (x-y)² ≥ 0)
用户：Is x² + y² ≥ 2xy always true?
Claude: uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/z3_solve.py" prove "x**2 + y**2 >= 2*x*y"
结果：PROVED（等价于(x-y)² ≥ 0）

Convert Units

单位转换

User: How many kilometers in 26.2 miles?
Claude: uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/pint_compute.py" convert 26.2 miles kilometers
Result: 42.16 km
用户：26.2英里等于多少公里？
Claude: uv run python "$CLAUDE_PROJECT_DIR/.claude/scripts/cc_math/pint_compute.py" convert 26.2 miles kilometers
结果：42.16 km

When to Use /prove Instead

何时使用 /prove 替代

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.
当你需要以下功能时，使用 
/prove
：
  • 机器验证的形式化证明（Lean 4）
  • 范畴论证明（函子、米田引理等）
  • 可用于发表的验证结果
  • 抽象代数证明
/math
用于计算，
/prove
用于验证。