---
id: sm-math-help
name: "math-help"
url: https://skills.yangsir.net/skill/sm-math-help
author: parcadei
domain: education
tags: ["algebra", "calculus", "geometry", "statistics", "mathematical-problem-solving"]
install_count: 405
rating: 4.20 (22 reviews)
github: https://github.com/parcadei/continuous-claude-v3
---

# math-help

> 提供数学计算辅助，指导用户选择合适的工具来解决各种数学任务。

**Stats**: 405 installs · 4.2/5 (22 reviews)

## Before / After 对比

### 优化数学问题解决流程与工具选择

## Readme

# math-help

# Math Cognitive Stack Guide

Cognitive prosthetics for exact mathematical computation. This guide helps you choose the right tool for your math task.

## Quick Reference

I want to...
Use this
Example

Solve equations
sympy_compute.py solve
`solve "x**2 - 4 = 0" --var x`

Integrate/differentiate
sympy_compute.py
`integrate "sin(x)" --var x`

Compute limits
sympy_compute.py limit
`limit "sin(x)/x" --var x --to 0`

Matrix operations
sympy_compute.py / numpy_compute.py
`det "[[1,2],[3,4]]"`

Verify a reasoning step
math_scratchpad.py verify
`verify "x = 2 implies x^2 = 4"`

Check a proof chain
math_scratchpad.py chain
`chain --steps '[...]'`

Get progressive hints
math_tutor.py hint
`hint "Solve x^2 - 4 = 0" --level 2`

Generate practice problems
math_tutor.py generate
`generate --topic algebra --difficulty 2`

Prove a theorem (constraints)
z3_solve.py prove
`prove "x + y == y + x" --vars x y`

Check satisfiability
z3_solve.py sat
`sat "x > 0, x < 10, x*x == 49"`

Optimize with constraints
z3_solve.py optimize
`optimize "x + y" --constraints "..."`

Plot 2D/3D functions
math_plot.py
`plot2d "sin(x)" --range -10 10`

Arbitrary precision
mpmath_compute.py
`pi --dps 100`

Numerical optimization
scipy_compute.py
`minimize "x**2 + 2*x" "5"`

Formal machine proof
Lean 4 (lean4 skill)
`/lean4`

## The Five Layers

### Layer 1: SymPy (Symbolic Algebra)

**When:** Exact algebraic computation - solving, calculus, simplification, matrix algebra.

**Key Commands:**

```
# Solve equation
uv run python -m runtime.harness scripts/sympy_compute.py \
    solve "x**2 - 5*x + 6 = 0" --var x --domain real

# Integrate
uv run python -m runtime.harness scripts/sympy_compute.py \
    integrate "sin(x)" --var x

# Definite integral
uv run python -m runtime.harness scripts/sympy_compute.py \
    integrate "x**2" --var x --bounds 0 1

# Differentiate (2nd order)
uv run python -m runtime.harness scripts/sympy_compute.py \
    diff "x**3" --var x --order 2

# Simplify (trig strategy)
uv run python -m runtime.harness scripts/sympy_compute.py \
    simplify "sin(x)**2 + cos(x)**2" --strategy trig

# Limit
uv run python -m runtime.harness scripts/sympy_compute.py \
    limit "sin(x)/x" --var x --to 0

# Matrix eigenvalues
uv run python -m runtime.harness scripts/sympy_compute.py \
    eigenvalues "[[1,2],[3,4]]"

```

**Best For:** Closed-form solutions, calculus, exact algebra.

### Layer 2: Z3 (Constraint Solving & Theorem Proving)

**When:** Proving theorems, checking satisfiability, constraint optimization.

**Key Commands:**

```
# Prove commutativity
uv run python -m runtime.harness scripts/cc_math/z3_solve.py \
    prove "x + y == y + x" --vars x y --type int

# Check satisfiability
uv run python -m runtime.harness scripts/cc_math/z3_solve.py \
    sat "x > 0, x < 10, x*x == 49" --type int

# Optimize
uv run python -m runtime.harness scripts/cc_math/z3_solve.py \
    optimize "x + y" --constraints "x >= 0, y >= 0, x + y <= 100" \
    --direction maximize --type real

```

**Best For:** Logical proofs, constraint satisfaction, optimization with constraints.

### Layer 3: Math Scratchpad (Reasoning Verification)

**When:** Verifying step-by-step reasoning, checking derivation chains.

**Key Commands:**

```
# Verify single step
uv run python -m runtime.harness scripts/cc_math/math_scratchpad.py \
    verify "x = 2 implies x^2 = 4"

# Verify with context
uv run python -m runtime.harness scripts/cc_math/math_scratchpad.py \
    verify "x^2 = 4" --context '{"x": 2}'

# Verify chain of reasoning
uv run python -m runtime.harness scripts/cc_math/math_scratchpad.py \
    chain --steps '["x^2 - 4 = 0", "(x-2)(x+2) = 0", "x = 2 or x = -2"]'

# Explain a step
uv run python -m runtime.harness scripts/cc_math/math_scratchpad.py \
    explain "d/dx(x^3) = 3*x^2"

```

**Best For:** Checking your work, validating derivations, step-by-step verification.

### Layer 4: Math Tutor (Educational)

**When:** Learning, getting hints, generating practice problems.

**Key Commands:**

```
# Step-by-step solution
uv run python scripts/cc_math/math_tutor.py steps "x**2 - 5*x + 6 = 0" --operation solve

# Progressive hint (level 1-5)
uv run python scripts/cc_math/math_tutor.py hint "Solve x**2 - 4 = 0" --level 2

# Generate practice problem
uv run python scripts/cc_math/math_tutor.py generate --topic algebra --difficulty 2

```

**Best For:** Learning, tutoring, practice.

### Layer 5: Lean 4 (Formal Proofs)

**When:** Rigorous machine-verified mathematical proofs, category theory, type theory.

**Access:** Use `/lean4` skill for full documentation.

**Best For:** Publication-grade proofs, dependent types, category theory.

## Numerical Tools

For numerical (not symbolic) computation:

### NumPy (160 functions)

```
# Matrix operations
uv run python scripts/cc_math/numpy_compute.py det "[[1,2],[3,4]]"
uv run python scripts/cc_math/numpy_compute.py inv "[[1,2],[3,4]]"
uv run python scripts/cc_math/numpy_compute.py eig "[[1,2],[3,4]]"
uv run python scripts/cc_math/numpy_compute.py svd "[[1,2,3],[4,5,6]]"

# Solve linear system
uv run python scripts/cc_math/numpy_compute.py solve "[[3,1],[1,2]]" "[9,8]"

```

### SciPy (289 functions)

```
# Minimize function
uv run python scripts/cc_math/scipy_compute.py minimize "x**2 + 2*x" "5"

# Find root
uv run python scripts/cc_math/scipy_compute.py root "x**3 - x - 2" "1.5"

# Curve fitting
uv run python scripts/cc_math/scipy_compute.py curve_fit "a*exp(-b*x)" "0,1,2,3" "1,0.6,0.4,0.2" "1,0.5"

```

### mpmath (153 functions, arbitrary precision)

```
# Pi to 100 decimal places
uv run python scripts/cc_math/mpmath_compute.py pi --dps 100

# Arbitrary precision sqrt
uv run python -m scripts.mpmath_compute mp_sqrt "2" --dps 100

```

## Visualization

### math_plot.py

```
# 2D plot
uv run python scripts/cc_math/math_plot.py plot2d "sin(x)" \
    --var x --range -10 10 --output plot.png

# 3D surface
uv run python scripts/cc_math/math_plot.py plot3d "x**2 + y**2" \
    --xvar x --yvar y --range 5 --output surface.html

# Multiple functions
uv run python scripts/cc_math/math_plot.py plot2d-multi "sin(x),cos(x)" \
    --var x --range -6.28 6.28 --output multi.png

# LaTeX rendering
uv run python scripts/cc_math/math_plot.py latex "\\int e^{-x^2} dx" --output equation.png

```

## Educational Features

### 5-Level Hint System

Level
Category
What You Get

1
Conceptual
General direction, topic identification

2
Strategic
Approach to use, technique selection

3
Tactical
Specific steps, intermediate goals

4
Computational
Intermediate results, partial solutions

5
Answer
Full solution with explanation

**Usage:**

```
# Start with conceptual hint
uv run python scripts/cc_math/math_tutor.py hint "integrate x*sin(x)" --level 1

# Get more specific guidance
uv run python scripts/cc_math/math_tutor.py hint "integrate x*sin(x)" --level 3

```

### Step-by-Step Solutions

```
uv run python scripts/cc_math/math_tutor.py steps "x**2 - 5*x + 6 = 0" --operation solve

```

Returns structured steps with:

- Step number and type

- From/to expressions

- Rule applied

- Justification

## Common Workflows

### Workflow 1: Solve and Verify

- Solve with sympy_compute.py

- Verify solution with math_scratchpad.py

- Plot to visualize (optional)

```
# Solve
uv run python -m runtime.harness scripts/sympy_compute.py \
    solve "x**2 - 4 = 0" --var x

# Verify the solutions work
uv run python -m runtime.harness scripts/cc_math/math_scratchpad.py \
    verify "x = 2 implies x^2 - 4 = 0"

```

### Workflow 2: Learn a Concept

- Generate practice problem with math_tutor.py

- Use progressive hints (level 1, then 2, etc.)

- Get full solution if stuck

```
# Generate problem
uv run python scripts/cc_math/math_tutor.py generate --topic calculus --difficulty 2

# Get hints progressively
uv run python scripts/cc_math/math_tutor.py hint "..." --level 1
uv run python scripts/cc_math/math_tutor.py hint "..." --level 2

# Full solution
uv run python scripts/cc_math/math_tutor.py steps "..." --operation integrate

```

### Workflow 3: Prove and Formalize

- Check theorem with z3_solve.py (constraint-level proof)

- If rigorous proof needed, use Lean 4

```
# Quick check with Z3
uv run python -m runtime.harness scripts/cc_math/z3_solve.py \
    prove "x*y == y*x" --vars x y --type int

# For formal proof, use /lean4 skill

```

## Choosing the Right Tool

```
Is it SYMBOLIC (exact answers)?
  └─ Yes → Use SymPy
      ├─ Equations → sympy_compute.py solve
      ├─ Calculus → sympy_compute.py integrate/diff/limit
      └─ Simplify → sympy_compute.py simplify

Is it a PROOF or CONSTRAINT problem?
  └─ Yes → Use Z3
      ├─ True/False theorem → z3_solve.py prove
      ├─ Find values → z3_solve.py sat
      └─ Optimize → z3_solve.py optimize

Is it NUMERICAL (approximate answers)?
  └─ Yes → Use NumPy/SciPy
      ├─ Linear algebra → numpy_compute.py
      ├─ Optimization → scipy_compute.py minimize
      └─ High precision → mpmath_compute.py

Need to VERIFY reasoning?
  └─ Yes → Use Math Scratchpad
      ├─ Single step → math_scratchpad.py verify
      └─ Chain → math_scratchpad.py chain

Want to LEARN/PRACTICE?
  └─ Yes → Use Math Tutor
      ├─ Hints → math_tutor.py hint
      └─ Practice → math_tutor.py generate

Need MACHINE-VERIFIED formal proof?
  └─ Yes → Use Lean 4 (see /lean4 skill)

```

## Related Skills

- `/math` or `/math-mode` - Quick access to the orchestration skill

- `/lean4` - Formal theorem proving with Lean 4

- `/lean4-functors` - Category theory functors

- `/lean4-nat-trans` - Natural transformations

- `/lean4-limits` - Limits and colimits

## Requirements

All math scripts are installed via:

```
uv sync

```

Dependencies: sympy, z3-solver, numpy, scipy, mpmath, matplotlib, plotly
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---
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