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math-help

Guide to the math cognitive stack - what tools exist and when to use each

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vibeeval/vibecosystem

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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 + 2x" "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

리뷰

아직 리뷰가 없습니다. 사용해 본 소감을 남겨 주세요.

로그인 없이 쓸 수 있습니다. 사용 후기, 질문, 작동하지 않은 환경 등을 편하게 남겨 주세요.

아직 댓글이 없습니다. 첫 댓글을 남겨 보세요.

같은 저장소의 스킬

accessibility-patterns

무료

WCAG 2.2 AA compliance, ARIA patterns, keyboard navigation, screen reader optimization

한국어 요약은 준비 중입니다. 원문 설명을 표시하고 있습니다.

vibeeval/vibecosystem5382026년 8월 9일 업데이트

accessibility-testing

무료

axe-core integration, WCAG 2.2 AA checklist, keyboard navigation testing, screen reader testing, and ARIA pattern validation.

한국어 요약은 준비 중입니다. 원문 설명을 표시하고 있습니다.

vibeeval/vibecosystem5382026년 8월 9일 업데이트

achievements

무료

Steam-style achievement system with XP, levels, streaks, and skill trees. Gamifies the development workflow. 25 achievements across 5 categories.

한국어 요약은 준비 중입니다. 원문 설명을 표시하고 있습니다.

vibeeval/vibecosystem5382026년 8월 9일 업데이트

Framework for measuring and tracking agent response quality over time. Detects regressions before they reach production. Use when evaluating agent changes, auditing quality, or establishing performance baselines.

한국어 요약은 준비 중입니다. 원문 설명을 표시하고 있습니다.

vibeeval/vibecosystem5382026년 8월 9일 업데이트

agent-context-isolation

무료

Agent Context Isolation

한국어 요약은 준비 중입니다. 원문 설명을 표시하고 있습니다.

vibeeval/vibecosystem5382026년 8월 9일 업데이트

agent-linter

무료

Agent ve skill dosyalarinin yapisal dogrulamasi. Frontmatter kontrol, naming convention, zorunlu bolum kontrolu, tutarlilik denetimi. Yeni agent/skill eklendiginde veya mevcut dosyalar duzenlediginde otomatik calistirilir.

한국어 요약은 준비 중입니다. 원문 설명을 표시하고 있습니다.

vibeeval/vibecosystem5382026년 8월 9일 업데이트

vibeeval의 스킬 모두 보기

이 스킬의 문제 신고

설치

명령으로 설치

npx skills add https://github.com/vibeeval/vibecosystem --skill math-help

터미널에 붙여 넣고 실행합니다(Node.js 필요). Claude Code, Codex 등 설치할 에이전트를 고를 수 있습니다.

에이전트에게 부탁하기

다음 Agent Skill을 설치해 주세요.
https://github.com/vibeeval/vibecosystem/tree/main/skills/math-help

먼저 SKILL.md와 첨부 파일의 내용을 확인해 수상한 처리(외부 전송, 인증 정보 읽기 등)가 없는지 확인한 뒤 Claude Code는 ~/.claude/skills/math-help/, Codex는 ~/.agents/skills/math-help/ 에 배치해 주세요.

이 문장을 그대로 Claude Code나 Codex에 보내면 내용을 확인한 뒤 설치해 줍니다.

GitHub에서 소스 보기

저장소: vibeeval/vibecosystem
스타: 538
포크: 44
카테고리: 기타
라이선스: MIT
원문 언어: 영어
최종 업데이트: 2026년 8월 9일

스킬은 에이전트를 위한 지시와 스크립트의 묶음입니다. cccskills는 내용의 안전성을 보증하지 않습니다. 설치하기 전에 내용을 확인하세요.

포함된 파일(1)

SKILL.md(원문)

Math Cognitive Stack Guide

Quick Reference

The Five Layers

Layer 1: SymPy (Symbolic Algebra)

Layer 2: Z3 (Constraint Solving & Theorem Proving)

Layer 3: Math Scratchpad (Reasoning Verification)

Layer 4: Math Tutor (Educational)

Layer 5: Lean 4 (Formal Proofs)

Numerical Tools

NumPy (160 functions)

SciPy (289 functions)

mpmath (153 functions, arbitrary precision)

Visualization

math_plot.py

Educational Features

5-Level Hint System

Step-by-Step Solutions

Common Workflows

Workflow 1: Solve and Verify

Workflow 2: Learn a Concept

Workflow 3: Prove and Formalize

Choosing the Right Tool

Related Skills

Requirements

리뷰

댓글

같은 저장소의 스킬

accessibility-patterns

accessibility-testing

achievements

agent-benchmark

agent-context-isolation

agent-linter