Math

Name: Math
Author: parcadei

parcadei/continuous-claude-v3

795 installs
3.9k repo stars
Updated January 26, 2026
parcadei/continuous-claude-v3

math is an agent skill that provides symbolic computation, equation solving, unit conversion, and mathematical explanations through a SymPy-based cognitive stack for developers embedding exact math inside Claude workflow

About

math is a parcadei/continuous-claude-v3 cognitive stack guide that routes agent tasks to sympy_compute.py for exact symbolic work instead of LLM guesswork. The quick-reference table maps goals to commands such as solve for equations, integrate and differentiate for calculus, and limit for analysis boundaries. Developers invoke math when agents must return provably correct algebra, calculus, or unit conversions inside Claude Code or similar environments. The skill is user-invocable false for help mode but documents when to pick each math tool so coding agents choose the right SymPy CLI invocation.

One unified entry point that intelligently routes calculate, solve, integrate, derivative, matrix, and explain requests
SymPy-powered symbolic math for solving equations, computing integrals, derivatives, limits, series, and simplifications
Supports matrix operations, eigenvalues, differential equations, and unit conversions via Pint.
Z3 integration for formal proofs and satisfiability questions.
Includes category-theory explanations and routes formal proofs to the dedicated /prove skill.

Math by the numbers

795 all-time installs (skills.sh)
+14 installs in the week ending Jul 26, 2026 (Skillselion tracking)
Ranked #1,312 of 16,659 AI & Agent Building skills by installs in the Skillselion catalog
Security screen: LOW risk (skills.sh audit)
Data as of Jul 28, 2026 (Skillselion catalog sync)

npx skills add https://github.com/parcadei/continuous-claude-v3 --skill math

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Last updated	January 26, 2026
Repository	parcadei/continuous-claude-v3 ↗

How do you solve equations symbolically in Claude agents?

Get accurate symbolic computation, equation solving, unit conversion, and mathematical explanations directly inside their Claude workflow.

Who is it for?

Developers building agent workflows that need exact SymPy symbolic math instead of approximate LLM arithmetic.

Skip if: Heavy numerical simulation workloads that require dedicated MATLAB, NumPy GPU, or HPC clusters rather than symbolic CLI tools.

When should I use this skill?

A developer asks the agent to solve equations, integrate, differentiate, compute limits, or convert units with exact symbolic math.

What you get

SymPy command outputs, solved equation results, integral or derivative expressions, and unit-converted numeric answers.

Symbolic equation solutions
Calculus results

Files

SKILL.mdMarkdownGitHub ↗

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

1. Solve with sympy_compute.py 2. Verify solution with math_scratchpad.py 3. 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

1. Generate practice problem with math_tutor.py 2. Use progressive hints (level 1, then 2, etc.) 3. 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

1. Check theorem with z3_solve.py (constraint-level proof) 2. 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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FAQ

Which tool does math use for equation solving?

math directs agents to sympy_compute.py with the solve action, for example solving quadratic expressions with an explicit variable flag. The cognitive stack guide maps each math goal to the correct SymPy CLI invocation so results stay symbolically exact.

When should developers invoke the math skill?

math fits Claude workflows needing calculus, limits, algebra, or unit conversion with verified SymPy output. Invoke it when LLM prose math is insufficient and a command-line symbolic result is required inside the agent session.

Is Math safe to install?

skills.sh reports 3 of 3 security scanners passed. Review the Security Audits panel on this page before installing in production.

AI & Agent Buildingagentsautomation

About

Math by the numbers

Add your badge

How do you solve equations symbolically in Claude agents?

Who is it for?

When should I use this skill?

What you get

Files

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

Related skills

FAQ

Which tool does math use for equation solving?

When should developers invoke the math skill?

Is Math safe to install?

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