Find the right tool for equations, calculus, numerical calculations, proof checks, or math practice. The guide connects tasks to commands for computing results, verifying steps, requesting hints, and plotting functions.
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Guide to the math cognitive stack - what tools exist and when to use each
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Cognitive prosthetics for exact mathematical computation. This guide helps you choose the right tool for your math task.
| 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 |
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.
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.
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.
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.
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.
For numerical (not symbolic) computation:
# 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]"
# 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"
# 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
# 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
| 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
uv run python scripts/cc_math/math_tutor.py steps "x**2 - 5*x + 6 = 0" --operation solve
Returns structured steps with:
# 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"
# 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
# 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
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)
/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 colimitsAll math scripts are installed via:
uv sync
Dependencies: sympy, z3-solver, numpy, scipy, mpmath, matplotlib, plotly
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Coordinate background agents through saved files, keeping lengthy work transcripts out of the main conversation. It defines how to pass results between agents, monitor progress, and verify completed work with tests.
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Delegate implementation, file reading, and testing to separate agents, then bring concise summaries back to the main conversation. The rules explain when delegation helps and when a small edit is better handled directly.
한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.
Organize implementation work across research, planning, validation, implementation, and review agents. Each stage passes files to the next, while implementation starts with failing tests and the main conversation coordinates the workflow.
한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.
Connect Agentica SDK agents to Claude Code CLI through a proxy, an intermediary server. Use setup and debugging guidance to address file permissions, streamed responses, result formatting, and agents reporting success without performing the requested operations.
한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.
Consult Agentica APIs when building workflows where multiple AI agents cooperate. This reference covers eleven coordination patterns, agent tracking, shared state, handoffs, and ways to combine results, with pointers to detailed API specifications.
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Write clearer instructions for Agentica and REPL agents by specifying roles, file operations, and output formats. Includes templates for dividing research, coordinating specialists, reviewing solutions, and passing results between agents through files.
한국어 요약은 준비 중입니다. 영어 요약을 표시하고 있습니다.