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 (Sy...