# Zero-free cones turn slow decrease into reciprocal bounds

The two Markdown chapters contain the complete original proofs, four examples and eight exercises with full solutions. The examples and figures use the Fourier convention given in the chapters.

Run python -B make_figures249.py to regenerate the two PNG/SVG pairs and figures/geometry249.json. This needs Matplotlib, NumPy and mpmath. The temporary Matplotlib configuration is removed on exit.

Run python -B check_numerics249.py for the supplementary checks at 85 decimal digits. The complete mathematical arguments remain in the chapters. The infinite-product samples have the rigorous relative omitted-tail bound proved there.

Original chapters, illustrations and programs are released under CC0 1.0. DejaVu font components retain the accompanying font licence. The preceding linked course chapters provide the exact compactness, logarithmic and Fourier-growth proofs used here.