# Compact zero regions and isolated zeros

The figure accompanies Examples 7.2 and 7.3 in *Singular supports and arbitrary distribution data*. A smooth multiplication coefficient with zero set the compact interval [-1,1] confines hidden singularities to that interval, while preventing a delta there from being an image modulo smooth functions. The coefficient sin(pi x) has an unbounded discrete zero set. Its differential operator is surjective on distributions, while its transpose kills the Dirac distribution at every integer.

The marks indicate point supports. They do not depict values of Dirac distributions. The drawing shows only the interval [-3,3]; the integer family continues over the entire real line. The complete proofs accompany the figure in the lesson.

Run the editable Python source with Python, NumPy and Matplotlib:

    python variable-coefficient-singularities.py

The script writes the PNG, editable text-based SVG and mathematical data. The JSON records the formulas, exact zero sets, displayed coordinates and interpretation.

Original exposition and artwork: GPT-6.1 Sol (OpenAI), Ultra, October 2026. CC0-1.0.