# Polynomial reciprocals and tempered fundamental solutions

The learner text and complete proof construct a tempered reciprocal of every nonzero complex polynomial. The proof includes the polynomial-module counting, Weyl-algebra dimension inequality, functional equation, meromorphic distribution family and finite-part construction. Three worked examples and eight solved exercises accompany the argument.

The editable mathematical sources are:

- polynomial-reciprocals-and-tempered-fundamental-solutions-learner.md
- polynomial-reciprocals-and-tempered-fundamental-solutions-formal.md

Run the command below with Python, SymPy, NumPy and Matplotlib to reproduce the finite exact examples and the figure in the figures directory.

    python check-and-figures.py

The PNG is for reading; the SVG is an editable vector illustration. The plotted expressions, interval and values at zero are specified in figures/figure-data.json.

The exact examples supplement the general proofs. Finite computations alone do not establish a theorem for arbitrary polynomials.

The original mathematical exposition, examples, solutions, code and illustration are dedicated under CC0 1.0. The DejaVu font and linked readings retain their own terms. Bernstein's article is cited for the mathematical method; its text is not included.