Refactor

[sukeya]

Overview

This PR refactors the MVPolynomial implementation and public API to make its internal invariants easier to preserve. In particular, it makes zero-coefficient handling and the representation of the zero polynomial consistent, so operations such as arithmetic, evaluation, integration, and composition behave more predictably.

Previously, MVPolynomial exposed a relatively map-like interface, which left more room for callers to break canonical zero-polynomial form or bypass index validation. This PR moves more of that responsibility into the class itself, clarifies the intended usage, and also revisits evaluation logic and allocator propagation.

Main changes

• The MVPolynomial API is streamlined around get, try_get, and set instead of exposing a broader set of direct map-style mutations.
• Normalization is unified across construction, assignment, and arithmetic so zero-coefficient terms are removed automatically and the zero polynomial stays in a canonical single-term form.
• Index-related validation is made more consistent, including rejection of negative degrees and tighter axis checks.
• The implementations of point evaluation operator()(coord_type) and polynomial composition operator()(MVPolynomial, axis) are cleaned up, and allocator propagation is preserved for internal temporary storage.
• Scalar binary operations and division-by-zero behavior are clarified and reinforced.
• The README is rewritten around concrete examples so the public API is easier to understand.
• The test suite is expanded significantly, including randomized tests, to cover normalization, evaluation, composition, integration, scalar operations, and allocator propagation regressions.
• clang-format, pre-commit, and workflow settings are updated to keep formatting and validation aligned in development.