formula-environment-and-readability

name	formula-environment-and-readability
description	Use when improving mathematical formulas, displayed derivations, theorem/proof environments, equation alignment, cases blocks, long displays, or formula-to-prose readability in paper drafts.

Formula Environment And Readability

Improve displayed mathematics so formulas communicate the argument. Environment choice is part of exposition: it should reveal structure without changing meaning.

Inputs

• TeX or draft text containing formulas, theorem statements, proofs, algorithms, or derivations.
• Optional venue class constraints and style preferences.

Output Contract

Return:

• Formula findings: location, issue, proposed environment or rewrite, and meaning-risk level.
• Revised snippets for high-value displays.
• Notes where a formula requires a correctness or notation audit before rewrite.

Workflow

1. Identify long, dense, or ambiguous displayed formulas.
2. Check whether the surrounding prose states what the formula does.
3. Choose environments by role: equation for a single object, align for aligned derivations, split for one numbered multi-line equation, multline for long expressions, and cases for piecewise definitions.
4. Remove brittle manual spacing and avoid eqnarray and raw $$.
5. Preserve labels, numbering intent, punctuation, and mathematical meaning.

Review Rules

• Do not make formulas shorter by deleting assumptions, quantifiers, or terms.
• Flag a displayed formula when the prose and formula disagree.
• Prefer readability over clever compression in proof-critical derivations.