feat: add const-generic Gram matrix construction

[acgetchell]

• Add allocation-free, const-evaluable gram_matrix with independent vector count and dimension
• Preserve bitwise symmetry and typed dot-product overflow diagnostics
• Document geometric uses, conditioning, and floating-point limitations
• Add benchmarks for square and rectangular vector collections
• Simplify exact rational scaling using canonical positive denominators
• Deduplicate factorization property-test fixtures and assertions

Closes #219

Summary by CodeRabbit

• New Features

  • Added gram_matrix for allocation-free construction of symmetric Gram matrices from fixed-size vectors.
  • Exported the feature through the crate root and prelude.
  • Preserves computation errors and supports zero-size and compile-time use cases.

• Documentation

  • Added guidance on Gram matrices, geometric measures, numerical limitations, and benchmarking.

• Tests

  • Added broad coverage for precision, dependent and orthogonal inputs, scaling, underflow, overflow, and edge cases.
  • Added benchmarks across dimensions and input scenarios.

• Refactor

  • Simplified rational-number denominator handling.

[coderabbitai]

No actionable comments were generated in the recent review. 🎉

ℹ️ Recent review info

⚙️ Run configuration

Configuration used: Path: .coderabbit.yaml

Review profile: CHILL

Plan: Essentials

Run ID: cbe92bef-62a2-4f08-a0f6-25e234e5135a

📥 Commits

Reviewing files that changed from the base of the PR and between 8e8c24b and a62e72a.

📒 Files selected for processing (9)

• Cargo.toml
• README.md
• REFERENCES.md
• benches/gram.rs
• src/gram.rs
• src/lib.rs
• src/rational.rs
• tests/proptest_factorizations.rs
• tests/proptest_gram.rs

Included review availability: 2 reviews are currently available. Your included PR review attempts over the past 7 days set your current allowance at 3 reviews per hour.

---

📝 Walkthrough

Walkthrough

The pull request adds a fixed-size gram_matrix API with public exports, tests, benchmarks, and documentation. It also simplifies rational denominator handling and consolidates factorization property-test helpers.

Changes

Gram matrix API

Layer / File(s)	Summary
Gram matrix API and exports src/gram.rs, src/lib.rs	gram_matrix computes each upper-triangle dot product once, mirrors values for exact symmetry, propagates LaError, and is available from the crate root and prelude.
Gram matrix validation tests/proptest_gram.rs	Tests cover independent integer oracles, geometric cases, rectangular and zero-size inputs, const evaluation, numerical edge cases, symmetry, and overflow diagnostics.
Gram benchmarks and documentation Cargo.toml, benches/gram.rs, README.md, REFERENCES.md	Benchmarks compare gram_matrix with checked hand-written assembly across dimensions and fixture families. Documentation describes construction, formulas, limitations, and benchmark usage.

Rational denominator handling

Layer / File(s)	Summary
Canonical denominator arithmetic src/rational.rs	Denominator clearing uses canonical positive denominators directly and removes redundant sign normalization and the unused helper.

Factorization test helpers

Layer / File(s)	Summary
Shared factorization verification tests/proptest_factorizations.rs	LDLT and LU property tests use shared matrix, multiplication, determinant, solve, and row-swap verification helpers.

Estimated code review effort: 3 (Moderate) | ~25 minutes

Merge Risk: ⚪ Minimal · up to a62e7

The Gram matrix API, rational arithmetic cleanup, tests, benchmarks, and documentation do not present an identified merge-blocking risk.

🚥 Pre-merge checks | ✅ 4

✅ Passed checks (4 passed)

Check name	Status	Explanation
Description Check	✅ Passed	Check skipped - CodeRabbit’s high-level summary is enabled.
Title check	✅ Passed	The title clearly identifies the primary change: adding const-generic Gram matrix construction.
Linked Issues check	✅ Passed	The PR implements the requested fixed-size gram_matrix API, exact symmetric construction, typed dot-product error propagation, allocation-free operation, stable Rust support, documentation, tests, and…
Out of Scope Changes check	✅ Passed	The documentation, benchmark additions, rational scaling cleanup, and factorization test deduplication are included in the stated PR objectives and support the Gram matrix feature or its validation. N…

✨ Finishing Touches

📝 Generate docstrings

• Create stacked PR
• Commit on current branch

🧪 Generate unit tests (beta)

• Create PR with unit tests
• Commit unit tests in branch feat/219-gram-matrix

---

_{Comment @coderabbitai help to get the list of available commands.}

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 97.99%. Comparing base (8e8c24b) to head (a62e72a).
⚠️ Report is 2 commits behind head on main.
✅ All tests successful. No failed tests found.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #236      +/-   ##
==========================================
+ Coverage   97.93%   97.99%   +0.06%     
==========================================
  Files          12       13       +1     
  Lines        6574     6579       +5     
==========================================
+ Hits         6438     6447       +9     
+ Misses        136      132       -4     

Flag	Coverage Δ
unittests	97.99% <100.00%> (+0.06%)	⬆️

Flags with carried forward coverage won't be shown. Click here to find out more.

☔ View full report in Codecov by Harness.
📢 Have feedback on the report? Share it here.