A proposal for a first-class numerical computing module in Jai

numerics exists to make numerical and statistical programming a first-class capability of the Jai ecosystem, without burdening the core language or forcing external dependencies onto users.

It provides practical, mainstream numerical tools—dense arrays, linear algebra, and foundational statistics—with an emphasis on clarity, correctness, and predictable performance.

numerics targets the common, real-world use cases of numerical computing:

• dense numerical arrays and views,
• linear algebra for solving systems and least-squares problems,
• core statistical routines used in modeling and analysis.

It explicitly avoids:

• symbolic mathematics,
• domain-specific modeling frameworks,
• experimental or niche algorithms.

1. Official, but Optional

   numerics is intended as a Tier-1 standard module: shipped, documented, and versioned with Jai, but imported explicitly and not required by non-numerical programs.

2. Friction Reduction Over Abstraction

   The module prioritizes removing unnecessary friction over introducing clever abstractions. APIs are explicit, boring, and predictable.

3. Correctness Before Cleverness

   Numerical stability, edge-case handling, and clearly documented behavior take precedence over minimal code size or theoretical elegance.

4. Performance Without Mystery

   Implementations aim for high performance while remaining readable and auditable. Optimizations must be explainable and testable.

5. Stable Public Surface

   Public APIs are designed to remain stable even as internal implementations evolve.

6. Progressive Independence

   Where appropriate, well-established numerical libraries may be used initially. Over time, critical routines are replaced with native implementations validated against independent test oracles.

numerics does not attempt to:

• replicate the full scope of NumPy, SciPy, or statsmodels,
• expose every available numerical algorithm,
• impose a single mathematical worldview or workflow.

numerics aims to become the obvious and trusted foundation for numerical work in Jai: not because it is exhaustive or fashionable, but because it is correct, available, and unsurprising.