Define CS/applied-math feature track (excluding #1/#4)

[sacchen]

Define a focused CS/applied-math feature track for phil that strengthens terminal workflows without turning the project into a simulator platform.

Scope Boundary

This issue is for CS-facing math workflows outside dedicated number-theory and stats tracks.

• Number theory track lives in: Exact arithmetic ergonomics pack: gcd/lcm + core number-theory helpers #1
• Stats/probability track lives in: Add exact-first stats/probability helper surface #4
• Prioritization/meta planning lives in: Umbrella: prioritize math branch roadmap across feature tracks #6

Goal

Make phil a first-stop math tool for CS practitioners while preserving exactness, safety, and scriptability.

Proposed Scope (phased)

Phase 1 (high value)

• Bit/number helpers: base conversion ergonomics, popcount/parity helpers.
• Performance/back-of-envelope helpers suitable for terminal use.
• Lightweight graph/discrete helpers for small examples.

Phase 2 (targeted depth)

• Information theory basics (entropy/KL for discrete distributions).
• Additional CS workflow helpers validated by user observations.

Product Constraints

• Exact-first behavior where possible.
• Explicit hint when numeric approximation is used.
• Deterministic, pipe-friendly output.
• No hidden semantics changes.

Acceptance Criteria

• Initial CS helper set is documented and reachable from help commands.
• High-value workflows have examples in one-shot and REPL contexts.
• Errors retain actionable E: + hint: quality.
• Tests cover behavior and output stability.

Non-Goals

• No full algorithm/data-structure simulation engine.
• No DB/OS emulation layer.
• No graphing UI.

Test Gate

• uv run --group dev pytest
• uv run --group dev pytest --cov=calc --cov-report=term-missing --cov-fail-under=90

[sacchen]

Related cross-cutting implementation issue: #8 (Prefer SymPy built-ins over custom math plumbing).\n\nIf #3 expands matrix/discrete helpers, #8’s principle applies: prefer SymPy-native primitives over custom math internals where possible.

[sacchen]

Roadmap status update (from #6): this is currently Later, after #7/#8 foundation work and #4 first-wave delivery.

[sacchen]

Linked strategy anchor: #9 (Product principles and design decision framework).\n\nAs #3 is revisited, use #9 to keep scope disciplined and aligned with terminal-first reliability priorities.