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Support operations in layers, from basic → “this can replace WolframAlpha-lite”.

Level 1 — Core Arithmetic (minimum viable calculator)

These are non-negotiable.

  • Addition: +
  • Subtraction: -
  • Multiplication: *
  • Division: /
  • Parentheses for order: ( )
  • Decimals: 3.14
  • Negative numbers: -5

Example

(3 + 4) * 2 - 5 / 10

Level 2 — Powers & Structure

Makes it feel like a real calculator.

  • Exponents: ^ → 2^10

  • Roots

    • Square root: sqrt(x)
    • General root: root(n, x) or x^(1/n)

  • Absolute value: abs(x)

  • Modulo: mod or % → 10 % 3

Level 3 — Scientific Functions

Now you're in scientific calculator territory.

Trig

  • sin(x)
  • cos(x)
  • tan(x)
  • Inverses: asin, acos, atan

Logs

  • Natural log: ln(x)
  • Log base 10: log(x)
  • Log base n: log(base, x)

Constants

  • pi
  • e

Level 4 — Advanced Math

Useful for students, engineers, finance.

  • Factorial: n!
  • Permutations: nPr(n, r)
  • Combinations: nCr(n, r)
  • Floor/Ceil: floor(x), ceil(x)
  • Round: round(x, n)
  • Min/Max: min(a, b), max(a, b)

Level 5 — Algebra Support (HUGE upgrade)

Now you're not just computing numbers — you're manipulating math.

  • Variables: x = 5
  • Expressions: 2x + 3
  • Substitution: f(x) = x^2, f(3)
  • Solve equations: solve(2x + 3 = 7, x)

Level 6 — Linear Algebra (power users)

  • Vectors: [1, 2, 3]

  • Dot product: dot(a, b)

  • Cross product: cross(a, b)

  • Matrices:

    • Multiply: A * B
    • Determinant: det(A)
    • Inverse: inv(A)

Level 7 — Calculus (elite tier)

If you support this, it's basically a CAS.

  • Derivatives: d/dx(x^2)
  • Integrals: integral(x^2, x)
  • Limits: limit(x→0, sin(x)/x)
  • Summation: sum(i=1 to 10, i^2)

Level 8 — Programmer Mode

Appeals to CS people.

  • Bitwise ops: & | ^ ~ << >>
  • Binary/hex: 0b1010, 0xFF
  • Conversions: bin(x), hex(x)

Level 9 — Financial (high real-world value)

  • Compound interest FV(P, r, n, t)
  • Present value
  • Payment calculators
  • Growth rates

🔥 Practical Build Strategy

Stage What to Ship
V1 Levels 1–2
V2 + Level 3
V3 + Level 4
Power Mode Levels 5–7

Most calculators never go past Level 3. Level 5+ is where you start competing with symbolic math tools.

If you want, next I can break down how to parse expressions (parser design) — that’s the real challenge, not the math.