# TODO
## Done
### Core
- [x] Expression AST, parser, evaluator with Context
- [x] Expression equality checking (canonical form with commutative sorting, constant folding)
### Symbolic algebra
- [x] Symbolic differentiation (product, quotient, chain rules)
- [x] Algebraic simplification (constant folding, identities)
- [x] **Symbolic integration** for polynomial, exponential, trigonometric, and inverse-trigonometric primitives
### Numerical calculus
- [x] Numerical derivatives (high-order finite difference) and gradients
- [x] Trapezoidal, Simpson's, and adaptive quadrature
- [x] **Romberg with Richardson extrapolation**
### Equation solving
- [x] Bisection, Newton–Raphson, secant
- [x] Durand–Kerner polynomial root finding
- [x] **Newton's method for nonlinear systems** (central-difference Jacobian)
### FFT
- [x] Cooley–Tukey radix-2 from scratch: forward, inverse, 2D, real-input
- [x] Magnitude / power spectra
- [x] Convolution and cross-correlation
- [x] Window functions (Hann, Hamming, Blackman, Rectangular)
### Matrix
- [x] Arithmetic (add, sub, mul, scalar), transpose, trace
- [x] Gaussian elimination: determinant, inverse, linear solve
- [x] **Rank** estimation
- [x] **LU decomposition** with partial pivoting
- [x] **Cholesky decomposition** `A = L · Lᵀ` for symmetric positive-definite matrices
- [x] **SVD** `A = U · Σ · Vᵀ` via one-sided Jacobi rotations
- [x] **Power iteration** for the dominant eigenvalue/eigenvector
### Statistics
- [x] Mean, median, variance, standard deviation
- [x] Quartiles, IQR
- [x] Pearson correlation
- [x] Linear regression
### Number theory
- [x] GCD, LCM, extended GCD, modular inverse, modular exponentiation
- [x] Primality (trial division + Miller–Rabin, deterministic for n < 3.3e24)
- [x] Prime factorization, sieve of Eratosthenes
- [x] Binomial coefficients, factorial, Fibonacci (fast doubling)
- [x] Euler's totient
- [x] **Jacobi symbol**
- [x] **Continued fractions** (rational and real-valued approximants)
- [x] **Linear Diophantine solver**
- [x] **Discrete logarithm** (baby-step giant-step)
- [x] Chinese Remainder Theorem
### ODE
- [x] Euler, RK4, RK4 systems
- [x] Adaptive RKF45
### Interpolation
- [x] Lagrange, Newton divided-difference, linear
- [x] **Natural / clamped cubic spline** (Thomas algorithm for second derivatives)
- [x] **Chebyshev polynomials** `T_n(x)`, Chebyshev nodes, series approximation, Clenshaw evaluation
- [x] **Legendre polynomials** `P_n(x)`, associated `P_n^m(x)`, **Gauss–Legendre quadrature**
### Special functions
- [x] Gamma, log-Gamma (Lanczos)
- [x] Beta function
- [x] erf, erfc (via incomplete gamma)
- [x] sinc, incomplete gamma P
- [x] **Bessel functions** `J_0(x)`, `J_1(x)`, integer-order `J_n(x)` (Maclaurin series + asymptotic + forward recurrence)
### Taylor series
- [x] Symbolic expansion around any point
### Other
- [x] Complex number type with arithmetic, polar conversion, powers
- [x] PNG plotting (line, multi-series, scatter) via `plotters`
- [x] LaTeX / TeX input (`\frac`, `\sqrt`, `\sin`, `\pi`, `\left(\right)`, `^{...}`, `\Gamma`, `\log_2`, …; `$...$`, `$$...$$`, `\[...\]`, `\(...\)`)
- [x] Interactive REPL (rustyline-powered with history)
- [x] CLI subcommands and REPL dispatch for all features
- [x] **209 inline unit tests** + 53 integration tests — all passing
- [x] AGENTS.md, README.md, ARCHITECTURE.md, SPEC.md
## Brainstorming
### High Priority
- [ ] QR algorithm for full symmetric eigenvalue decomposition
- [ ] Hessenberg / Schur decomposition
- [ ] Polynomial root isolation (Vincent–Akritas–Strzebonski)
### Medium Priority
- [ ] Multi-variable symbolic differentiation (partial derivatives and gradients)
- [ ] Series expansion (Laurent series, Fourier series)
- [ ] Rational number type (exact arithmetic)
- [ ] Big integer support for number theory (arbitrary precision)
- [ ] Chebyshev-based fast math library (e.g., `cos`/`sin` via Padé approximation)
- [ ] Monte Carlo integration
- [ ] Stochastic / probabilistic primitives (random sampling, distributions)
- [ ] Moment / cumulant helpers for distributions
- [ ] Hilbert-matrix-aware solvers (regularisation, pre-conditioners)
### Low Priority
- [ ] Arbitrary-precision arithmetic (BigDecimal)
- [ ] Interval arithmetic for rigorous bounds
- [ ] Automatic differentiation (dual numbers)
- [ ] Expression serialization (S-expressions, JSON, RPN)
- [ ] WebAssembly build for browser use
- [ ] Python bindings (PyO3)
- [ ] GPU-accelerated FFT (via `wgpu`)
- [ ] 3D plotting (surface plots, contour plots)
- [ ] Animated plot output (GIF/WebM)