V1 Roadmap

[UltiRequiem]

Calculetes Roadmap v1

Math for JavaScript.

1. Linear Algebra Essentials

Core Features

• Vectors
  • Create/initialize vectors
  • Operations: Addition, subtraction, scalar multiplication, dot product, cross product (3D)
  • Magnitude, normalization, angle between vectors
• Matrices
  • Matrix creation (identity, diagonal, random)
  • Operations: Addition, subtraction, scalar multiplication
  • Matrix multiplication (vector-matrix, matrix-matrix)
  • Transpose, trace, determinant (2x2, 3x3, nxn)
  • Inverse (for invertible matrices)
  • Row reduction, rank, and linear system solving

Stretch Goals

• Eigenvalues/eigenvectors (for 2x2/3x3)
• Matrix decompositions (LU, QR)

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2. Probability & Statistics

Core Features

• Distributions
  • PDF/PMF/CDF for Uniform, Normal, Binomial, Poisson
  • Random sampling (with seed support)
• Descriptive Stats
  • Mean, median, mode, variance, standard deviation
  • Covariance, correlation coefficients
• Regression
  • Linear regression (least squares)

Stretch Goals

• Hypothesis testing (t-test, z-test)
• Confidence intervals

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3. General Math & Utilities

Core Features

• Complex Numbers
  • Arithmetic operations, conjugate, modulus
  • Polar ↔ rectangular conversion
• Polynomials
  • Evaluate, add, multiply, find roots (quadratic/cubic)
• Numerical Methods
  • Root finding (Newton-Raphson, bisection)
  • Numerical integration (Simpson’s rule)
• Utilities
  • Precision handling (e.g., epsilon comparisons)
  • Unit conversions (degrees ↔ radians)

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4. Calculus Enhancements

Core Features

• Derivatives
  • Symbolic differentiation (basic rules)
  • Higher-order derivatives
• Integrals
  • Adaptive quadrature for better accuracy
• Limits
  • Implement limit evaluation (epsilon-delta approximation)

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5. Developer Experience

Core Features

• Error Handling
  • Custom errors (e.g., singular matrix, invalid dimensions)
• Validation
  • Check matrix invertibility, valid probability inputs
• Documentation
  • Full API docs with JSDoc
  • Interactive examples (CodePen/JSFiddle)
• Performance
  • Optimize loops with typed arrays (Float64Array)
  • Benchmarks vs. competitors (e.g., math.js)
• Testing
  • Unit tests (Jest) covering 100% of features

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6. Compatibility & Extras

• Support both browser & Node.js
• Add TypeScript type definitions
• Keep bundle size < 50kB (minified + gzipped)

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Future Ideas (Post-v1)

• Machine learning (gradient descent, PCA)
• Optimization (linear programming, gradient descent)
• Symbolic algebra engine