• Symbolic algebra algorithms
    • Sparse representations
    • Implementation of multivariate polynomials
    • Integration
    • Transforms
    • Finding real roots of polynomials
  • Number theory algorithms
    • Euclidean GCD algorithms
    • Prime numbers: the Miller-Rabin test and its improvements
    • Factorization of integers
    • The Jacobi symbol
    • Integer partitions
    • Miscellaneous functions
    • Gaussian integers
  • A simple factorization algorithm for univariate polynomials
    • Modular arithmetic
    • Factoring using modular arithmetic
    • Preparing the polynomial for factorization
    • Definition of division of polynomials
    • Determining possible factors modulo 2
    • Determining factors modulo 2^n given a factorization modulo 2
    • Efficiently deciding if a polynomial divides another
    • Extending the algorithm
    • Newton iteration
  • Numerical algorithms I: basic methods
    • Adaptive function plotting
    • Surface plotting
    • Parametric plots
    • The cost of arbitrary-precision computations
    • Estimating convergence of a series
    • Estimating the round-off error
    • Basic arbitrary-precision arithmetic
    • How many digits of Sin(Exp(Exp(1000))) do we need?
    • Continued fractions
    • Estimating convergence of continued fractions
    • Newton's method and its improvements
    • Fast evaluation of Taylor series
    • Using asymptotic series for calculations
    • The AGM sequence algorithms
    • The binary splitting method
  • Numerical algorithms II: elementary functions
    • Powers
    • Roots
    • Logarithm
    • Exponential
    • Calculation of Pi
    • Trigonometric functions
    • Inverse trigonometric functions
    • Factorials and binomial coefficients
    • Classical orthogonal polynomials: general case
    • Classical orthogonal polynomials: special cases
    • Series of orthogonal polynomials
  • Numerical algorithms III: special functions
    • Euler's Gamma function
    • Euler's constant gamma
    • Catalan's constant G
    • Riemann's Zeta function
    • Lambert's W function
    • Bessel functions
    • Bernoulli numbers and polynomials
    • Error function Erf(x) and related functions
  • References
  • GNU Free Documentation License