1. Symbolic algebra algorithms
1.1 Sparse representations
1.2 Implementation of multivariate polynomials
1.3 Integration
1.4 Transforms
1.5 Finding real roots of polynomials
2. Number theory algorithms
2.1 Euclidean GCD algorithms
2.2 Prime numbers: the Miller-Rabin test and its improvements
2.3 Factorization of integers
2.4 The Jacobi symbol
2.5 Integer partitions
2.6 Miscellaneous functions
2.7 Gaussian integers
3. A simple factorization algorithm for univariate polynomials
3.1 Modular arithmetic
3.2 Factoring using modular arithmetic
3.3 Preparing the polynomial for factorization
3.4 Definition of division of polynomials
3.5 Determining possible factors modulo 2
3.6 Determining factors modulo 2^n given a factorization modulo 2
3.7 Efficiently deciding if a polynomial divides another
3.8 Extending the algorithm
3.9 Newton iteration
4. Numerical algorithms I: basic methods
4.1 Adaptive function plotting
4.2 Surface plotting
4.3 Parametric plots
4.4 The cost of arbitrary-precision computations
4.5 Estimating convergence of a series
4.6 Estimating the round-off error
4.7 Basic arbitrary-precision arithmetic
4.8 How many digits of Sin(Exp(Exp(1000))) do we need?
4.9 Continued fractions
4.10 Estimating convergence of continued fractions
4.11 Newton's method and its improvements
4.12 Fast evaluation of Taylor series
4.13 Using asymptotic series for calculations
4.14 The AGM sequence algorithms
4.15 The binary splitting method
5. Numerical algorithms II: elementary functions
5.1 Powers
5.2 Roots
5.3 Logarithm
5.4 Exponential
5.5 Calculation of Pi
5.6 Trigonometric functions
5.7 Inverse trigonometric functions
5.8 Factorials and binomial coefficients
5.9 Classical orthogonal polynomials: general case
5.10 Classical orthogonal polynomials: special cases
5.11 Series of orthogonal polynomials
6. Numerical algorithms III: special functions
6.1 Euler's Gamma function
6.2 Euler's constant gamma
6.3 Catalan's constant G
6.4 Riemann's Zeta function
6.5 Lambert's W function
6.6 Bessel functions
6.7 Bernoulli numbers and polynomials
6.8 Error function Erf(x) and related functions
7. References
8. GNU Free Documentation License