Symbolic algebra algorithms
Sparse representations
Implementation of multivariate polynomials
Integration
Finding real roots of polynomials
Number theory algorithms
Prime numbers: the Miller-Rabin algorithm and its improvements
Factorization of integers
Number Theoretic Functions
Integer Partitions
Numerical algorithms I: basic methods
Adaptive plotting
Cost of arbitrary-precision computations
Basic arbitrary-precision arithmetic
How many digits of
Sin(Exp(Exp(1000)))
do we need?
Continued fractions
Newton's method and its improvements
Fast evaluation of Taylor series
Using asymptotic series for calculations
The AGM sequence algorithms
Numerical algorithms II: elementary functions
Powers
Roots
Logarithm
Exponential
Calculation of
Pi
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
Riemann's Zeta function
Lambert's
W
function
Bessel functions
Bernoulli numbers and polynomials
Error function
Erf(x)
and related functions
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