**Combinatorial Algorithms**

Generation of all subsets with `K` elements

Generation of permutation sequences

**Linear Algebraic Equations**
*LU* decomposition

Solution of linear algebraic equations

Determinant of a matrix

Inverse of a matrix

**Number-Theory**

Complex arithmetic

Diophantine linear equation

Euclid's GCD (and LCM) algorithm

Euler's number *e*

Euler's constant *gamma*

Extended Euclid's algorithm

Factorial

Fibonacci numbers

Modular linear equations

Number *Pi*

Number of combinations

Primes

Roman to decimal and the other way round

Rational arithmetic

**Functions**

Area of a triangle

Exponential function
`FLOOR`, `CEILING` and `MOD`

Natural logarithm

Logarithms with other bases than *e*

Sine and cosine function

Square root of positive real numbers
`SQRT(P**2 + Q**2)`

Power - integer exponent

Power - real exponent

**Polynomials and Matrices**

Evaluation

Evaluation of polynomial and its derivatives

Addition

Addition for sparse polynomials

Division

Matrix multiplication

**Random Numbers and Permutations**

Linear congruential generator

Random permutation

Random sampling

**Interpolation and Extrapolation**

Polynomial

Rational function

Cubic spline interpolation