Programs: math

17 verified Soma programs in the math domain. Each page shows the source and what soma check, soma test, soma verify and soma run printed on it.

Program	Lines	Uses
Bisection — bracket a root of a continuous function and halve	61	[native] handlers
Combinatorics — factorial, permutations, combinations factorial folds product over range(1, n+1)	64
Complex numbers — records carrying real and imaginary parts	63
Extended Euclidean algorithm — Bezout coefficients and modular inverse	70
Fibonacci — iterative, and the closed-form Binet approximation	66
Gcd / lcm — Euclid's algorithm and its consequences gcd() is a builtin (Euclid on absolute values)	54	pipes (\|>), lambdas
Numerical integration — trapezoidal and Simpson's rule	66	[native] handlers
Solving 2x2 linear systems — Cramer's rule via determinants	46
Matrix algebra — product, transpose, determinant, trace	56
Modular arithmetic — fast exponentiation and Fermat primality pow_mod(base, exp, m) is a builtin doing square-and-multiply mod m	54
Monte Carlo — estimate pi by dart-throwing	44
Newton's method — square root and reciprocal without division/sqrt sqrt(a) is the positive root of f(x) = x² − a; Newton's iteration becomes the Babylonian update x ← (x + a/x) / 2	67	[native] handlers
Primes — primality test, prime list, factorization	76
Quadratic equations — discriminant and the two real roots	54
Power series — e via 1/k!, and pi via the Leibniz / Nilakantha series e = Σ 1/k!	75	[native] handlers
Descriptive statistics — mean, variance, stddev, median via sort	69	pipes (\|>), lambdas
Vector operations — dot product, norm, cosine similarity	56	pipes (\|>), lambdas