With careful attention to branch cuts, Mathematica supports trigonometric functions everywhere in the complex plane, with extensive exact and algebraic transformations, ...

There are often many different ways to write the same algebraic expression. As one example, the expression (1+x)^2 can be written as 1+2x+x^2. Mathematica provides a large ...

PrimeOmega[n] gives the number of prime factors counting multiplicities \[CapitalOmega](n) in n.

PrimeNu[n] gives the number of distinct primes \[Nu](n) in n.

Mathematica's extensive base of state-of-the-art algorithms, efficient handling of very long integers, and powerful built-in language make it uniquely suited to both research ...

RandomInteger[{i_min, i_max}] gives a pseudorandom integer in the range {i_min, i_max}. RandomInteger[i_max] gives a pseudorandom integer in the range {0, ...

Mathematica can work with polynomials whose coefficients are in the finite field Z_p of integers modulo a prime p. Functions for manipulating polynomials over finite fields. ...

Polynomial algorithms are at the core of classical "computer algebra". Incorporating methods that span from antiquity to the latest cutting-edge research at Wolfram Research, ...

AlgebraicNumberDenominator[a] gives the smallest positive integer n such that n a is an algebraic integer.