General issues about the internal implementation of Mathematica are discussed in "The Internals of Mathematica". Given here are brief notes on particular features. These ...

Multinomial[n_1, n_2, ...] gives the multinomial coefficient (n_1 + n_2 + ...)!/(n_1! n_2! ...).

In two decades of intense algorithmic development, Mathematica has established a new level of numerical computation. Particularly notable are its many original highly ...

Cyclotomic[n, x] gives the n\[Null]^th cyclotomic polynomial in x.

Mathematica provides powerful functions for constructing lists of any size and structure.

Mathematica's sophisticated algorithms for handling higher mathematical functions to arbitrary precision—and in symbolic form—immediately brings a new level of accuracy—and ...

Mathematica applies its strengths in calculus to the intricacies of integral transforms, with a host of original algorithms that probably now reach almost any closed form ...

Mathematica incorporates the latest algorithms for solving industrial-scale linear systems, automatically switching between optimal dense and sparse algorithms—and handling ...

Built on powerful and elegant long-standing principles, the core Mathematica language has been gradually enhanced under tight control over its twenty-year history. Version ...

Built on powerful and elegant principles, the core Mathematica language has emerged over the past 20 years as perhaps the world's richest and deepest programming language. ...