PowersRepresentations[n, k, p] gives the distinct representations of the integer n as a sum of k non-negative p\[Null]^th integer powers.

EllipticPi[n, m] gives the complete elliptic integral of the third kind \[CapitalPi] (n \[VerticalSeparator] m). EllipticPi[n, \[Phi], m] gives the incomplete elliptic ...

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

SingularValueList[m] gives a list of the nonzero singular values of a matrix m. SingularValueList[{m, a}] gives the generalized singular values of m with respect to a. ...

Huge numerical datasets are routine for Mathematica. Its powerful array primitives make large-scale array manipulation both easy to specify and highly efficient. And its ...

Mathematica contains hundreds of original algorithms for computing integer functions involving integers of any size.

WeierstrassPPrime[u, {g_2, g_3}] gives the derivative of the Weierstrass elliptic function \[WeierstrassP](u; g_2, g_3).

Most of the documentation provided for Mathematica is concerned with explaining what Mathematica does, not how it does it. But the purpose of this is to say at least a little ...

Functions that are specified by simple algebraic formulas tend to be such that when their input is changed only slightly, their output also changes only slightly. But ...

NumberFieldDiscriminant[a] gives the discriminant of the field \[DoubleStruckCapitalQ][a] generated by the algebraic number a.