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

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 ...

DifferentialRootReduce[expr, x] attempts to reduce expr to a single DifferentialRoot object as a function of x.DifferentialRootReduce[expr, {x, x_0}] takes the initial ...

Directly integrated into Mathematica's uniform architecture for handling lists of data is an array of highly optimized algorithms for transforming and smoothing datasets that ...

Version 6.0 added a collection of carefully optimized functions to Mathematica's powerful arsenal of numerical handling capabilities.

Extension is an option for various polynomial and algebraic functions that specifies generators for the algebraic number field to be used.

LegendreQ[n, z] gives the Legendre function of the second kind Q_n (z). LegendreQ[n, m, z] gives the associated Legendre function of the second kind Q_n^m(z).

CountRoots[poly, x] gives the number of real roots of the polynomial poly in x.CountRoots[poly, {x, a, b}] gives the number of roots between a and b.

Mathematica has a wide coverage of named functions defined by sums and recurrence relations. Often using original algorithms developed at Wolfram Research, Mathematica ...

In calculus even more than other areas, Mathematica packs centuries of mathematical development into a small number of exceptionally powerful functions. Continually enhanced ...