Mathematica can handle numbers of essentially unlimited length, in any base, using state-of-the-art platform-optimized algorithms, including several developed at Wolfram ...

A core activity in exploratory experimental mathematics is recognition of numbers: going backward from a number to find out how it can be generated. Mathematica provides ...

Mathematica allows convenient automated selection of plotting and image regions using a family of specially developed robust algorithms, as well as allowing detailed manual ...

Packed into functions like Solve and Reduce are a wealth of sophisticated algorithms, many created specifically for Mathematica. Routinely handling both dense and sparse ...

Factoring a quadratic polynomial in one variable is straightforward. But Mathematica routinely factors degree-100 polynomials in 3 variables—by making use of a tower of ...

Mathematica supports state-of-the-art sound generation, providing both arbitrary waveform synthesis from functions and data, and symbolic note-based MIDI-style sound ...

Mathematica has special sparse-array technology for efficiently handling arrays with literally astronomical numbers of elements when only a small fraction of the elements are ...

Mathematica's uniform representation of vectors and matrices as lists automatically extends to tensors of any rank, allowing Mathematica's powerful list manipulation ...

Mathematica's symbolic timing framework allows timing information not only to be analyzed but also to be used in the structure of algorithms. Mathematica provides functions ...

DiscretePlot[expr, {n, n_max}] generates a plot of the values of expr when n runs from 1 to n_max.DiscretePlot[expr, {n, n_min, n_max}] generates a plot of the values of expr ...