Fourier[list] finds the discrete Fourier transform of a list of complex numbers.

ExcludedForms is an option for FullSimplify which can be set to a list of patterns for expressions that should not be touched if they are encountered at intermediate steps in ...

Array[f, n] generates a list of length n, with elements f[i]. Array[f, {n_1, n_2, ...}] generates an n_1*n_2*... array of nested lists, with elements f[i_1, i_2, ...]. ...

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 not only has systemwide support for arbitrary Unicode characters, but also includes nearly a thousand carefully designed characters for mathematical notation and ...

Density and contour plots. This gives a density plot of sin(x) sin(y). Lighter regions show higher values of the function. Some options for DensityPlot.

CosIntegral[z] gives the cosine integral function Ci(z).

Compiled is an option for various numerical and plotting functions which specifies whether the expressions they work with should automatically be compiled.

ArcTanh[z] gives the inverse hyperbolic tangent tanh -1 (z) of the complex number z.

ZeroTest is an option to various linear algebra functions that gives a function to use in testing whether symbolic expressions should be treated as zero.