SmoothHistogram3D[{{x_1, y_1}, {x_2, y_2}, ...}] plots a 3D smooth kernel histogram of the values {x_i, y_i}.SmoothHistogram3D[{{x_1, y_1}, {x_2, y_2}, ...}, espec] plots a ...

Sphere[{x, y, z}, r] represents a sphere of radius r centered at (x, y, z). Sphere[{x, y, z}] represents a sphere of radius 1. Sphere[{{x_1, y_1, z_1}, {x_2, y_2, z_2}, ...}, ...

TeXForm[expr] prints as a TeX version of expr.

$MachineEpsilon gives the difference between 1.0 and the next-nearest number representable as a machine-precision number.

The representation of algebraic numbers. When you enter a Root object, the polynomial that appears in it is automatically reduced to a minimal form. This extracts the pure ...

Converting between strings, boxes, and expressions. Here is a simple expression. This gives the InputForm of the expression as a string.

Eigenvalues and eigenvectors. The eigenvalues of a matrix m are the values λ_i for which one can find nonzero vectors v_i such that m.v_i λ_iv_i. The eigenvectors are the ...

If you have an equation like 2x==0, it is perfectly clear that the only possible solution is x->0. However, if you have an equation like ax==0, things are not so clear. If a ...

Ways to label two-dimensional plots. Here is a plot, using the default Axes->True. Setting Frame->True generates a frame with axes, and removes tick marks from the ordinary ...

Searching for local minima and maxima. This finds the value of x which minimizes Γ(x), starting at x2. The last element of the list gives the value at which the minimum is ...