If you make a definition like f[x_]:=x Sin[x], Mathematica will store the expression x Sin[x] in a form that can be evaluated for any x. Then when you give a particular value ...

LowerTriangularize[m] gives a matrix in which all but the lower triangular elements of m are replaced with zeros. LowerTriangularize[m, k] replaces with zeros only the ...

VectorQ[expr] gives True if expr is a list or a one-dimensional SparseArray object, none of whose elements are themselves lists, and gives False otherwise. VectorQ[expr, ...

Mathematica contains some powerful primitives for making structural changes to expressions. You can use these primitives both to implement mathematical properties such as ...

CompilationOptions is an option for Compile that specifies settings for the compilation process.

Plot[f, {x, x_min, x_max}] generates a plot of f as a function of x from x_min to x_max. Plot[{f_1, f_2, ...}, {x, x_min, x_max}] plots several functions f_i.

Minimization and maximization. Minimize and Maximize yield lists giving the value attained at the minimum or maximum, together with rules specifying where the minimum or ...

On[symbol::tag] switches on a message, so that it can be printed. On["name"] switches on a named group of messages.On[s] switches on tracing for the symbol s. On[m_1, m_2, ...

With origins stretching back several centuries, discrete calculus is now an increasingly central methodology for many problems related to discrete systems and algorithms. ...

Lists are at the core of Mathematica 's symbolic language. These "How tos" give step-by-step instructions for common tasks related to creating and manipulating lists.