Vectors and Matrices (Mathematica Tutorial)

Vectors and matrices in Mathematica are simply represented by lists and by lists of lists, respectively. The representation of vectors and matrices by lists. This is a 2×2 ...

Introduction to Patterns (Mathematica Tutorial)

Patterns are used throughout Mathematica to represent classes of expressions. A simple example of a pattern is the expression f[x_]. This pattern represents the class of ...

Applying Transformation Rules (Mathematica Tutorial)

Applying transformation rules. The replacement operator /. (pronounced "slash-dot") applies rules to expressions. You can give a list of rules to apply. Each rule will be ...

Map (Built-in Mathematica Symbol)

Map[f, expr] or f /@ expr applies f to each element on the first level in expr. Map[f, expr, levelspec] applies f to parts of expr specified by levelspec.

Table (Built-in Mathematica Symbol)

Table[expr, {i_max}] generates a list of i_max copies of expr. Table[expr, {i, i_max}] generates a list of the values of expr when i runs from 1 to i_max. Table[expr, {i, ...

Tensors (Mathematica Tutorial)

Tensors are mathematical objects that give generalizations of vectors and matrices. In Mathematica, a tensor is represented as a set of lists, nested to a certain number of ...

Data Transforms and Smoothing (Mathematica Guide)

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 ...

Files (Mathematica Guide)

Mathematica provides convenient and efficient system-independent functions for handling file-related constructs at all levels.

Set (Built-in Mathematica Symbol)

lhs = rhs evaluates rhs and assigns the result to be the value of lhs. From then on, lhs is replaced by rhs whenever it appears. {l_1, l_2, ...} = {r_1, r_2, ...} evaluates ...

Structural Operations (Mathematica Tutorial)

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