Computational Systems (Mathematica Guide)

Mathematica is the tool that has made possible Stephen Wolfram's exploration of the computational universe, and the emerging field of Wolfram Science (NKS). Whether for ...

Replace (Built-in Mathematica Symbol)

Replace[expr, rules] applies a rule or list of rules in an attempt to transform the entire expression expr. Replace[expr, rules, levelspec] applies rules to parts of expr ...

The Ordering of Definitions (Mathematica Tutorial)

When you make a sequence of definitions in Mathematica, some may be more general than others. Mathematica follows the principle of trying to put more general definitions ...

NIntegrate (Built-in Mathematica Symbol)

NIntegrate[f, {x, x_min, x_max}] gives a numerical approximation to the integral \[Integral]_x_min^x_max\ f\ d \ x. NIntegrate[f, {x, x_min, x_max}, {y, y_min, y_max}, ...] ...

Manipulating Value Lists (Mathematica Tutorial)

Finding and setting values of symbols. Mathematica effectively stores all definitions you give as lists of transformation rules. When a particular symbol is encountered, the ...

ReplaceAll (Built-in Mathematica Symbol)

expr /. rules applies a rule or list of rules in an attempt to transform each subpart of an expression expr.

Making Definitions (Mathematica Tutorial)

The replacement operator /. allows you to apply transformation rules to a specific expression. Often, however, you want to have transformation rules automatically applied ...

ReplaceList (Built-in Mathematica Symbol)

ReplaceList[expr, rules] attempts to transform the entire expression expr by applying a rule or list of rules in all possible ways, and returns a list of the results ...

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 ...

BellY (Built-in Mathematica Symbol)

BellY[n, k, {x_1, ..., x n - k + 1}] gives the partial Bell polynomial Y n, k (x_1, ..., x n - k + 1). BellY[n, k, m] gives the generalized partial Bell polynomial of a ...