Assumptions and Domains

The Wolfram Language has a flexible system for specifying arbitrary symbolic assumptions about variables. It uses a wide range of sophisticated algorithms to infer the consequences of assumptionsoften in the process automatically proving a sequence of necessary mathematical theorems.

Element () specify membership in a domain (entered as elem)

NotElement () specify exclusion from a domain (!elem)

Less (<), Greater (>), ... define inequalities, implicitly for real numbers

ForAll () universal quantifier (entered as fa)

Exists () existential quantifier (entered as ex)


Reals  ▪  Integers  ▪  Complexes  ▪  Algebraics  ▪  Primes  ▪  Rationals  ▪  Booleans

PositiveReals  ▪  NegativeReals  ▪  NonNegativeReals  ▪  NonPositiveReals

PositiveRationals  ▪  NegativeRationals  ▪  NonNegativeRationals  ▪  NonPositiveRationals

PositiveIntegers  ▪  NegativeIntegers  ▪  NonNegativeIntegers  ▪  NonPositiveIntegers

Refine evaluate an expression using assumptions

Simplify, FullSimplify simplify using assumptions

FunctionExpand expand in terms of simpler functions, using assumptions

Assuming set up assumptions to be used by functions inside

$Assumptions global default for Assumptions option

Functions Allowing Domain Specifications

Reduce  ▪  Resolve  ▪  FindInstance  ▪  Minimize  ▪  NMinimize  ▪  ...

Computing Domain and Range of Functions

FunctionDomain find the domain of a function

FunctionRange find the range of a function