Assumptions and Domains

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


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

NotElement () — specify exclusion from a domain (Esc!elemEsc)

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

ForAll () — universal quantifier (entered as EscfaEsc)

Exists () — existential quantifier (entered as EscexEsc)


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

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 ▪

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