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
Esc elem Esc)
NotElement (
) — specify exclusion from a domain (
Esc !elem Esc)
Less (
<),
Greater (
>),
... — define inequalities, implicitly for real numbers
ForAll (
) — universal quantifier (entered as
Esc fa Esc)
Exists (
) — existential quantifier (entered as
Esc ex Esc)
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
