# Simplifying with Assumptions

 Simplify[expr,assum] simplify expr with assumptions

Simplifying with assumptions.

The Wolfram Language does not automatically simplify this, since it is only true for some values of x:
 In:= Out=  is equal to for , but not otherwise:
 In:= Out= This tells Simplify to make the assumption x>0, so that simplification can proceed:
 In:= Out= No automatic simplification can be done on this expression:
 In:= Out= If and are assumed to be positive, the expression can however be simplified:
 In:= Out= Here is a simple example involving trigonometric functions:
 In:= Out= Element[x,dom] state that x is an element of the domain dom Element[{x1,x2,…},dom] state that all the xi are elements of the domain dom Reals real numbers Integers integers Primes prime numbers

Some domains used in assumptions.

This simplifies assuming that is a real number:
 In:= Out= This simplifies the sine assuming that is an integer:
 In:= Out= With the assumptions given, Fermat's little theorem can be used:
 In:= Out= This uses the fact that , but not , is real when is real:
 In:= Out= 