# Wolfram Language & System 10.4 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
WOLFRAM LANGUAGE TUTORIAL

# 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 .
 In[1]:=
 Out[1]=
is equal to for , but not otherwise.
 In[2]:=
 Out[2]=
This tells Simplify to make the assumption , so that simplification can proceed.
 In[3]:=
 Out[3]=
No automatic simplification can be done on this expression.
 In[4]:=
 Out[4]=
If and are assumed to be positive, the expression can however be simplified.
 In[5]:=
 Out[5]=
Here is a simple example involving trigonometric functions.
 In[6]:=
 Out[6]=
 Element[x,dom] state that x is an element of the domain dom Element[{x1,x2,…},dom] state that all the 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[7]:=
 Out[7]=
This simplifies the sine assuming that is an integer.
 In[8]:=
 Out[8]=
With the assumptions given, Fermat's little theorem can be used.
 In[9]:=
 Out[9]=
This uses the fact that , but not , is real when is real.
 In[10]:=
 Out[10]=