Some Mathematical Functions

The Wolfram Language includes a very large collection of mathematical functions. "Mathematical Functions" gives the complete list. Here are a few of the common ones.

Sqrt[x]	square root ( )
Exp[x]	exponential ( )
Log[x]	natural logarithm ( )
Log[b,x]	logarithm to base ()
Sin[x], Cos[x], Tan[x]	trigonometric functions (with arguments in radians)
ArcSin[x], ArcCos[x], ArcTan[x]	inverse trigonometric functions
n!	factorial (product of integers )
Abs[x]	absolute value
Round[x]	closest integer to
Mod[n,m]	modulo (remainder on division of by )
RandomReal[]	pseudorandom number between 0 and 1
Max[x,y,…], Min[x,y,…]	maximum, minimum of , , …
FactorInteger[n]	prime factors of (see "Integer and Number Theoretic Functions")

Some common mathematical functions.

■ The arguments of all Wolfram Language functions are enclosed in square brackets.

■ The names of built‐in Wolfram Language functions begin with capital letters.

Two important points about functions in the Wolfram Language.

It is important to remember that all function arguments in the Wolfram Language are enclosed in square brackets, not parentheses. Parentheses in the Wolfram Language are used only to indicate the grouping of terms, and never to give function arguments.

This gives

. Notice the capital letter for Log, and the square brackets for the argument:

In[1]:= 1

✖

https://wolfram.com/xid/0fz3kl17reacnn-zhz

Out[1]= 1

Just as with arithmetic operations, the Wolfram Language tries to give exact values for mathematical functions when you give it exact input.

This gives

as an exact integer:

In[2]:= 2

✖

https://wolfram.com/xid/0fz3kl17reacnn-mhh

Out[2]= 2

This gives an approximate numerical result for

:

In[3]:= 3

✖

https://wolfram.com/xid/0fz3kl17reacnn-qx5

Out[3]= 3

The presence of an explicit decimal point tells the Wolfram Language to give an approximate numerical result:

In[4]:= 4

✖

https://wolfram.com/xid/0fz3kl17reacnn-wie

Out[4]= 4

Since you are not asking for an approximate numerical result, the Wolfram Language leaves the number here in an exact symbolic form:

In[5]:= 5

✖

https://wolfram.com/xid/0fz3kl17reacnn-yo7

Out[5]= 5

Here is the exact integer result for

. Computing factorials like this can give you very large numbers. You should be able to calculate up to at least 2000! in a short time:

In[6]:= 6

✖

https://wolfram.com/xid/0fz3kl17reacnn-ba3

Out[6]= 6

This gives the approximate numerical value of the factorial:

In[7]:= 7

✖

https://wolfram.com/xid/0fz3kl17reacnn-rh2

Out[7]= 7

Pi
E	(normally output as )
Degree	: degrees-to-radians conversion factor (normally output as )
I	(normally output as )
Infinity

Some common mathematical constants.

Notice that the names of these built‐in constants all begin with capital letters.

This gives the numerical value of

:

In[8]:= 8

✖

https://wolfram.com/xid/0fz3kl17reacnn-y1s

Out[8]= 8

This gives the exact result for

. Notice that the arguments to trigonometric functions are always in radians:

In[9]:= 9

✖

https://wolfram.com/xid/0fz3kl17reacnn-ylw

Out[9]= 9

This gives the numerical value of

. Multiplying by the constant Degree converts the argument to radians:

In[10]:= 10

✖

https://wolfram.com/xid/0fz3kl17reacnn-sdt

Out[10]= 10

Log[x] gives logarithms to base

:

In[11]:= 11

✖

https://wolfram.com/xid/0fz3kl17reacnn-wj8

Out[11]= 11

You can get logarithms in any base b using Log[b,x]. As in standard mathematical notation, the b is optional:

In[12]:= 12

✖

https://wolfram.com/xid/0fz3kl17reacnn-dmh

Out[12]= 12

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