# Assignment, Equality, and Arithmetic¶

With some minor exceptions, Sage uses the Python programming language, so most introductory books on Python will help you to learn Sage.

Sage uses `=`

for assignment. It uses `==`

, `<=`

, `>=`

, `<`

and `>`

for
comparison:

```
sage: a = 5
sage: a
5
sage: 2 == 2
True
sage: 2 == 3
False
sage: 2 < 3
True
sage: a == 5
True
```

Sage provides all of the basic mathematical operations:

```
sage: 2**3 # ** means exponent
8
sage: 2^3 # ^ is a synonym for ** (unlike in Python)
8
sage: 10 % 3 # for integer arguments, % means mod, i.e., remainder
1
sage: 10/4
5/2
sage: 10//4 # for integer arguments, // returns the integer quotient
2
sage: 4 * (10 // 4) + 10 % 4 == 10
True
sage: 3^2*4 + 2%5
38
```

The computation of an expression like `3^2*4 + 2%5`

depends on
the order in which the operations are applied; this is specified in
the “operator precedence table” in Arithmetical binary operator precedence.

Sage also provides many familiar mathematical functions; here are just a few examples:

```
sage: sqrt(3.4)
1.84390889145858
sage: sin(5.135)
-0.912021158525540
sage: sin(pi/3)
1/2*sqrt(3)
```

As the last example shows, some mathematical expressions return
‘exact’ values, rather than numerical approximations. To get a
numerical approximation, use either the function `n`

or the method
`n`

(and both of these have a longer name, `numerical_approx`

, and
the function `N`

is the same as `n`

)). These take optional
arguments `prec`

, which is the requested number of bits of
precision, and `digits`

, which is the requested number of decimal
digits of precision; the default is 53 bits of precision.

```
sage: exp(2)
e^2
sage: n(exp(2))
7.38905609893065
sage: sqrt(pi).numerical_approx()
1.77245385090552
sage: sin(10).n(digits=5)
-0.54402
sage: N(sin(10),digits=10)
-0.5440211109
sage: numerical_approx(pi, prec=200)
3.1415926535897932384626433832795028841971693993751058209749
```

Python is dynamically typed, so the value referred to by each variable has a type associated with it, but a given variable may hold values of any Python type within a given scope:

```
sage: a = 5 # a is an integer
sage: type(a)
<type 'sage.rings.integer.Integer'>
sage: a = 5/3 # now a is a rational number
sage: type(a)
<type 'sage.rings.rational.Rational'>
sage: a = 'hello' # now a is a string
sage: type(a)
<... 'str'>
```

The C programming language, which is statically typed, is much different; a variable declared to hold an int can only hold an int in its scope.