CoCalc -- Chapter 2-3: Functions, Indentation, and Counting.ipynb

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2.3 Functions, Indentation, and Counting

To define a new function in Sage, use the def command and a colon after the list of variable names.

For example:

In [3]:

def is_even(n):
    return n % 2 == 0

In [4]:

is_even(2)

Out[4]:

True

In [5]:

is_even(3)

Out[5]:

False

In [6]:

from sage.all import *
def is_even(n):
    return n % Integer(2) == Integer(0)

In [7]:

is_even(Integer(2))

Out[7]:

True

In [8]:

is_even(Integer(3))

Out[8]:

False

Note: Depending on which version of the tutorial you are viewing, you may see three dots ....: on the second line of this example. Do not type them; they are just to emphasize that the code is indented. Whenever this is the case, press [Return/Enter] once at the end of the block to insert a blank line and conclude the function definition.

You do not specify the types of any of the input arguments. You can specify multiple inputs, each of which may have an optional default value. For example, the function below defaults to divisor=2 if divisor is not specified.

In [9]:

def is_divisible_by(number, divisor=2):
    return number % divisor == 0

In [10]:

is_divisible_by(6, 2)

Out[10]:

True

In [11]:

is_divisible_by(6)

Out[11]:

True

In [12]:

is_divisible_by(6, 5)

Out[12]:

False

In [13]:

from sage.all import *
def is_divisible_by(number, divisor=Integer(2)):
    return number % divisor == Integer(0)

In [14]:

is_divisible_by(Integer(6), Integer(2))

Out[14]:

True

In [15]:

is_divisible_by(Integer(6))

Out[15]:

True

In [16]:

is_divisible_by(Integer(6), Integer(5))

Out[16]:

False

You can also explicitly specify one or either of the inputs when calling the function; if you specify the inputs explicitly, you can give them in any order:

In [17]:

is_divisible_by(6, divisor=5)

Out[17]:

False

In [18]:

is_divisible_by(divisor=2, number=6)

Out[18]:

True

In [19]:

from sage.all import *
is_divisible_by(Integer(6), divisor=Integer(5))

Out[19]:

False

In [20]:

is_divisible_by(divisor=Integer(2), number=Integer(6))

Out[20]:

True

2.3 Functions, Indentation, and Counting

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