An integer in Python, also known as a 'numeric literal', is simply a name used for a numeric value. For this reason, these values are commonly called integers even if they are assigned the value of a real number in the form of an integer and a decimal value. Integers are immutable data types, which means that changing the value of a number data type results in a newly allocated object.
Integer object is created when you assign a integer value to variable, For Ex;
>>> x = 32 >>> y = 55 >>> type(x) <type 'int'> >>> type(y) <type 'int'>
In above example x is variable name and assigned value '32' and checking it’s type using type() function shows 'int'.
- Python has four different types of integers;int : Integers or int's are whole numbers with no decimal points.
- float : Floating point numbers or floats are real numbers with decimal points.
- long : long integers are of unlimited size.
- complex : Complex integers are x + yj, where x and y are floats and j (or J) represents the square root of -1.
Examples of different integer types.
int : 34, 5, -78
float : 34.5, -2.453213, 666.45
long : 7543856L, -349752587L, 9824365768798L
complex : 5.54j, 884-3k+4.32, -23+34k+234
>>> x = 34 >>> type(x) <type 'int'>
>>> y = -5333.33 >>> type(y) <type 'float'> >>> z = 2127372373473747574757 >>> type(z) <type 'long'>
>>> w = -323+45.34-34J >>> type(w) <type 'complex'>
Python Convert integer type:
Some time we need change the type of integer to make good sense in programming, Python allows to change the type of integer as shown below;
- To convert any integer type to plain 'int' use int() function as shown in example;
>>> x = 3.14 >>> int(x) 3
- To convert any integer type to float use float() function as shown in example;
>>> x = 3 >>> float(x) 3.0
- To convert any integer type to long number use long() function as shown in example;
>>> x = 3 >>> long(x) 3L
- To convert any integer type to complex number use complex() function as shown in example;
>>> x = 3 >>> complex(x) (3+0j)
Python mathematical operations for integers:
Python has builtin library called 'math' to perform mathematical operations. Following table contains the list of all mathematical functions and example of each function is given below.
Math Function | Description |
---|---|
abs(x) | The positive distance between x and zero, i.e the absolute value of x. |
ceil(x) | The ceiling of x: the smallest integer not less than x. |
cmp(x, y) | Returns -1 if x < y, Returns 0 if x == y, Returns 1 if x > y. |
exp(x) | The exponential of x. |
fabs(x) | The absolute value of x. |
floor(x) | The floor of x: the largest integer not greater than x. |
log(x) | The natural logarithm of x, for x> 0. |
log10(x) | The base-10 logarithm of x for x> 0. |
max(x1, x2,…) | The largest of it’s arguments. |
min(x1, x2,…) | The smallest of it’s arguments. |
modf(x) | The fractional and integer parts of x in a two-item tuple. Both parts have the same sign as x. The integer part is returned as a float. |
pow(x, y) | The value of x**y. |
round(x [,n]) | x rounded to n digit’s from the decimal point. Python rounds away from zero as a tie-breaker: round(0.5) is 1.0 and round(-0.5) is -1.0. |
sqrt(x) | The square root of x for x > 0 |
Examples of Above functions:
- abs(x) Returns the positive distance between x and zero, i.e the absolute value of x.
>>> x = -33.56 >>> abs(x) 33.56
- ceil(x) Returns the ceiling of x: the smallest integer not less than x.
>>> from math import ceil >>> x = 55.23 >>> ceil(x) 56.0
- cmp(x, y) Returns -1 if x < y, Returns 0 if x == y, Returns 1 if x > y.
>>> x = 2 >>> y = 4 >>> cmp(x, y) -1
- exp(x) The exponential of x.
>>> from math import exp >>> x = 55.32 >>> exp(x) 1.0596702429230294e+24
- fabs(x) The absolute value of x.
>>> from math import fabs >>> x = 55.32 >>> fabs(x) 55.32
- floor(x) The floor of x: the largest integer not greater than x.
>>> from math import floor >>> x = 55.32 >>> floor(x) 55.0
- log(x) The natural logarithm of x, for x> 0.
>>> from math import log >>> x = 2 >>> log(x) 0.6931471805599453
- log10(x) The base-10 logarithm of x for x> 0.
>>> from math import log10 >>> x = 2 >>> log10(x) 0.3010299956639812
- max(x1, x2,..) The largest of it’s arguments.
>>> max(0,1,2,3,4,5,6,7,8,9) 9
min(x1, x2,…) The smallest of it’s arguments.
>>> min(0,1,2,3,4,5,6,7,8,9) 0
- modf(x) The fractional and integer parts of x in a two-item tuple. Both parts have the same sign as x. The integer part is returned as a float.
>>> from math import modf >>> x = 2 >>> modf(2) (0.0, 2.0)
pow(x, y) The value of x**y.
>>> from math import pow >>> x = 2 >>> y = 4 >>> pow(x, y) 16.0
- round(x [,n]) x rounded to n digit’s from the decimal point. Python rounds away from zero as a tie-breaker: round(0.5) is 1.0 and round(-0.5) is -1.0.
>>> x = 33.22 >>> round(x) 33.0
- sqrt(x) The square root of x for x > 0.
>>> from math import sqrt >>> x = 4 >>> sqrt(x) 2.0
Trigonometric Functions for Integers:
Python math library includes few trigonometric functions which are useful for mathematical operations;
Functions | Description |
---|---|
acos(x) | Return the arc cosine of x, in radians. |
asin(x) | Return the arc sine of x, in radians. |
atan(x) | Return the arc tangent of x, in radians. |
atan2(y, x) | Return atan(y / x), in radians. |
cos(x) | Return the cosine of x radians. |
hypot(x, y) | Return the Euclidean norm, sqrt(x*x + y*y). |
sin(x) | Return the sine of x radians. |
tan(x) | Return the tangent of x radians. |
degrees(x) | Converts angle x from radians to degrees. |
radians(x) | Converts angle x from degrees to radians. |
Examples of above functions;
- acos(x) Return the arc cosine of x, in radians.
>>> from math import acos >>> x = 0 >>> acos(x) 1.5707963267948966
- asin(x) Return the arc sine of x, in radians.
>>> from math import asin >>> x = 1 >>> asin(x) 1.5707963267948966
- atan(x) Return the arc tangent of x, in radians.
>>> from math import atan >>> x = 1 >>> atan(x) 0.7853981633974483
- cos(x) Return the cosine of x radians.
>>> from math import cos >>> x = 1 >>> cos(x) 0.5403023058681398
- hypot(x, y) Return the Euclidean norm, sqrt(x*x + y*y).
>>> from math import hypot >>> x = 2 >>> y = 3 >>> hypot(x, y) 3.605551275463989
- sin(x) Return the sine of x radians.
>>> from math import sins >>> x = 1 >>> sin(x) 0.8414709848078965
- tan(x) Return the tangent of x radians.
>>> from math import tan >>> x = 1 >>> tan(x) 1.5574077246549023
- degrees(x) Converts angle x from radians to degrees.
>>> from math import degrees >>> x = 1 >>> degrees(x) 57.29577951308232
- radians(x) Converts angle x from degrees to radians.
>>> from math import radians >>> x = 1 >>> radians(x) 0.017453292519943295
- pi Mathematical constant pi
>>> from math import pi >>> pi 3.141592653589793
- e Mathematical constant pi
>>> from math import e >>> e 2.718281828459045
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