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Python Cheat Sheet


Before you can use libraries, you need to import them. For maths:

import maths

For random:

import random

If the library name i slong, such as for plotting, you can set a shortened name:

import matplotlib.pyplot as plot

Useful random functions

To generate a random number, n, in the range 0 ≤ n < 1:

n = random.random()

To generate a random integer, n, in the range a ≤ n ≤ b:

n = random.randint(a,b)

Therefore, a function for rolling a standard six-sided die is:

roll = random.randint(1,6)

Lists / Arrays

n number of data points can be stored in lists, where each data point is given an index address. The first term has address [0], and the last term has address [n-1]. Indexing can be done in negative: in this case, the last term has address [-1] and the first term has address [n].

Defining Lists

To define lists manually:

Age = [18, 18, 19, 18, 17 ... ]
Colour = ['Blue', 'Green', 'Yellow' ...]

Note that you need to put strings in quote marks.

To define lists automatically as a list of integers from a range of a to b:

R = range(a, b+1)
A = []
for members in R:
    A = A + [members]

To generate a list from a series of values, for example a set of random numbers:

for members in A:
    members = random.randint(1,6)

Integer Lists

To sum all the terms in a list:

for members in List:
    members = sum(List)

To apply maths on every member of a list, L:

Lx2 = list(map(lambda x: x * 2, L))
Lplus1 = list(map(lambda x: x + 1, L))
Lsquared = list(map(lambda x: x ** 2, L))

To multiply all the numbers in a list together:

def multiply(List):
    total = 1
    for n in List:
        total *= n
    return total

To swap two elements in a list:

L = [1,2,3,4,5]
#to swap 2 and 3:
temp = L[1]
L[1] = L[2]
L[2] = temp

Searching Lists

To search for a value in a list, there are two options. The first is to use a for loop - this is used when you want to carry on searching the list even after you found the value:

List = #define list
find = input()
# Convert to integer if necessary
found = False
for members in List:
    if members == find:
        found = True

The second is to use a while loops - this will stop counting either when you reach the value, or when the whole list has been counted:

List = #define list
N = len(List)
find = input()
# Convert to integer if necessary
found = False
count = 0
while (not found) and count < N:
    if List[count] == find:
        found = True
        count = count + 1

Boolean Operations

The if-else function is used to test boolean outcomes (where the outcome is either 'yes' or 'no').

  • a == b a equals b

  • a != b a does not equal b

  • a < b a is less than b

  • a > b a is greater than b

  • a <= b a is smaller than or equal to b

  • a => b a is greater than or equal to b

A nice example is rolling two dice. This requires two loops, the first tests for a draw, the second for a winner.

import random as rn

#Setting up rolling functions
Die1 = rn.randint(1,6)
Die2 = rn.randint(1,6)

#Rolling the dice
print('Die 1 lands on a', Die1)
print('Die 2 lands on a', Die2)

if Die1 == Die2:
    #it is a draw
    print('It is a draw.')
    if Die1 < Die2:
        #Die2 wins
        print('Die 2 wins.')
        #Die1 wins
        print('Die 1 wins.')

Quick Functions

Type function

To find what type of variable a variable is:

    #for variable = var

    #to print this:

Remainder Function

To find the remainder of a division:

    # a is the numerator
    # b is the denominator
    # r is the remainder
r = a//b

I/O Files

Data can be input directly or indirectly to a code. Direct inputs are provided interactively, while the programme is running (e.g. using a keyboard and the input() function). Indirect inputs are when data is read from a predefined location, such as a file.

Writing to Files

Just like libraries, files need to be uploaded before they can be accessed:

f = open('FileName.txt', 'w')

This opens the file 'FileName.txt' to write to it, and assigns it to variable f. To write something to the file, for example a number of strings, use the write command:

    # To add strings a and b to the file on separate lines:
f.write(str(a) + '\n')
f.write(str(b) + '\n')

To write from a list:

    # To add a list to a file, with each element on a new line:
for item in a:
    f.write(str(item) + '\n')

To create a file with numbers from 1 to 100:

f = open('Numbers100.txt', 'w')
R = range(1, 101)
for i in R:
	f.write(str(i) + '\n')

Reading from Files

Instead of using a 'w', an 'r' represents reading:

f = open('FileName.txt', 'r')

By default, the program will read a file exactly as it is:

f = open('FileName.txt, 'r')
a =

If, however, you want to compile all the lines into a list, use the .readlines command:

f = open('FileName.txt', 'r')
a = f.readlines()

This produces a list of strings with operators '\n' attached. The new line trail can be removed using a strip function:

f = open('FileName.txt', 'r')
a = f.readlines()
b = []
for items in a:
    b = b + [items.rstrip()]

Creating a List of Integers from a .txt File

f = open('IntegerList.txt', 'r')
a = f.readlines()
b = []
for items in a:
    b = b + [int(items.rstrip())]

Closing Files

When finished with a file, it needs to be closed (this is like saving it):



Python is a very powerful tool for computing data stored in matrices.

Defining a Matrix from a List

  • n is the number of rows

  • m is the number of columns

  • 'List' is... the list

def Matrix(n, m, List):
    row = []
    matrix = [0 for height in range(0, n)
    for p in range(0, n, 1):
        for i in range((p*m), ((p+1)*m)):
            row = row + [List[i]]
        matrix[p] = row
        row = []
    return matrix

Finding the Transpose of a Matrix

  • M is the matrix we want to transpose

  • n is the number of rows in M

  • m is the number of columns in M

def Transpose(n, m, M):
    #M is an nxm matrix
    row = []
    transpose = [0 for height in range(0, m)]
    #B is the column number
    for B in range(0, m):
        #A is the row number
        for A in range(0, n):
            row = row + [M[A][B]}
        transpose[B] = row
        row = []
    return transpose

Finding the Product of Two Matrices

def MatrixMult(A, B):
    #A and B are the matrices, AB = C
    if len(A[0]) == len(B):
        add = 0
        C = [[0 for width in range(len(B[0]))] for height in range(len(A))[
        for x in range(0, len(A)):
            for y in range(0, len(B[0])):
                for z in range(0, len(A[0])):
                    add = add + (A[x][z]*B[z][y])
                C[x][y] = add
                add = 0
        return C

Approximating Pi

import matplotlib.pyplot as plot
import random as rn

print('Input n:')
n = input()
r = range(1,n)

xout = []
xin = []
yout = []
yin = []

pointsinside = 0
pointsoutside = 0

for c in r:
    x = rn.random()-0.5
    y = rn.random()-0.5
    if(x**2 + y**2 < 0.25):
        xin = xin + [x]
        yin = yin + [y]
        xout = xout + [x]
        yout = yout + [y]

pi = len(xin)*4/n
print('Pi =', pi)

plot.scatter(xin, yin, color = 'green')
plot.scatter(xout, yout, color = 'black')

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Notes by Category

University Engineering

A-Level Further Maths

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