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

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)

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].

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)
  die.append(members)

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
 print(multiply((List)))

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

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
 print(found)

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
  else:
  count = count + 1
 print(found)

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

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.')
 else:
  if Die1 < Die2:
  #Die2 wins
  print('Die 2 wins.')
  else:
  #Die1 wins
  print('Die 1 wins.')

To find what type of variable a variable is:

#for variable = var
 type(var)
 
  #to print this:
 print(type(var))

To find the remainder of a division:

# a is the numerator
  # b is the denominator
  # r is the remainder
 r = a//b
 print(r)

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.

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')
 f.close()

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 = f.read()
 f.close()
 print(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()
 f.close
 print(a)

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()
 f.close()
 b = []
 for items in a:
  b = b + [items.rstrip()]
 print(b)

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

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

f.close()

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

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

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

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
  else:
  return

import matplotlib.pyplot as plot
 import random as rn
 
 print('Input n:')
 n = input()
 n=int(n)
 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]
  else:
  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')

TEST FOR jqMATH

$$y-y_0=m(x-x_0)$$

$$y-y_0=m(x-x_0)$$

$$ax^2$$

is there an equation here? \( ax^2 \) I wonder if it works