# Python Cheat Sheet

## Libraries

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)
die.append(members)
```

### 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
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
```

### 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
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)
```

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

## Quick Functions

### Type function

To find what type of variable a variable is:

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

### Remainder Function

To find the remainder of a division:

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

## 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')
f.close()
```

### 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 = 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)
```

### Creating a List of Integers from a .txt File

```
f = open('IntegerList.txt', 'r')
a = f.readlines()
f.close()
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):

`f.close()`

## Matrices

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
else:
return
```

## Approximating Pi

```
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