# Basic math operations​
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Questions to [David Rotermund](mailto:davrot@uni-bremen.de)

## Number is Python

In Python everything is a class. Numbers are classes as well. 

### Integer

```python
a_number = 0​
print(type(a_number))​ # -> <class 'int'>​
```

## FLOATing point number

```python
a_second_number = 3.33​
print(type(a_second_number))​ # -> <class 'float'>​
```

## Conversion (i.e. casts) between types

```python
a_second_number = 3.33​
a_second_number = int(a_second_number)​
print(type(a_second_number))​ # -> <class 'int'>​
```

|Examples|
|---|
|[float(x=0.0)](https://docs.python.org/3/library/functions.html#float)|
|[bin(x)](https://docs.python.org/3/library/functions.html#bin)|
|[bool(x=False)](https://docs.python.org/3/library/functions.html#bool)|
|[bytes(source=b'')](https://docs.python.org/3/library/functions.html#func-bytes)|
|[complex(real=0, imag=0)](https://docs.python.org/3/library/functions.html#complex)|
|[hex(x)](https://docs.python.org/3/library/functions.html#hex)|
|[int(x=0)](https://docs.python.org/3/library/functions.html#int)|
|[str(object='')](https://docs.python.org/3/library/functions.html#func-str)|

## [Basic math operations​](https://docs.python.org/3/library/stdtypes.html#numeric-types-int-float-complex​)

Order of operations​:
1. Parentheses
2. Exponents
3. Multiplication/Division
4. Addition/Subtraction

|Operator​|Description​|
|---|---|
|x + y​|sum of x and y​|
|x - y​|difference of x and y​|
|x * y​|product of x and y​|
|x / y​|quotient of x and y​|
|x // y​|floored quotient of x and y​|
|x % y​|remainder of x / y​|
|-x​|x negated​|
|+x​|x unchanged​|

|Operator|Description​|
|---|---|
|abs(x)​|absolute value or magnitude of x​|
|int(x)​|x converted to integer​|
|float(x)​|x converted to floating point​|
|complex(re, im)​|a complex number with real part re, imaginary part im. im defaults to zero.​|
|c.conjugate()​|conjugate of the complex number c​|
|divmod(x, y)​|the pair (x // y, x % y)​|
|pow(x, y)​|x to the power y​|
|x ** y​|x to the power y​|


## "True division"

```python
print(5 / 2)​ # -> 2.5
print(6 / 2)​ # -> 3.0
```

## “Floor division”

```python
print(5 // 2)​ # -> 2
print(6 // 2)​ # -> 3
```

## [Boolean Operations — and, or, not​](https://docs.python.org/3/library/stdtypes.html#boolean-operations-and-or-not)

|Operation​|Result​|
|---|---|
|x or y​|if x is false, then y, else x​|
|x and y​|if x is false, then x, else y​|
|not x​|if x is false, then True, else False​|

## [Comparisons](https://docs.python.org/3/library/stdtypes.html#boolean-operations-and-or-not)

|Operation|Meaning|
|---|---|
|<|strictly less than|
|<=|less than or equal|
|>|strictly greater than|
|>=|greater than or equal|
|==|equal|
|!=|not equal|
|is|object identity|
|is not|negated object identity


## [Bitwise Operations on Integer Types​](https://docs.python.org/3/library/stdtypes.html?highlight=elif#bitwise-operations-on-integer-types​)

|Operation​|Result​|
|---|---|
|x \| y​| bitwise or of x and y​|
|x ^ y​|bitwise exclusive or of x and y​|
|x & y​|bitwise and of x and y​|
|x << n​|x shifted left by n bits​|
|x >> n​|x shifted right by n bits​|
|~x​|the bits of x inverted​|

## [More math operations​ (math lib)](https://docs.python.org/3/library/math.html​)

You need to include the math lib for that! (Only once per .py file and in the beginning of the file)

However, don't get used to it. As a data scientist you will not use it. You will use Numpy. 

```python
import math
print(math.cos(math.pi))​
```

### Examples

|[Number-theoretic and representation functions](https://docs.python.org/3/library/math.html#number-theoretic-and-representation-functions)|
|---|
|math.ceil(x)​|
|math.comb(n, k)|
|math.fabs(x)​|
|math.factorial(n)|
|math.floor(x)​|
|math.fmod(x, y)​|
|math.fsum(iterable)​|
|math.isclose(a, b, *, rel_tol=1e-09, abs_tol=0.0)|
|math.isfinite(x)​|
|math.isinf(x)​|
|math.isnan(x)|
|math.perm(n, k=None)|
|math.prod(iterable, *, start=1)​|
|math.trunc(x)​|

|[Constants](https://docs.python.org/3/library/math.html#constants)|
|---|
|math.pi​|
|math.e​|
|math.inf​|
|math.nan​|

|[Power and logarithmic functions](https://docs.python.org/3/library/math.html#power-and-logarithmic-functions)|
|---|
|math.cbrt(x)​|
|math.exp(x)​|
|math.exp2(x)​|
|math.expm1(x)|
|math.log(x[,base])​|
|math.log1p(x)|
|math.log2(x)​|
|math.log10(x)​|
|math.pow(x, y)​|
|math.sqrt(x)​|


|[Trigonometric functions](https://docs.python.org/3/library/math.html#trigonometric-functions)|
|---|
|math.acos(x)​|
|math.asin(x)​|
|math.atan(x)​|
|math.atan2(y, x)​|
|math.cos(x)​|
|math.sin(x)​|
|math.tan(x)​|
|math.dist(p, q)​|

|[Angular conversion](https://docs.python.org/3/library/math.html#angular-conversion)|
|---|
|math.degrees(x)​|
|math.radians(x)​|

|[Hyperbolic functions](https://docs.python.org/3/library/math.html#hyperbolic-functions)|
|---|
|math.acosh(x)​|
|math.asinh(x)​|
|math.atanh(x)​|
|math.cosh(x)​|
|math.sinh(x)​|
|math.tanh(x)​|





## [Behind the curtain ](https://docs.python.org/3/library/operator.html)

{: .topic-optional}
This is an optional topic!

If you do a + b, in reality this is internally replaced by add(a, b). 

These are the ["Mapping Operators to Functions"](https://docs.python.org/3/library/operator.html#mapping-operators-to-functions):

|Operation|Syntax|Function|
|---|---|---|
|Addition|a + b|add(a, b)|
|Concatenation|seq1 + seq2|concat(seq1, seq2)|
|Containment Test|obj in seq|contains(seq, obj)|
|Division|a / b|truediv(a, b)|
|Division|a // b|floordiv(a, b)|
|Bitwise And|a & b|and_(a, b)|
|Bitwise Exclusive Or|a ^ b|xor(a, b)|
|Bitwise Inversion|~ a|invert(a)|
|Bitwise Or|a \| b|or_(a, b)|
|Exponentiation|a ** b|pow(a, b)|
|Identity|a is b|is_(a, b)|
|Identity|a is not b|is_not(a, b)|
|Indexed Assignment|obj[k] = v|setitem(obj, k, v)|
|Indexed Deletion|del obj[k]|delitem(obj, k)|
|Indexing|obj[k]|getitem(obj, k)|
|Left Shift|a << b|lshift(a, b)|
|Modulo|a % b|mod(a, b)|
|Multiplication|a * b|mul(a, b)|
|Matrix Multiplication|a @ b|matmul(a, b)|
|Negation (Arithmetic)|- a|neg(a)|
|Negation (Logical)|not a|not_(a)|
|Positive|+ a|pos(a)|
|Right Shift|a >> b|rshift(a, b)|
|Slice Assignment|seq[i:j] = values|setitem(seq, slice(i, j), values)|
|Slice Deletion|del seq[i:j]|delitem(seq, slice(i, j))|
|Slicing|seq[i:j]|getitem(seq, slice(i, j))|
|String Formatting|s % obj|mod(s, obj)|
|Subtraction|a - b|sub(a, b)|
|Truth Test|obj|truth(obj)|
|Ordering|a < b|lt(a, b)|
|Ordering|a <= b|le(a, b)|
|Equality|a == b|eq(a, b)|
|Difference|a != b|ne(a, b)|
|Ordering|a >= b|ge(a, b)|
|Ordering|a > b|gt(a, b)|