298 lines
7.5 KiB
Markdown
298 lines
7.5 KiB
Markdown
# Basic math operations
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{:.no_toc}
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<nav markdown="1" class="toc-class">
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* TOC
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{:toc}
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</nav>
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Questions to [David Rotermund](mailto:davrot@uni-bremen.de)
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## Number is Python
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In Python everything is a class. Numbers are classes as well.
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### Integer
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```python
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a_number = 0
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print(type(a_number)) # -> <class 'int'>
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```
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## FLOATing point number
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```python
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a_second_number = 3.33
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print(type(a_second_number)) # -> <class 'float'>
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```
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## Conversion (i.e. casts) between types
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```python
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a_second_number = 3.33
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a_second_number = int(a_second_number)
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print(type(a_second_number)) # -> <class 'int'>
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```
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|Examples|
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|---|
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|[float(x=0.0)](https://docs.python.org/3/library/functions.html#float)|
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|[bin(x)](https://docs.python.org/3/library/functions.html#bin)|
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|[bool(x=False)](https://docs.python.org/3/library/functions.html#bool)|
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|[bytes(source=b'')](https://docs.python.org/3/library/functions.html#func-bytes)|
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|[complex(real=0, imag=0)](https://docs.python.org/3/library/functions.html#complex)|
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|[hex(x)](https://docs.python.org/3/library/functions.html#hex)|
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|[int(x=0)](https://docs.python.org/3/library/functions.html#int)|
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|[str(object='')](https://docs.python.org/3/library/functions.html#func-str)|
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## [Basic math operations](https://docs.python.org/3/library/stdtypes.html#numeric-types-int-float-complex)
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Order of operations:
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1. Parentheses
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2. Exponents
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3. Multiplication/Division
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4. Addition/Subtraction
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|Operator|Description|
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|---|---|
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|x + y|sum of x and y|
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|x - y|difference of x and y|
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|x * y|product of x and y|
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|x / y|quotient of x and y|
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|x // y|floored quotient of x and y|
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|x % y|remainder of x / y|
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|-x|x negated|
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|+x|x unchanged|
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|Operator|Description|
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|---|---|
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|abs(x)|absolute value or magnitude of x|
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|int(x)|x converted to integer|
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|float(x)|x converted to floating point|
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|complex(re, im)|a complex number with real part re, imaginary part im. im defaults to zero.|
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|c.conjugate()|conjugate of the complex number c|
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|divmod(x, y)|the pair (x // y, x % y)|
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|pow(x, y)|x to the power y|
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|x ** y|x to the power y|
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## "True division"
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```python
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print(5 / 2) # -> 2.5
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print(6 / 2) # -> 3.0
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```
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## “Floor division”
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```python
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print(5 // 2) # -> 2
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print(6 // 2) # -> 3
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```
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## Inplace Operation
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|Inplace Operation|Short for|
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|---|---|
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|a += b| a = a + b|
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|a &= b| a = a & b |
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|a //= b|a = a // b|
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|a <<= b| a = a << b|
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|a %= b| a = a % b|
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|a *= b| a = a * b|
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|a @= b| a = a @ b|
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|a \|= b| a = a \| b|
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|a **= b| a = a ** b|
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|a >>= b| a = a >> b|
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|a -= b| a = a - b|
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|a /= b| a = a / b|
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|a ^= b| a = a ^ b|
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## [Boolean Operations — and, or, not](https://docs.python.org/3/library/stdtypes.html#boolean-operations-and-or-not)
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|Operation|Result|
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|---|---|
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|x or y|if x is false, then y, else x|
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|x and y|if x is false, then x, else y|
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|not x|if x is false, then True, else False|
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## [Comparisons](https://docs.python.org/3/library/stdtypes.html#boolean-operations-and-or-not)
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|Operation|Meaning|
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|---|---|
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|<|strictly less than|
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|<=|less than or equal|
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|>|strictly greater than|
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|>=|greater than or equal|
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|==|equal|
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|!=|not equal|
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|is|object identity|
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|is not|negated object identity
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## [Bitwise Operations on Integer Types](https://docs.python.org/3/library/stdtypes.html?highlight=elif#bitwise-operations-on-integer-types)
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|Operation|Result|
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|x \| y| bitwise or of x and y|
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|x ^ y|bitwise exclusive or of x and y|
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|x & y|bitwise and of x and y|
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|x << n|x shifted left by n bits|
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|x >> n|x shifted right by n bits|
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|~x|the bits of x inverted|
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## [More math operations (math lib)](https://docs.python.org/3/library/math.html)
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You need to include the math lib for that! (Only once per .py file and in the beginning of the file)
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However, don't get used to it. As a data scientist you will not use it. You will use Numpy.
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```python
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import math
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print(math.cos(math.pi))
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```
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### Examples
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|[Number-theoretic and representation functions](https://docs.python.org/3/library/math.html#number-theoretic-and-representation-functions)|
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|math.ceil(x)|
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|math.comb(n, k)|
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|math.fabs(x)|
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|math.factorial(n)|
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|math.floor(x)|
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|math.fmod(x, y)|
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|math.fsum(iterable)|
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|math.isclose(a, b, *, rel_tol=1e-09, abs_tol=0.0)|
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|math.isfinite(x)|
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|math.isinf(x)|
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|math.isnan(x)|
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|math.perm(n, k=None)|
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|math.prod(iterable, *, start=1)|
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|math.trunc(x)|
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|[Constants](https://docs.python.org/3/library/math.html#constants)|
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|---|
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|math.pi|
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|math.e|
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|math.inf|
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|math.nan|
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|[Power and logarithmic functions](https://docs.python.org/3/library/math.html#power-and-logarithmic-functions)|
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|math.cbrt(x)|
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|math.exp(x)|
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|math.exp2(x)|
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|math.expm1(x)|
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|math.log(x[,base])|
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|math.log1p(x)|
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|math.log2(x)|
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|math.log10(x)|
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|math.pow(x, y)|
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|math.sqrt(x)|
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|[Trigonometric functions](https://docs.python.org/3/library/math.html#trigonometric-functions)|
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|math.acos(x)|
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|math.asin(x)|
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|math.atan(x)|
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|math.atan2(y, x)|
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|math.cos(x)|
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|math.sin(x)|
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|math.tan(x)|
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|math.dist(p, q)|
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|[Angular conversion](https://docs.python.org/3/library/math.html#angular-conversion)|
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|math.degrees(x)|
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|math.radians(x)|
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|[Hyperbolic functions](https://docs.python.org/3/library/math.html#hyperbolic-functions)|
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|math.acosh(x)|
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|math.asinh(x)|
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|math.atanh(x)|
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|math.cosh(x)|
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|math.sinh(x)|
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|math.tanh(x)|
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## [Behind the curtain ](https://docs.python.org/3/library/operator.html)
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{: .topic-optional}
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This is an optional topic!
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If you do a + b, in reality this is internally replaced by add(a, b).
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These are the ["Mapping Operators to Functions"](https://docs.python.org/3/library/operator.html#mapping-operators-to-functions):
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|Operation|Syntax|Function|
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|Addition|a + b|add(a, b)|
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|Concatenation|seq1 + seq2|concat(seq1, seq2)|
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|Containment Test|obj in seq|contains(seq, obj)|
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|Division|a / b|truediv(a, b)|
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|Division|a // b|floordiv(a, b)|
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|Bitwise And|a & b|and_(a, b)|
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|Bitwise Exclusive Or|a ^ b|xor(a, b)|
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|Bitwise Inversion|~ a|invert(a)|
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|Bitwise Or|a \| b|or_(a, b)|
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|Exponentiation|a ** b|pow(a, b)|
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|Identity|a is b|is_(a, b)|
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|Identity|a is not b|is_not(a, b)|
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|Indexed Assignment|obj[k] = v|setitem(obj, k, v)|
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|Indexed Deletion|del obj[k]|delitem(obj, k)|
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|Indexing|obj[k]|getitem(obj, k)|
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|Left Shift|a << b|lshift(a, b)|
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|Modulo|a % b|mod(a, b)|
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|Multiplication|a * b|mul(a, b)|
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|Matrix Multiplication|a @ b|matmul(a, b)|
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|Negation (Arithmetic)|- a|neg(a)|
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|Negation (Logical)|not a|not_(a)|
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|Positive|+ a|pos(a)|
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|Right Shift|a >> b|rshift(a, b)|
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|Slice Assignment|seq[i:j] = values|setitem(seq, slice(i, j), values)|
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|Slice Deletion|del seq[i:j]|delitem(seq, slice(i, j))|
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|Slicing|seq[i:j]|getitem(seq, slice(i, j))|
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|String Formatting|s % obj|mod(s, obj)|
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|Subtraction|a - b|sub(a, b)|
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|Truth Test|obj|truth(obj)|
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|Ordering|a < b|lt(a, b)|
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|Ordering|a <= b|le(a, b)|
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|Equality|a == b|eq(a, b)|
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|Difference|a != b|ne(a, b)|
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|Ordering|a >= b|ge(a, b)|
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|Ordering|a > b|gt(a, b)|
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[In-place Operators](https://docs.python.org/3/library/operator.html#in-place-operators)
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|a += b| a = iadd(a, b)|
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|a &= b| a = iand(a, b) |
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|a += b for a and b **sequences**| a = iconcat(a, b)|
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|a //= b|a = ifloordiv(a, b)|
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|a <<= b| a = ilshift(a, b)|
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|a %= b| a = imod(a, b)|
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|a *= b| a = imul(a, b)|
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|a @= b| a = imatmul(a, b)|
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|a \|= b| a = ior(a, b)|
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|a **= b| a = ipow(a, b)|
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|a >>= b| a = irshift(a, b)|
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|a -= b| a = isub(a, b)|
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|a /= b| a = itruediv(a, b)|
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|a ^= b| a = ixor(a, b)|
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