Avmath

[Find release](https://github.com/ballandt/avmath/releases/tag/v3.1.1)

Patch level changes

* PEP8 compatible line length 79
* `analysis`
* `Function`
* `derivative`
* h calculation does not fail if f(x) = 0
* `__init__`
* added `sgn` function to `scope`
* removed `Fraction` scope because of errors in `Function.derivative` and `integral`
* `sinh` and `cosh`:
* x values with |x| > 710 cause `ArgumentError`
* constants got typehints
* `pi`
* `e`
* `phi`
* `gamma`

[Find release](https://github.com/ballandt/avmath/releases/tag/v3.1.0)

Announcement

* `analysis`
* `Function`
* The methods `num_dif`, `second_num_dif` and `num_int` are abandoned for `derivative`, `second_derivative` and `integral` yet are still usable
* `Polynom` is cancelled

Minor changes

* `__init__`
* `Fraction`
* `__init__`
* fractions can be used for initialisation
* `complex` method to convert Fraction to complex
* `analysis`
* `Function`
* new method `newton_method_extrema`
* uses newton method with differentiations for the calculation of extrema
* new method `derivative`
* new method for function derivatives
* preferred over `numd_dif`
* new method `second_derivative`
* method for second derivative
* preferred over `second_num_dif`
* new method `integral`
* calculates numerical integral
* in default case uses rectangular rule
* `option="trapeze"` instructs to use trapeze rule
* preferred over `num_int`
* new method `__rtruediv__` for reversed division
* new method `tangent`
* constructs a tangent on a function at a given x
* returns a linear `Function` (y = a * x + b)
* new method `normal`
* constructs a normal on a function at a given x
* returns a linear `Function` (y = a * x + b)

Patch level changes

* `__init__`
* `Fraction`
* `__truediv__`
* formula fixes
* `__add__` supports complex
* `__sub__` supports complex
* `arcsin`
* exception fixed for values < -1
* `analysis`
* `Function`
* `max`-method uses newton method and is much faster and more accurate
* `numdif` developments for accuracy
* `replace`-method does not crash while handling x with no parameter
* `__mul__` can handle REAL argument
* `__truediv__` can handle REAL argument
* `__rtruediv__` can handle REAL argument
* `newton_method` takes a `1e-2` step if the derivative is 0
* `algebra`
* `Structure`
* `area`
* fixes for angles > 180°

---

[Find release](https://github.com/ballandt/avmath/releases/tag/v3.0.0)

API Changes

* `__init__`
* redesigned function `avmath.pi()` to constant `avmath.pi`
* redesigned function `avmath.e()` to constant `avmath.e`
* `_FLOAT_EQ`
* __Deletion__
* `_Point`
* __Deletion__
* `DimensionError`
* moved from `algebra`
* `algebra`
* `Angle`
* __Deletion__
* `Vector`
* `avmath.algebra.Vector.angle()` returns float
* changed location of vector product from `__pow__` to `cross`
* `pow` returns vector multiplied n times by itself
* `Straight`
* __Deletion__
* `Point` -> `Tuple`
* renamed `Point` to `Tuple`
* `AmountOfDimensionsError`
* __Deletion__
* `DimensionError`gets called instead.
* `MatrixMultiplicationError`
* __Deletion__
* `MatrixError` gets called instead
* `Matrix`
* `row`
* returns `Vector` type
* `column`
* returns `Vector` type
* `Structure`
* `circ` -> `circumference`
* renamed `circ` to `circumference`
* `analysis`
* `f` -> `Function`
* renamed `f` to `Function`

Minor changes

* `__all__` for `__init__.py`, `algebra.py` and `analysis.py`
* `__init__`
* imports time module
* new constant `_TAYLOR_DIFFERENCE` as minimal difference between results for taylor-loops with value `1e-16`
* new constant `_MAX_CALCULATION_TIME` for maximum calculation time in taylor-loops with value 5 seconds
* `fac`
* parameter `opt` for double faculty
* new function `_check_types`
* checks if all members of tuple are of specified types
* new constant `phi`
* for golden ratio
* new constant `gamma`
* for Euler-Mascheroni constant
* new function `sgn`
* for signum function
* new function `is_prime`
* checks whether integer is a prime
* new constant `two_digit_primes`
* contains all two digit primes
* new function `gcd`
* returns the greatest common divisor of two integers
* new function `lcm`
* returns the least common multiply of two integers
* new class `Fraction`
* handling of fractions, particularly in linear algebra
* see [Documentation](https://github.com/ballandt/avmath/wiki/Avmath-root#fraction) for all methods
* `analysis`
* `Function`
* new function `newton_method`
* for Newton's method from given x_n
* new function `root`
* returns all roots of the function in given domain
* new function `replace`
* allows `^` as power and coefficients
* new method `second_num_dif`
* numerical second differentiation
* `algebra`
* `Tuple`
* new method `truediv`
* returns tuple divided by scalar for less float inaccuracies
* new method `no_fractions`
* returns copy of `Tuple` with no fractions
* `Vector`
* new method `truediv`
* see `Tuple`
* new method `no_fractions`
* see `Tuple`
* `Matrix`
* new method `truediv`
* see `Tuple`
* new method `no_fractions`
* see `Tuple`
* new method `ref`
* returns row echelon form
* new method `rank`
* returns rank of the matrix
* new method `rref`
* returns reduced row echelon form of the matrix

Bug fixes

* `__init__`
* `fac`
* checks if input _can be interpreted_ as integer
* `ln` works properly and much faster
* trigonometric functions use `while`-loops and `_TAYLOR_DIFFERENCE` to calculate to the best return value possible
* `cos` works properly with negative values
* `algebra`
* `Matrix`
* `inverse`
* works more accurately due to fractions
* `arsinh`
* works in negative domain due to correct spelling of formula
* `artanh`
* does not allow value 1 only to crash afterwards
* `tanh`
* surpassing a value of 20 simply returns 1 instead of calculating (and crashing)
* `arcsin`
* new structure for formula
* does not crash at 710, but is stopped by the maximal time control

---