Avmath root

The avmath.__init__.py file provides basic math features. It can be used importing:

# pip install avmath
import avmath

Constants

Mathematical constants

Avmath includes the following constants:

Constant name	accessible name in module	accurate post comma decimal digits digits	Implemented in version	Last change
Pi (π)	avmath.pi	21	v1.0.0	v3.0.0
Euler`s number (e)	avmath.e	21	v1.0.0	v3.0.0
Golden ratio (φ)	avmath.phi	21	v3.0.0	v3.0.0
Euler-Mascheroni constant (γ)	avmath.gamma	21	v3.0.0	v3.0.0
Two digit prime numbers	avmath.two_digit_primes	-	v3.0.0	v3.0.0

Backend constants

Constant name	Default value	usage	Implemented in version	Last change
avmath._TAYLOR_DIFFERENCE	1e-16	Loops of functions using Taylor-series calculate until the difference of the values is less equal this value	v3.0.0	v3.0.0
avmath._MAX_CALCULATION_TIME	5	Some loops may need a long time for calculation. These loops may not calculate longer as this time (in seconds)	v3.0.0	v3.0.0
avmath.REAL	typing.Union[int, float, 'Fraction']	Real numbers for type hints	v3.0.0	v3.0.0
avmath.scope	dictionary that contains all functions for REALs and Fraction	scope for analysis.Function	v2.0.0	v3.1.1

Fraction

Implemented in v3.0.0 | Last change v3.0.0

Avmath's fractions are used to bypass the float inaccuracies.

Attributes

Attribute	Usage	Implemented in version	Last Change
`self.a`	numerator	v3.0.0	v3.0.0
`self.b`	denominator	v3.0.0	v3.0.0

Methods

All methods simulate an immutable type.

Fraction.init(numerator, denominator)

Implemented in v3.0.0 | Last change v3.1.0

Initialises Fraction with given numerator and denominator. Can contain float values too.

A fraction can be initialised by giving numerator and denominator as parameters to the constructor.

import avmath

my_fraction = avmath.Fraction(3, 7)

Now the fraction is initialised and is ready to be used. It is not automatically reduced and never reduced to int.

Fraction.repr()

Implemented in v3.0.0 | Last change v3.0.0

Returns string representation of Fraction. Gets always printed in reduced shape.

import avmath

a = avmath.Fraction(2, 4)
b = avmath.Fraction(6, 3)
print(a)
print(b)

gives the output

1/2

2

Fraction.neg()

Implemented in v3.0.0 | Last change v3.0.0

Returns negative fraction.

Fraction.eq(other)

Implemented in v3.0.0 | Last change v3.0.0

Returns whether Fraction is equal to given REAL.

Fraction.lt(other)

Implemented in v3.0.0 | Last change v3.0.0

Returns whether Fraction is less than given REAL.

Fraction.gt(other)

Implemented in v3.0.0 | Last change v3.0.0

Returns whether Fraction is greater than given REAL.

Fraction.add(other) / Fraction.radd(other)

Implemented in v3.0.0 | Last change v3.1.0

Adds a Fraction with a REAL. Return value is always a Fraction.

Fraction.sub(other) / Fraction.rsub(other)

Implemented in v3.0.0 | Last change v3.1.0

Subtracts a REAL from a Fraction. Returns always Fractions.

Fraction.mul(other) / Fraction.rmul(other)

Implemented in v3.0.0 | Last change v3.0.0

Multiplies a Fraction with a REAL.

Fraction.truediv(other) / Fraction.rtruediv(other)

Implemented in v3.0.0 | Last change v3.1.0

Divides a Fraction by a REAL.

Fraction.pow(power)

Implemented in v3.0.0 | Last change v3.0.0

Power operation for Fraction and REAL. If power=-1; switches numerator and denominator.

Fraction.rpow(other)

Implemented in v3.0.0 | Last change v3.0.0

Power operation with Fraction as exponent.

Fraction.mod(other) / Fraction.rmod(other)

Implemented in v3.0.0 | Last change v3.0.0

Modulo operation for Fraction and REAL.

Fraction.int()

Implemented in v3.0.0 | Last change v3.0.0

Returns integer representation of Fraction.

Fraction.float()

Implemented in v3.0.0 | Last change v3.0.0

Returns float representation of Fraction.

Fraction.complex()

Implemented in v3.1.0 | Last change v3.1.0

Returns float representation of Fraction.

Fraction.abs()

Implemented in v3.0.0 | Last change v3.0.0

Returns absolute of the Fraction.

Fraction.reduce()

Implemented in v3.0.0 | Last change v3.0.0

Returns reduced fraction.

Fraction.int_args()

Implemented in v3.0.0 | Last change v3.0.0

Returns whether the numerator and denominator are integers or integer-like.

Arithmetic functions

is_prime(x)

Implemented in: v3.0.0 | Last change: v3.0.0

This function returns True if the integer x is a prime number. The method checks, whether the integer less than the square root of the argument is divisible by any number.

is_even(x)

Implemented in: v2.0.0 | Last change: v3.0.0

Function returning True if the integer x is an even number. Used by avmath.fac.

gcd(x, y)

Implemented in: v3.0.0 | Last change: v3.0.0

Function returning the greatest common divisor of two integers x and y.

lcm(x, y)

Implemented in: v3.0.0 | Last change: v3.0.0

Function that returns the least common multiply of two integers x and y.

sgn(x)

Implemented in: v3.0.0 | Last change: v3.0.0

Function that returns the signum of a number. For values <0 returns -1 for 0 returns 0 and for values >0 returns 1

fac(x [, opt])

Implemented in: v1.0.0 | Last change: v3.0.0

Function returning the faculty x! of a number.

Parameters for opt:

'double': Returns double faculty [^1]

[^1]: Double faculty is an operation that factorizes all odd numbers less equal the value if the value is odd and all even numbers less equal the value if it is even

ln(x)

Implemented in: v1.0.0 | Last change: v3.0.0

Function that returns the natural logarithm of a number using Taylor-series. Takes only not negative values. Function is recommended to use for values between 1e-300 and. 1e300

x domain	precise post comma decimal places
`1e-300` to `1e300`	12
`1e-3` to `1e3`	14

log(x, base)

Implemented in: v1.0.0 | Last change: v1.0.0

Function that returns the logarithm of any base of a number. Returns only ln(x) / ln(base) and in this way is dependent to the natural logarithm.

See Natural logarithm

sin(x)

Implemented in: v1.0.0 | Last change: v3.0.0

Sine function using Taylor -series. The function is recommended to use in the domain between -100'000 and 100'000 because of inaccuracies of the modulo operator that increase with the value.

x-domain	precise post comma decimal places
`-1e4` to `1e4`	12
`-1e5` to `1e5`	10
`-1e6` to `1e6`	9-10

cos(x)

Implemented in: v1.0.0 | Last change: v3.0.0

Function returning the cosine of a number using Taylor -series. Shares modulo problem with sine and is also recommended between -100'000 and 100'000.

x-domain	precise post comma decimal places
`-1e4` to `1e4`	12
`-1e5` to `1e5`	10
`-1e6` to `1e6`	9-10

tan(x)

Implemented in: v1.0.0 | Last change: v3.0.0

Function returning the tangent of a number calculating sin(x) / cos(x). Shares modulo problem with sine and cosine and is also inaccurate when approaching the asymptotes.

x-domain	precise post comma decimal places
`-1e4` to `1e4` (normal case)	12
`-1e5` to `1e5` (normal case)	10
`-1e6` to `1e6` (normal case)	9-10
`1e-3` difference to asymptote	10
`1e-3` difference to asymptote	7

arcsin(x)

Implemented in: v2.0.0 | Last change: v3.0.0

Function returning the arc sine of a number -1 < x < 1 using Taylor-series. Calculation time increases when approaching |1|. Function may be stopped by _MAX_CALCULATION_TIME. Values of -1 and 1 are manually set.

Difference of x-value to `abs(1)`	precise post comma decimal places
`0.1` to `0.9`	15
`0.01` to `0.1`	13
`0.001` to `0.01`	4

arccos(x)

Implemented in: v2.0.0 | Last change: v3.0.0

Function returning the arc cosine of a number -1 < x < 1 using arccos(x) = π / 2 - arcsin(x). Due to the usage of arcsin(x), the accuracy stays the same.

Difference of x-value to `abs(1)`	precise post comma decimal places
`0.1` to `0.9`	15
`0.01` to `0.1`	13
`0.001` to `0.01`	4

arctan(x)

Implemented in: v2.0.0 | Last change: v3.0.0

Function that returns the arc tangent of a number using two Taylor-series. Calculation time increases when approaching |1|.

absolute of x-domain	precise post comma decimal places
`0` to `0.9`	14-15
at least 0.01 difference to 1	13-14
at least 0.001 difference to 1	13
`1`	6

sinh(x)

Implemented in: v2.0.0 | Last change: v3.1.1

Function returning the hyperbolic sine of a number using Taylor-series. Does only work for x values |x| < 710 then throws ArgumentError.

x-domain	precise decimal places
`-710` to `710`	14-15

cosh(x)

Implemented in: v2.0.0 | Last change: v3.1.1

Function returning the hyperbolic cosine of a number using Taylor-series. Does only work for x values |x| < 710 then throws ArgumentError.

x-domain	precise decimal places
`-710` to `710`	14-15

tanh(x)

Implemented in: v2.0.0 | Last change: v3.0.0

Function returning the hyperbolic tangent of a number using sinh(x) / cosh(x). When surpassing x-value 20, returns 1.0

x-domain	precise post comma decimal places
`-20` to `20`	14-15
`abs(x) > 20`	(returns 1.0)

arsinh(x)

Implemented in: v2.0.0 | Last change: v3.0.0

Function that returns the inverse hyperbolic sine (Areasinus hyperbolicus) of a number using Arsinh(x) = sgn(x) ln(|x| + sqrt(x² + 1)). Values must lie between -1e150 and 1e150 else cause OverflowError.

x-domain	precise post comma decimal places
`-1e150` to `1e150`	13-14

arcosh(x)

Implemented in: v2.0.0 | Last change: v3.0.0

Function returning the inverse hyperbolic cosine (Areacosinus hyperbolicus) of a number x >= 1 using Arcosh(x) = ln(x + sqrt(x² - 1)). Values must lie between -1e150 and 1e150 else cause OverflowError.

x-domain	precise post comma decimal places
`-1e150` to `1e150`	13-14

artanh(x)

Implemented in: v2.0.0 | Last change: v3.0.0

Function returning the inverse hyperbolic tangent (Areatangens hyperbolicus) of a number -1 < x < 1. Therefore, uses Artanh(x) = 0.5 ln((1 + x) / (1 - x)).

x-domain	precise post comma decimal places
entire domain	12-14

Backend functions

_check_types(arg)

Implemented in: v3.0.0 | Last change: v3.0.0

Checks whether all items of the iterable object are of the given types.

Avmath Avmath on PyPi Camillo Ballandt

Avmath root

Contents

Constants

Mathematical constants

Backend constants

Fraction

Attributes

Methods

Fraction.__init__(numerator, denominator)

Fraction.__repr__()

Fraction.__neg__()

Fraction.__eq__(other)

Fraction.__lt__(other)

Fraction.__gt__(other)

Fraction.__add__(other) / Fraction.__radd__(other)

Fraction.__sub__(other) / Fraction.__rsub__(other)

Fraction.__mul__(other) / Fraction.__rmul__(other)

Fraction.__truediv__(other) / Fraction.__rtruediv__(other)

Fraction.__pow__(power)

Fraction.__rpow__(other)

Fraction.__mod__(other) / Fraction.__rmod__(other)

Fraction.__int__()

Fraction.__float__()

Fraction.__complex__()

Fraction.__abs__()

Fraction.reduce()

Fraction.int_args()

Arithmetic functions

is_prime(x)

is_even(x)

gcd(x, y)

lcm(x, y)

sgn(x)

fac(x [, opt])

ln(x)

log(x, base)

sin(x)

cos(x)

tan(x)

arcsin(x)

arccos(x)

arctan(x)

sinh(x)

cosh(x)

tanh(x)

arsinh(x)

arcosh(x)

artanh(x)

Backend functions

_check_types(arg)

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Fraction.init(numerator, denominator)

Fraction.repr()

Fraction.neg()

Fraction.eq(other)

Fraction.lt(other)

Fraction.gt(other)

Fraction.add(other) / Fraction.radd(other)

Fraction.sub(other) / Fraction.rsub(other)

Fraction.mul(other) / Fraction.rmul(other)

Fraction.truediv(other) / Fraction.rtruediv(other)

Fraction.pow(power)

Fraction.rpow(other)

Fraction.mod(other) / Fraction.rmod(other)

Fraction.int()

Fraction.float()

Fraction.complex()

Fraction.abs()