ContFrac
===============================================================================
Continued fractions are a representation of numbers expressed as recursive
sums of integer parts and reciprocals of other numbers. _ContFrac_ is a
pure-Python3 lightweight module to compute and evaluate continued fractions,
as well as using them to approximate any number.
Features
----------------------------------------
- Supports conversion into continued fractions of `int`, `float`,
`fractions.Fraction` and rational numbers expressed as tuples of 2 integers
`(numerator, denominator)`, generated iteratively.
- Computes the convergents of the same data types, generated iteratively.
- Computes the value of a finite continued fraction.
- Generates the arithmetical expression as string of a continued fraction.
Installation
----------------------------------------
```bash
pip install contfrac
```
or just include the `contfrac.py` file in your project (copy-paste).
Example usage
----------------------------------------
```python
>>> import contfrac
>>> value = 415/93 # Express as (415, 93) to avoid rounding continued frac.
>>> coefficients = list(contfrac.continued_fraction(value))
>>> print(coefficients)
[4, 2, 6, 7]
>>> expression = contfrac.arithmetical_expr(coefficients)
>>> print('Value: {:f} = {:s}'.format(value, expression))
Value: 4.462366 = 4 + 1/(2 + 1/(6 + 1/(7)))
>>> # The evaluation of a float value from a continued fraction is subject
>>> # to floating point rounding errors
>>> eval_value = contfrac.evaluate(coefficients)
>>> print(eval_value, value) # Visible rounding errors
4.46236559139785 4.462365591397849
>>> convergents = list(contfrac.convergents(value))
>>> print(convergents)
[(4, 1), (9, 2), (58, 13), (415, 93)]
>>> import math
>>> coefficients = list(contfrac.continued_fraction(math.e, maxlen=10))
>>> print(coefficients)
[2, 1, 2, 1, 1, 4, 1, 1, 6, 1]
>>> convergent = contfrac.convergent(math.e, 3) # Low convergent grade
>>> print(convergent, convergent[0]/convergent[1], math.e)
(11, 4) 2.75 2.718281828459045
>>> convergent = contfrac.convergent(math.e, 7) # Higher grade = more accurate
>>> print(convergent, convergent[0]/convergent[1], math.e)
(193, 71) 2.7183098591549295 2.718281828459045
```
Similar libraries
----------------------------------------
- [Continued](https://github.com/MostAwesomeDude/continued), also available
through `pip`
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"description": "ContFrac\n===============================================================================\n\nContinued fractions are a representation of numbers expressed as recursive\nsums of integer parts and reciprocals of other numbers. _ContFrac_ is a\npure-Python3 lightweight module to compute and evaluate continued fractions,\nas well as using them to approximate any number. \n\n\nFeatures\n----------------------------------------\n\n- Supports conversion into continued fractions of `int`, `float`,\n `fractions.Fraction` and rational numbers expressed as tuples of 2 integers\n `(numerator, denominator)`, generated iteratively.\n- Computes the convergents of the same data types, generated iteratively.\n- Computes the value of a finite continued fraction.\n- Generates the arithmetical expression as string of a continued fraction.\n\n\nInstallation\n----------------------------------------\n\n```bash\npip install contfrac\n```\n\nor just include the `contfrac.py` file in your project (copy-paste).\n\n\nExample usage\n----------------------------------------\n\n```python\n>>> import contfrac\n>>> value = 415/93 # Express as (415, 93) to avoid rounding continued frac.\n>>> coefficients = list(contfrac.continued_fraction(value))\n>>> print(coefficients)\n[4, 2, 6, 7]\n\n>>> expression = contfrac.arithmetical_expr(coefficients)\n>>> print('Value: {:f} = {:s}'.format(value, expression))\nValue: 4.462366 = 4 + 1/(2 + 1/(6 + 1/(7)))\n\n>>> # The evaluation of a float value from a continued fraction is subject\n>>> # to floating point rounding errors\n>>> eval_value = contfrac.evaluate(coefficients)\n>>> print(eval_value, value) # Visible rounding errors\n4.46236559139785 4.462365591397849\n\n>>> convergents = list(contfrac.convergents(value))\n>>> print(convergents)\n[(4, 1), (9, 2), (58, 13), (415, 93)]\n\n>>> import math\n>>> coefficients = list(contfrac.continued_fraction(math.e, maxlen=10))\n>>> print(coefficients)\n[2, 1, 2, 1, 1, 4, 1, 1, 6, 1]\n\n>>> convergent = contfrac.convergent(math.e, 3) # Low convergent grade\n>>> print(convergent, convergent[0]/convergent[1], math.e)\n(11, 4) 2.75 2.718281828459045\n\n>>> convergent = contfrac.convergent(math.e, 7) # Higher grade = more accurate\n>>> print(convergent, convergent[0]/convergent[1], math.e)\n(193, 71) 2.7183098591549295 2.718281828459045\n```\n\n\nSimilar libraries\n----------------------------------------\n\n- [Continued](https://github.com/MostAwesomeDude/continued), also available\n through `pip` \n\n\n",
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