Repeating digits of rational numbers
Project description
Due to slow computation of Egyptian Fraction (see end of this doc.), some variables have been transformed to methods since previous versions.
This package provides a way to access repeating decimals in the decimal representation of rational numbers.
class object
>>> from dvtDecimal import *
Once package importation completed, you have to create a rational number using:
- a fraction representation
>>> f = dvtDecimal(-604, 260)
for the fraction whose numerator is -604 and denominator is 260.
- or a decimal representation
>>> f = dvtDecimal(2.5)
- or repeating decimals as a string
>>> f = dvtDecimal('00765')
thus creating a number (w/o irregular part) between 0 and 1. In the example, 0.007650076500765... and so on.
object methods and variables
Once you created the object, you can access to those variables:
>>> f.initValues
[-604, 260]
>>> f.simpValues
[-151, 65]
>>> f.intPart
-2
>>> f.repPart
[2, 3, 0, 7, 6, 9]
>>> f.sign
-1
>>> f.gcd
4
and to those methods:
>>> f.fraction
-604/260
>>> f.irrPart()
0.3
>>> f.repPartC()
230769
>>> f.periodLen()
6
>>> f.mixedF()
[-2, 21, 65]
>>> f.isDecimal()
False
>>> f.dotWrite(20)
-2.32307692307692307692
>>> f.dispResults()
For fraction: -604/260
integer part : -2
irregular part : 0.3
periodic part : [2, 3, 0, 7, 6, 9]
mixed fraction : [-2, 21, 65]
simp. fraction : [-151, 65]
gcd : 4
Python outputs : -2.3230769230769233
Entering via repeating decimals string allows:
>>> f = dvtDecimal('0123456789')
>>> f.simpValues
[13717421, 1111111111]
dvtDecimal also supports minimal operations (+,-,*,/) in between elements of the class but also with integers:
>>> f = dvtDecimal(1, 5)
>>> g = dvtDecimal(10, 3)
>>> h = f + g
>>> h.mixedF
[3, 8, 15]
>>> i = f / g
>>> i.mixedF
[0, 3, 50]
>>> f = dvtDecimal(1, 5)
>>> g = 5
>>> h = f * g
>>> h.isDecimal()
True
>>> f = dvtDecimal(1, 5)
>>> g = dvtDecimal(7, 5)
>>> h = f - g
>>> h.simpValues
[-6, 5]
egyptian fractions
IMPORTANT 1: Egyptian fractions features are quite slow (could be VERY slow) because it uses dvtDecimal representation of numbers (unlike previous versions). As it doenst' use algebraic computation, you have to untrust some results or at least to verify them with another method...
IMPORTANT 2: This part gives you results for the fractionnal part of
the rational number you work with i.e. the last two numbers in the
mixedF
list, so that you only get results for <=1 fractions.
dvtDecimal provides the method egyptFractions
to get all
the
egyptian fractions equal to your current fraction.
egyptFractions
outputs a list of lists. Each of these lists are
denominators (increasing) for unitary fractions whose sum equals to
your fraction.
Two optional arguments:
eF
number of fractions in the sums, default is3
lim
max. number of solutions in the results, default is10
lim
can be0
for all fractions!
>>> f = dvtDecimal(18,5)
>>> f.mixedF
[3, 3, 5]
>>> f.egyptFractions()
[[2, 11, 110], [2, 12, 60], [2, 14, 35], [2, 15, 30], [2, 20, 20], [3, 4, 60], [3, 5, 15], [3, 6, 10]]
>>> f.egyptFractions(lim=5)
[[2, 11, 110], [2, 12, 60], [2, 14, 35], [2, 15, 30], [3, 4, 60]]
>>> f.egyptFractions(eF=4, lim=1)
[[2, 11, 111, 12210]]
>>> f.egyptFractions(eF=4, lim=0)
[[2, 11, 111, 12210], [2, 11, 112, 6160], [2, 11, 114, 3135], [2, 11, 115, 2530], [2, 11, 120, 1320], [2, 11, 121, 1210], [2, 11, 130, 715], [2, 11, 132, 660], [2, 11, 135, 594], [2, 11, 154, 385], [2, 11, 160, 352], [2, 11, 165, 330], [2, 11, 210, 231], [2, 12, 61, 3660], [2, 12, 62, 1860], [2, 12, 63, 1260], [2, 12, 64, 960], [2, 12, 65, 780], [2, 12, 66, 660], [2, 12, 68, 510], [2, 12, 69, 460], [2, 12, 70, 420], [2, 12, 72, 360], [2, 12, 75, 300], [2, 12, 76, 285], [2, 12, 78, 260], [2, 12, 80, 240], [2, 12, 84, 210], [2, 12, 85, 204], [2, 12, 90, 180], [2, 12, 96, 160], [2, 12, 100, 150], [2, 12, 105, 140], [2, 12, 108, 135], [2, 12, 110, 132], [2, 13, 44, 2860], [2, 13, 45, 1170], [2, 13, 50, 325], [2, 13, 52, 260], [2, 13, 60, 156], [2, 13, 65, 130], [2, 14, 36, 1260], [2, 14, 40, 280], [2, 14, 42, 210], [2, 14, 60, 84], [2, 15, 31, 930], [2, 15, 32, 480], [2, 15, 33, 330], [2, 15, 34, 255], [2, 15, 35, 210], [2, 15, 36, 180], [2, 15, 39, 130], [2, 15, 40, 120], [2, 15, 42, 105], [2, 15, 45, 90], [2, 15, 48, 80], [2, 15, 50, 75], [2, 15, 55, 66], [2, 16, 27, 2160], [2, 16, 28, 560], [2, 16, 30, 240], [2, 16, 32, 160], [2, 16, 35, 112], [2, 16, 40, 80], [2, 16, 48, 60], [2, 17, 25, 850], [2, 17, 34, 85], [2, 18, 23, 1035], [2, 18, 24, 360], [2, 18, 25, 225], [2, 18, 27, 135], [2, 18, 30, 90], [2, 18, 35, 63], [2, 18, 36, 60], [2, 20, 21, 420], [2, 20, 22, 220], [2, 20, 24, 120], [2, 20, 25, 100], [2, 20, 28, 70], [2, 20, 30, 60], [2, 20, 36, 45], [2, 21, 28, 60], [2, 21, 35, 42], [2, 24, 30, 40], [3, 4, 61, 3660], [3, 4, 62, 1860], [3, 4, 63, 1260], [3, 4, 64, 960], [3, 4, 65, 780], [3, 4, 66, 660], [3, 4, 68, 510], [3, 4, 69, 460], [3, 4, 70, 420], [3, 4, 72, 360], [3, 4, 75, 300], [3, 4, 76, 285], [3, 4, 78, 260], [3, 4, 80, 240], [3, 4, 84, 210], [3, 4, 85, 204], [3, 4, 90, 180], [3, 4, 96, 160], [3, 4, 100, 150], [3, 4, 105, 140], [3, 4, 108, 135], [3, 4, 110, 132], [3, 5, 16, 240], [3, 5, 18, 90], [3, 5, 20, 60], [3, 5, 24, 40], [3, 6, 11, 110], [3, 6, 12, 60], [3, 6, 14, 35], [3, 6, 15, 30], [3, 7, 10, 42], [3, 8, 10, 24], [3, 9, 10, 18], [4, 5, 7, 140], [4, 5, 8, 40], [4, 5, 10, 20], [4, 5, 12, 15], [4, 6, 10, 12]]
In the above example, egyptian fractions are thus calculated with fraction 3/5.
First solution [2, 11, 111, 12210]
(in the last command result)
has to be interpreted as: 3/5 = 1/2 + 1/11 + 1/111 + 1/12210
dvtDecimal also provides egyptG2
method. This gives you a list
of two denominators of unitary fractions whose sum equals your
fraction.
This is an implementation of the greedy algorithm. It gives you naturally matching pairs for unitary fractions input.
The result may be an empty list since all numbers cannot be written as so.
>>> f = dvtDecimal(18,5)
>>> f.intPart
3
>>> f.egyptG2
[2, 10]
So: 18/5 = 3 + 1/2 + 1/10
further
More operations!
about
dvtDecimal is rather an attempt to publish on the PyPi
packages
index than a fully completed python project, I do not recommend
dvtDecimal usage for professionnal use. You have to consider this
package as an experiment.
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