scmlab367104703 0.1.0

Basic number theory tools: GCD calculation, solving linear Diophantine equations, and listing primes..

scmlab367104703

scmlab367104703 This is a basic number theory module consisting of three functions euclidean(),extended(),eratosthenes()

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Features

• Euclidean Algorithm: Use euclidean() to find the greatest common divisor (gcd) of two integers
• Extended Euclidean Algorithm: Use extended() to find
• The greatest common divisor (gcd) of two numbers a and b
• And two numbers x and y such that:

[ a \times x + b \times y = \gcd(a, b) ]

• Sieve of Eratosthenes:Use eratosthenes(n) to find all prime numbers up to a certain n.

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Installation

You can install the package directly from PyPI:

pip install scmlab367104703

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Example1(Euclidean Algorithm)

#input
>>>import scmlab367104703 as scm
>>> scm.euclidean(807, 481)

#output
gcd(807, 481)
807 = 481 x 1 + 326
481 = 326 x 1 + 155
326 = 155 x 2 + 16
155 = 16 x 9 + 11
16 = 11 x 1 + 5
11 = 5 x 2 + 1
5 = 1 x 5 + 0
gcd is 1

Example2(Extended Euclidean Algorithm)

#input
>>> import scmlab367104703 as scm
>>> scm.extended(120, 23)

#output
120*(-9) + 23*(47) = 1
x = -9, y = 47

Example3(Sieve of Eratosthenes)

#input
>>> import scmlab367104703 as scm
>>> scm.eratosthenes(50)

#output
+------+-----+------+----+-----+----+------+----+------+----+
|  1   | *2* | *3*  | 4  | *5* | 6  | *7*  | 8  |  9   | 10 |
| *11* |  12 | *13* | 14 |  15 | 16 | *17* | 18 | *19* | 20 |
|  21  |  22 | *23* | 24 |  25 | 26 |  27  | 28 | *29* | 30 |
| *31* |  32 |  33  | 34 |  35 | 36 | *37* | 38 |  39  | 40 |
| *41* |  42 | *43* | 44 |  45 | 46 | *47* | 48 |  49  | 50 |
+------+-----+------+----+-----+----+------+----+------+----+