scm203lab367112755 0.1.0

Number theory: Euclidean Algorithm ,Extended Euclidean Algorithm and Sieve of Eratosthenes.

mypackage = scm203lab367112755

scm203lab367112755 This is an example of Python packaging that combines important Number Theory algorithms into an easy-to-use format: Euclidean Algorithm, Extended Euclidean Algorithm, and Sieve of Eratosthenes.It is designed mainly for learning purposes and as an example of Python packaging.

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Features

• Euclidean Algorithm: Purpose: Compute the greatest common divisor (GCD) of two integers $a$ and $b$. Idea: Uses repeated division with remiander. [ \gcd(a, b) = \gcd(b, ; a \bmod b) ] Complexity: $O(\log(\min(a,b)))$.
• Extended Euclidean Algorithm: Purpose: find greatest integer $x$ and $y$ such that [ ax+by = gcd(a, b) ] Application: Solving Diophantine equations modular inverse. Complexity: $O(\log(\min(a,b)))$.
• Sieve of Eratosthenes: Purpose: Generates all prime numbers up to $n$. Idea: Iteratively marks multiples of primes as composite. Complexity: $O(n\log(\log(n)))$.

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Installation

You can install the package directly from PyPI:

pip install scm203lab367112755

Example 1 Euclidean Algorithm

gcd(234, 42)

Example 2 Extended Euclidean Algorithm

extended_gcd_steps(7920, 4536)

Example 3 Sieve of Eratosthenes

sieve_steps(49)