Metadata-Version: 2.4
Name: scm203lab367112755
Version: 0.1.0
Summary: Number theory: Euclidean Algorithm ,Extended Euclidean Algorithm and Sieve of Eratosthenes.
Home-page: https://github.com/yourusername/mypackage
Author: Lewan
Author-email: natthapong.nn@mail.wu.ac.th
Requires-Python: >=3.7
Description-Content-Type: text/markdown
Dynamic: author
Dynamic: author-email
Dynamic: description
Dynamic: description-content-type
Dynamic: home-page
Dynamic: requires-python
Dynamic: summary

# 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.

---

## 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: $O(n\log(\log(n)))$.
---
## Installation
You can install the package directly from PyPI:
```bash
pip install scm203lab367112755
```
### Example 1 **Euclidean Algorithm**
```bash
gcd(234, 42)
```
### Example 2 **Extended Euclidean Algorithm**
```bash
extended_gcd_steps(7920, 4536)
```
### Example 3 **Sieve of Eratosthenes**
```bash
sieve_steps(49)
```
