Metadata-Version: 2.4
Name: oresme
Version: 0.1.4
Summary: Oresme numbers refer to the sums related to the harmonic series
Home-page: https://github.com/WhiteSymmetry/oresme
Author: Mehmet Keçeci
Author-email: Mehmet Keçeci <mkececi@yaani.com>
Maintainer: Mehmet Keçeci
Maintainer-email: mkececi@yaani.com
License-Expression: GPL-3.0-or-later
Project-URL: Homepage, https://github.com/WhiteSymmetry/oresme/
Project-URL: Documentation, https://WhiteSymmetry.github.io/oresme/
Project-URL: Repository, https://github.com/WhiteSymmetry/oresme/
Project-URL: Issues, https://github.com/WhiteSymmetry/oresme/issues
Keywords: oresme
Classifier: Programming Language :: Python :: 3
Classifier: Operating System :: OS Independent
Classifier: Intended Audience :: Science/Research
Classifier: Topic :: Scientific/Engineering :: Visualization
Requires-Python: >=3.11
Description-Content-Type: text/markdown
License-File: LICENSE
Requires-Dist: numpy
Requires-Dist: matplotlib
Requires-Dist: jax
Provides-Extra: test
Requires-Dist: pytest; extra == "test"
Requires-Dist: pytest-cov; extra == "test"
Requires-Dist: pytest-mock; extra == "test"
Requires-Dist: ruff; extra == "test"
Requires-Dist: numpy; extra == "test"
Requires-Dist: matplotlib; extra == "test"
Requires-Dist: jax; extra == "test"
Dynamic: author
Dynamic: home-page
Dynamic: keywords
Dynamic: license-file
Dynamic: maintainer
Dynamic: maintainer-email
Dynamic: requires-python

# Oresme

[![Zenodo DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.15833238.svg)](https://doi.org/10.5281/zenodo.15833238)

[![WorkflowHub DOI](https://img.shields.io/badge/DOI-10.48546/workflowhub.datafile.18.1-blue)](https://doi.org/10.48546/workflowhub.datafile.18.1)

[![figshare DOI](https://img.shields.io/badge/DOI-10.6084/m9.figshare.29504708-blue)](https://doi.org/10.6084/m9.figshare.29504708)

[![SciELO Preprints DOI](https://img.shields.io/badge/DOI-10.1590/SciELOPreprints.12584-blue)](https://doi.org/10.1590/SciELOPreprints.12584)

[![preprints.ru DOI](https://img.shields.io/badge/DOI-10.24108/preprints-3113623)](https://doi.org/10.24108/preprints-3113623)

[![Authorea DOI](https://img.shields.io/badge/DOI-10.22541/au.175199926.64529709/v1-blue)](https://doi.org/10.22541/au.175199926.64529709/v1)

[![Preprints DOI](https://img.shields.io/badge/DOI-10.20944/preprints202507.0781.v1-blue)](https://doi.org/10.20944/preprints202507.0781.v1)

[![OSF DOI](https://img.shields.io/badge/DOI-10.17605/osf.io/68r4v-blue)](https://doi.org/10.17605/osf.io/68r4v)

[![Knowledge Commons DOI](https://img.shields.io/badge/DOI-10.17613/gbdgx-d8y63)](https://doi.org/10.17613/gbdgx-d8y63)


[![Anaconda-Server Badge](https://anaconda.org/bilgi/oresme/badges/version.svg)](https://anaconda.org/bilgi/oresme)
[![Anaconda-Server Badge](https://anaconda.org/bilgi/oresme/badges/latest_release_date.svg)](https://anaconda.org/bilgi/oresme)
[![Anaconda-Server Badge](https://anaconda.org/bilgi/oresme/badges/platforms.svg)](https://anaconda.org/bilgi/oresme)
[![Anaconda-Server Badge](https://anaconda.org/bilgi/oresme/badges/license.svg)](https://anaconda.org/bilgi/oresme)
[![Open Source](https://img.shields.io/badge/Open%20Source-Open%20Source-brightgreen.svg)](https://opensource.org/)
[![AGPL-3.0 license](https://img.shields.io/badge/License-AGPL-yellow.svg)](https://opensource.org/license/agpl-v3)

[![Python CI](https://github.com/WhiteSymmetry/Oresme/actions/workflows/python_ci.yml/badge.svg?branch=main)](https://github.com/WhiteSymmetry/Oresme/actions/workflows/python_ci.yml)
[![codecov](https://codecov.io/gh/WhiteSymmetry/Oresme/graph/badge.svg?token=04SY6XPZAQ)](https://codecov.io/gh/WhiteSymmetry/Oresme)
[![Documentation Status](https://readthedocs.org/projects/Oresme/badge/?version=latest)](https://Oresme.readthedocs.io/en/latest/)
[![Binder](https://terrarium.evidencepub.io/badge_logo.svg)](https://terrarium.evidencepub.io/v2/gh/WhiteSymmetry/Oresme/HEAD)
[![PyPI version](https://badge.fury.io/py/Oresme.svg)](https://badge.fury.io/py/Oresme)
[![PyPI Downloads](https://static.pepy.tech/badge/Oresme)](https://pepy.tech/projects/Oresme)
[![Contributor Covenant](https://img.shields.io/badge/Contributor%20Covenant-2.1-4baaaa.svg)](CODE_OF_CONDUCT.md) 
[![Linted with Ruff](https://img.shields.io/badge/Linted%20with-Ruff-green?logo=python&logoColor=white)](https://github.com/astral-sh/ruff)

---

<p align="left">
    <table>
        <tr>
            <td style="text-align: center;">PyPI</td>
            <td style="text-align: center;">
                <a href="https://pypi.org/project/Oresme/">
                    <img src="https://badge.fury.io/py/Oresme.svg" alt="PyPI version" height="18"/>
                </a>
            </td>
        </tr>
        <tr>
            <td style="text-align: center;">Conda</td>
            <td style="text-align: center;">
                <a href="https://anaconda.org/bilgi/Oresme">
                    <img src="https://anaconda.org/bilgi/Oresme/badges/version.svg" alt="conda-forge version" height="18"/>
                </a>
            </td>
        </tr>
        <tr>
            <td style="text-align: center;">DOI</td>
            <td style="text-align: center;">
                <a href="https://doi.org/10.5281/zenodo.15833238">
                    <img src="https://zenodo.org/badge/DOI/10.5281/zenodo.15833238.svg" alt="DOI" height="18"/>
                </a>
            </td>
        </tr>
        <tr>
            <td style="text-align: center;">License: AGPL</td>
            <td style="text-align: center;">
                <a href="https://opensource.org/license/agpl-v3">
                    <img src="https://img.shields.io/badge/License-AGPL-yellow.svg" alt="License" height="18"/>
                </a>
            </td>
        </tr>
    </table>
</p>

---


Oresme numbers refer to the sums related to the harmonic series.

---
### **Türkçe Tanım:**
**Oresme Sayıları**, 14. yüzyılda Nicole Oresme tarafından incelenen matematiksel serilerdir. Oresme sayıları harmonik seriye ait toplamları ifade eder. İki türü vardır:  
1. **\( \frac{n}{2^n} \) serisi** (Oresme'nin orijinal çalışması),  
2. **Harmonik sayılar** (\( H_n = 1 + \frac{1}{2} + \cdots + \frac{1}{n} \)).  
Bu sayılar, analiz ve sayı teorisinde önemli rol oynar.

Bu modül (Numba/JAX olmadan) şunları sağlar:
- Harmonik sayı hesaplamaları (kesirli tam sonuçlar ve kayan noktalı)
- Oresme dizisi (n / 2^n) üretimi
- ℓ² (Hilbert uzayı) aidiyet testleri (matematiksel olarak doğru)
- Dizi analizi ve karşılaştırma yardımcıları
- Yaklaştırım yöntemleri ve yakınsama analizi

---

### **English Definition:**
**Oresme Numbers** are mathematical series studied by Nicole Oresme in the 14th century. Oresme numbers refer to the sums related to the harmonic series. They include two types:  
1. The **\( \frac{n}{2^n} \) sequence** (Oresme's original work),  
2. **Harmonic numbers** (\( H_n = 1 + \frac{1}{2} + \cdots + \frac{1}{n} \)).  
These numbers play a key role in analysis and number theory.

This module provides (without Numba/JAX):
- Harmonic number calculations (exact fractions and floating point)
- Oresme sequence (n / 2^n) generation
- Hilbert space (ℓ²) membership tests (mathematically sound)
- Sequence analysis and comparison utilities
- Approximation methods and convergence analysis

---

### **Fark/Karşılaştırma (Difference):**
- **Oresme'nin \( \frac{n}{2^n} \) serisi** ıraksaklık kanıtları için önemlidir.  
- **Harmonik sayılar** (\( H_n \)) ise logaritmik büyüme gösterir ve \( n \to \infty \) iken ıraksar.  
- Modern literatürde "Oresme numbers" terimi daha çok tarihsel bağlamda kullanılır.

---

## Kurulum (Türkçe) / Installation (English)

### Python ile Kurulum / Install with pip, conda, mamba
```bash
pip install Oresme -U
python -m pip install -U oresme
conda install bilgi::oresme -y
mamba install bilgi::oresme -y
```

```diff
- pip uninstall oresme -y
+ pip install -U oresme
+ python -m pip install -U oresme
```

[PyPI](https://pypi.org/project/oresme/)

### Test Kurulumu / Test Installation

```bash
pip install -i https://test.pypi.org/simple/ oresme -U
```

### Github Master Kurulumu / GitHub Master Installation

**Terminal:**

```bash
pip install git+https://github.com/WhiteSymmetry/Oresme.git
```

**Jupyter Lab, Notebook, Visual Studio Code:**

```python
!pip install git+https://github.com/WhiteSymmetry/Oresme.git
# or
%pip install git+https://github.com/WhiteSymmetry/Oresme.git
```

---

## Kullanım (Türkçe) / Usage (English)

```python
import oresme as ore 

# Example 1: Generate Oresme sequence
print(ore.oresme_sequence(5))  # [0.5, 0.5, 0.375, 0.25, 0.15625]

# Example 2: Get exact harmonic numbers as fractions
print(ore.harmonic_numbers(3))  # [Fraction(1, 1), Fraction(3, 2), Fraction(11, 6)]

# Example 3: Calculate single harmonic number
print(ore.harmonic_number(5))  # 2.283333333333333

# Example 4: Approximate large harmonic number
print(ore.harmonic_number_approx(1_000_000))  # ≈14.392726722865724

# Example 5: Use generator
for i, h in enumerate(ore.harmonic_generator(3), 1):
    print(f"H_{i} = {h}")

# Example 6: NumPy vectorized version
print(ore.harmonic_numbers_numpy(5))  # [1. 1.5 1.833... 2.083... 2.283...]

[0.5, 0.5, 0.375, 0.25, 0.15625]
[Fraction(1, 1), Fraction(3, 2), Fraction(11, 6)]
2.283333333333333
14.392726722865808
H_1 = 1.0
H_2 = 1.5
H_3 = 1.8333333333333333
[1.         1.5        1.83333333 2.08333333 2.28333333]

```

```python
import oresme
oresme.__version__
```
---

### Development
```bash
# Clone the repository
git clone https://github.com/WhiteSymmetry/Oresme.git
cd Oresme

# Install in development mode
python -m pip install -ve . # Install package in development mode

# Run tests
pytest

Notebook, Jupyterlab, Colab, Visual Studio Code
!python -m pip install git+https://github.com/WhiteSymmetry/Oresme.git
```
---

## Citation

If this library was useful to you in your research, please cite us. Following the [GitHub citation standards](https://docs.github.com/en/github/creating-cloning-and-archiving-repositories/creating-a-repository-on-github/about-citation-files), here is the recommended citation.

### BibTeX


### APA

```
Keçeci, M. (2025). Echoes of Constancy: Waves of Change in the Keçeci and Oresme Sequences. In SciELO Preprints. https://doi.org/10.1590/SciELOPreprints.12584

Keçeci, M. (2025). Between Chaos and Order: A Behavioural Portrait of Keçeci and Oresme Numbers. preprints.ru. https://doi.org/10.24108/preprints-3113623

Keçeci, M. (2025). Analysing the Dynamic and Static Structures of Keçeci and Oresme Sequences. Authorea. https://doi.org/10.22541/au.175199926.64529709/v1

Keçeci, M. (2025). Dynamic Sequences Versus Static Sequences: Keçeci and Oresme Numbers in Focus. Preprints. https://doi.org/10.20944/preprints202507.0781.v1

Keçeci, M. (2025). Mobility and Constancy in Mathematical Sequences: A Study on Keçeci and Oresme Numbers. OSF. https://doi.org/10.17605/osf.io/68r4v

Keçeci, Mehmet (2025). Dynamic and Static Approaches in Mathematics: Investigating Keçeci and Oresme Sequences. Knowledge Commons. https://doi.org/10.17613/gbdgx-d8y63

Keçeci, Mehmet (2025). Dynamic-Static Properties of Keçeci and Oresme Number Sequences: A Comparative Examination. figshare. Journal contribution. https://doi.org/10.6084/m9.figshare.29504960

Keçeci, M. (2025). Variability and Stability in Number Sequences: An Analysis of Keçeci and Oresme Numbers. WorkflowHub. https://doi.org/10.48546/workflowhub.document.37.1

Keçeci, M. (2025). Dynamic vs Static Number Sequences: The Case of Keçeci and Oresme Numbers. Open Science Articles (OSAs), Zenodo. https://doi.org/10.5281/zenodo.15833351

Keçeci, M. (2025). Oresme. figshare. https://doi.org/10.6084/m9.figshare.29504708

Keçeci, M. (2025). Oresme [Data set]. WorkflowHub. https://doi.org/10.48546/workflowhub.datafile.18.1 

Keçeci, M. (2025). Oresme (0.1.0). Open Science Articles (OSAs), Zenodo. https://doi.org/10.5281/zenodo.15833238
```

### Chicago

```
Keçeci, Mehmet. Echoes of Constancy: Waves of Change in the Keçeci and Oresme Sequences. In SciELO Preprints, 2025. https://doi.org/10.1590/SciELOPreprints.12584

Keçeci, Mehmet. Dynamic vs Static Number Sequences: The Case of Keçeci and Oresme Numbers. Open Science Articles (OSAs), Zenodo, 2025. https://doi.org/10.5281/zenodo.15833351

Keçeci, Mehmet. Oresme. figshare, 2025. https://doi.org/10.6084/m9.figshare.29504708

Keçeci, Mehmet. Oresme [Data set]. WorkflowHub, 2025. https://doi.org/10.48546/workflowhub.datafile.18.1 

Keçeci, Mehmet. Oresme. Open Science Articles (OSAs), Zenodo, 2025. https://doi.org/10.5281/zenodo.15833238

```


### Lisans (Türkçe) / License (English)

```
This project is licensed under the GPL-3.0-or-later License.
```
