Oresme

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PyPI
Conda
DOI
License: MIT

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

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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.

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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.

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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.

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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

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 ```

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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.harmonicnumberapprox(1000000)) # ≈14.392726722865724

Example 5: Use generator

for i, h in enumerate(ore.harmonicgenerator(3), 1): print(f"H{i} = {h}")

Example 6: NumPy vectorized version

print(ore.harmonicnumbersnumpy(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 H1 = 1.0 H2 = 1.5 H_3 = 1.8333333333333333 [1. 1.5 1.83333333 2.08333333 2.28333333]

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```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, 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 MIT License.