oresme 0.1.3

Oresme numbers refer to the sums related to the harmonic series

Oresme

---

PyPI
Conda
DOI
License: AGPL

---

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

pip install Oresme -U
python -m pip install -U oresme
conda install bilgi::oresme -y
mamba install bilgi::oresme -y

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

PyPI

Test Kurulumu / Test Installation

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

Github Master Kurulumu / GitHub Master Installation

Terminal:

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

Jupyter Lab, Notebook, Visual Studio Code:

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

---

Kullanım (Türkçe) / Usage (English)

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]

import oresme
oresme.__version__

---

Development

# 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.