Oresme

Name: Oresme
Creator: figshare
Published: 2025-07-08 12:10:16
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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:( \frac{n}{2^n} ) serisi (Oresme'nin orijinal çalışması),Harmonik sayılar (( H_n = 1 + \frac{1}{2} + \cdots + \frac{1}{n} )). Bu sayılar, analiz ve sayı teorisinde önemli rol oynar.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:The ( \frac{n}{2^n} ) sequence (Oresme's original work),Harmonic numbers (( H_n = 1 + \frac{1}{2} + \cdots + \frac{1}{n} )). These numbers play a key role in analysis and number theory.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<pre>pip install Oresme -U python -m pip install -U Oresme conda install bilgi::Oresme -y mamba install bilgi::Oresme -y</pre><pre>- pip uninstall Oresme -y + pip install -U Oresme + python -m pip install -U Oresme</pre>PyPITest Kurulumu / Test Installation<pre>pip install -i https://test.pypi.org/simple/ Oresme -U</pre>Github Master Kurulumu / GitHub Master InstallationTerminal:<pre>pip install git+https://github.com/WhiteSymmetry/Oresme.git</pre>Jupyter Lab, Notebook, Visual Studio Code:<pre>!pip install git+https://github.com/WhiteSymmetry/Oresme.git # or %pip install git+https://github.com/WhiteSymmetry/Oresme.git</pre>Kullanım (Türkçe) / Usage (English)<pre>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]</pre><pre>import oresme oresme.__version__</pre>Development<pre># 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</pre>

土耳其语描述：Oresme数（Oresme Numbers）是14世纪由尼古拉·奥雷姆（Nicole Oresme）研究的数学级数。Oresme数指与调和级数（harmonic series）相关的求和结果。其包含两种类型：((frac{n}{2^n})) 级数（奥雷姆的原始研究对象）、调和数（Harmonic numbers）（(H_n = 1 + frac{1}{2} + cdots + frac{1}{n})）。 这类数在分析学与数论中具有重要地位。英文定义：Oresme数（Oresme Numbers）是14世纪由尼古拉·奥雷姆（Nicole Oresme）研究的数学级数。Oresme数指代与调和级数相关的求和结果，包含两种类型：((frac{n}{2^n})) 序列（奥雷姆的原创研究成果）、调和数（Harmonic numbers）（(H_n = 1 + frac{1}{2} + cdots + frac{1}{n})）。 这类数在分析学与数论中发挥着关键作用。差异对比：奥雷姆的((frac{n}{2^n}))级数在级数发散性证明中具有重要价值。而调和数（Harmonic numbers） ((H_n)) 呈现对数增长趋势，当(n o infty)时趋于发散。在现代文献中，"Oresme数"这一术语更多用于历史语境下。安装说明：土耳其语版本 / 英语版本 可通过Python的pip、conda或mamba进行安装<pre>pip install Oresme -U python -m pip install -U Oresme conda install bilgi::Oresme -y mamba install bilgi::Oresme -y</pre><pre>- pip uninstall Oresme -y + pip install -U Oresme + python -m pip install -U Oresme</pre>PyPI测试版安装：<pre>pip install -i https://test.pypi.org/simple/ Oresme -U</pre>GitHub主分支安装：终端环境：<pre>pip install git+https://github.com/WhiteSymmetry/Oresme.git</pre>Jupyter Lab、Notebook、Visual Studio Code环境：<pre>!pip install git+https://github.com/WhiteSymmetry/Oresme.git # 或 %pip install git+https://github.com/WhiteSymmetry/Oresme.git</pre>使用方法：<pre>import oresme as ore # 示例1：生成Oresme序列 print(ore.oresme_sequence(5)) # [0.5, 0.5, 0.375, 0.25, 0.15625] # 示例2：以分数形式获取精确调和数 print(ore.harmonic_numbers(3)) # [Fraction(1, 1), Fraction(3, 2), Fraction(11, 6)] # 示例3：计算单个调和数 print(ore.harmonic_number(5)) # 2.283333333333333 # 示例4：近似计算大型调和数 print(ore.harmonic_number_approx(1_000_000)) # ≈14.392726722865724 # 示例5：使用生成器 for i, h in enumerate(ore.harmonic_generator(3), 1): print(f"H_{i} = {h}") # 示例6：NumPy向量化版本 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]</pre><pre>import oresme oresme.__version__</pre>开发流程：<pre># 克隆仓库 git clone https://github.com/WhiteSymmetry/Oresme.git cd Oresme # 以开发模式安装包 python -m pip install -ve . # 运行测试 pytest 适用于Notebook、Jupyterlab、Colab、Visual Studio Code环境 !python -m pip install git+https://github.com/WhiteSymmetry/Oresme.git</pre>

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2025-07-08

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