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<p>The paper presents <i>PyGrossone</i>, a general-purpose and domain-independent Python library for the Infinity Computer arithmetic allowing one to work numerically with different infinite and infinitesimal numbers. <i>PyGrossone</i> offers a set of arithmetic, elementary, trigonometric, and differentiation modules to perform computations with <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="500_2025_10661_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(\textcircled {1}\)</EquationSource> <EquationSource Format="MATHML"><math> <menclose notation="circle"> <mn>1</mn> </menclose> </math></EquationSource> </InlineEquation>-based numbers (where <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="500_2025_10661_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(\textcircled {1}\)</EquationSource> <EquationSource Format="MATHML"><math> <menclose notation="circle"> <mn>1</mn> </menclose> </math></EquationSource> </InlineEquation> is a new infinite number introduced in the series of papers by the last author) with exact precision up to the machine one, since the computations on the Infinity Computer are numeric, not symbolic. Experiments have been conducted to evaluate the validity and performances of the proposed library. The availability of a Python-based implementation of the Infinity Computer arithmetic enables its exploitation in further research fields, such as artificial intelligence, scientific computing, and machine learning.</p>

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Pygrossone: a python-powered library for operating with the infinity computer arithmetic

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • Alberto Falcone,
  • Alfredo Garro,
  • Yaroslav D. Sergeyev

摘要

The paper presents PyGrossone, a general-purpose and domain-independent Python library for the Infinity Computer arithmetic allowing one to work numerically with different infinite and infinitesimal numbers. PyGrossone offers a set of arithmetic, elementary, trigonometric, and differentiation modules to perform computations with \(\textcircled {1}\) 1 -based numbers (where \(\textcircled {1}\) 1 is a new infinite number introduced in the series of papers by the last author) with exact precision up to the machine one, since the computations on the Infinity Computer are numeric, not symbolic. Experiments have been conducted to evaluate the validity and performances of the proposed library. The availability of a Python-based implementation of the Infinity Computer arithmetic enables its exploitation in further research fields, such as artificial intelligence, scientific computing, and machine learning.