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International Meeting on Algebraic and Algorithmic Aspects of Differential and Integral Operators

AADIOS 2012: Algebraic and Algorithmic Aspects of Differential and Integral Operators pp 1–22Cite as

Constructions of Free Commutative Integro-Differential Algebras

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8372))

Abstract

In this survey, we outline two recent constructions of free commutative integro-differential algebras. They are based on the construction of free commutative Rota-Baxter algebras by mixable shuffles. The first is by evaluations. The second is by the method of Gröbner-Shirshov bases.

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Authors and Affiliations

  1. Department of Mathematics, Lanzhou University, Lanzhou, Gansu, 730000, China

    Xing Gao & Li Guo

  2. Department of Mathematics and Computer Science, Rutgers University, Newark, NJ, 07102, USA

    Li Guo

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  1. Xing Gao
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  2. Li Guo
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Editors and Affiliations

  1. XLIM, DMI, University of Limoges, 123, avenue Albert Thomas, 87060, Limoges cedex, France

    Moulay Barkatou  & Thomas Cluzeau  & 

  2. Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenberger Str. 69, 4040, Linz, Austria

    Georg Regensburger

  3. SMAS, University of Kent, CT2 7NF, Canterbury, UK

    Markus Rosenkranz

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Gao, X., Guo, L. (2014). Constructions of Free Commutative Integro-Differential Algebras. In: Barkatou, M., Cluzeau, T., Regensburger, G., Rosenkranz, M. (eds) Algebraic and Algorithmic Aspects of Differential and Integral Operators. AADIOS 2012. Lecture Notes in Computer Science, vol 8372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54479-8_1

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  • DOI: https://doi.org/10.1007/978-3-642-54479-8_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54478-1

  • Online ISBN: 978-3-642-54479-8

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