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Sagbi-Gröbner Bases Under Composition

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Abstract

The process of substituting variables in a polynomial with other polynomials is dubbed polynomial composition. The behaviour of Gröbner bases and Sagbi bases under composition is well known. In this paper, the authors provide a sufficient and necessary condition on a set Θ of polynomials under which the Sagbi-Gröbner basis computation commutes with composition. This has natural applications to the computations of Sagbi-Gröbner bases for subsets of composed polynomials of subalgebra.

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Authors and Affiliations

  1. Department of Sciences & Humanities, FAST-National University of Computer & Emerging Sciences, Karachi-campus, Karachi, Pakistan

    Nazish Kanwal & Junaid Alam Khan

  2. Department of Mathematical Sciences, School of Mathematics and Computer Science, Institute of Business Administration, Karachi, Pakistan

    Nazish Kanwal & Junaid Alam Khan

Authors
  1. Nazish Kanwal
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  2. Junaid Alam Khan
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Correspondence to Nazish Kanwal or Junaid Alam Khan.

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Kanwal, N., Khan, J.A. Sagbi-Gröbner Bases Under Composition. J Syst Sci Complex 36, 2214–2224 (2023). https://doi.org/10.1007/s11424-023-1294-x

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  • DOI: https://doi.org/10.1007/s11424-023-1294-x

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