Dr. Bertrand Teguia Tabuguia, Ph.D.

A mathematics lover!

Collaborative papers

• Concatenations of Terms of an Arithmetic Progression.
  With Luca, Florian. A substantial revision of
  Explicit formulas for concatenations of arithmetic progressions.
  May 2024. Submitted.
  
• On Rational Recursion for Holonomic Sequences.
  With Worrell, James. April 2024.
  

  In: Boulier, F., Mou, C., Sadykov, T.M., Vorozhtsov, E.V. (eds).
  CASC'24. LNCS, vol 14938. Springer, Cham.
  DOI:https://doi.org/10.1007/978-3-031-69070-9_18.

• D-Algebraic Functions.
  With Ait El Manssour, Rida and Sattelberger, Anna-Laura.
  Illustrations, software, and examples. January 2023.
  Journal of Symbolic Computation.
  

  DOI:https://doi.org/10.1016/j.jsc.2024.102377.

• On the Representation of Non-Holonomic Univariate Power Series.
  Teguia Tabuguia, Bertrand and Koepf, Wolfram.
  Maple Trans. 2, 1. Article 14315, 18 pages.
  August 2022.
• FPS in action: an easy way to find explicit
  formulas for interlaced hypergeometric sequences.
  Teguia Tabuguia, Bertrand and Koepf, Wolfram.
  ACM Communication in Computer Algebra. Volume 56, Issue 2. June 2022, pp 46-50. Pdf.
  Poster presentation at ISSAC'22.
• Symbolic Conversion of Holonomic Functions to Hypergeometric-Type Power Series.
  Teguia Tabuguia, Bertrand and Koepf, Wolfram.
  Computer Algebra issue of the Journal of Programming and Computer Software. April 2022. Volume 48. Pages 125-146. Preprint version.
• Hypergeometric-Type Power Series.
  Teguia Tabuguia, Bertrand and Koepf, Wolfram.
  Extended Abstract for the 4th International Conference "Computer Algebra", Moscow.
  Pages 105-108. June 2021.
• Power Series Representations of Hypergeometric-Type Functions.
  Teguia Tabuguia, Bertrand and Koepf, Wolfram.
  In Corless R., Gerhard J., Kotsireas I. (eds): Maple in Mathematics Education and Research. MC 2020. Communications in Computer and Information Science, Springer.

Personal Papers

• Computing with D-algebraic sequences.
  Teguia Tabuguia, Bertrand.
  December 2024. Under revision.
  
• Hypergeometric-Type Sequences.
  Teguia Tabuguia, Bertrand.
  Journal of Symbolic Computation.
  DOI: https://doi.org/10.1016/j.jsc.2024.102328. 
  Software and examples (GitHub).
  
• Computing with Hypergeometric-Type Terms.
  Teguia Tabuguia, Bertrand.
  ACM Commun. Comput. Algebra. Volume 58, Issue 2, Pages 23--26. June 2024.
  DOI (URL): https://doi.org/10.1145/3712023.3712025
• Arithmetic of D-Algebraic Functions.
  Teguia Tabuguia, Bertrand. Journal of Symbolic Computation
  MathRepo page.  May 2023 - June 2024 (publication).
  DOI: https://doi.org/10.1016/j.jsc.2024.102348
• Operations for D-algebraic Functions.
  Teguia Tabuguia, Bertrand.
  ACM Communications in Computer Algebra, Volume 57, Issue 2. Pages 51--56. June 2023.
  Visit this MathRepo repository.
  
•  A variant of van Hoeij's algorithm to compute hypergeometric
  term solutions of holonomic recurrence equations.
  Teguia Tabuguia, Bertrand.
  J. Algorithm Comput. Volume 53, Issue 2. pp 1-32. December 30, 2021.
  Maxima code. Comparison.
• An Algorithmic Random-Integer Generator based
  on the Distribution of Prime Numbers.
  Teguia Tabuguia, Bertrand.
  Research Journal of Mathematics and Computer Science, 2019; 3:16. DOI: 10.28933/rjmcs-2019-06-1705.
  

Other (unpublished but peer-reviewed) Papers

• Guessing with Quadratic Differential Equations.
  Teguia Tabuguia, Bertrand.
  Software presentation at ISSAC'22.
  July 2022. Pdf. Illustration.

Mathematical Software

I developed the following mathematical software packages. Follow the link for further details. I will now spend more time with NLDE as there seems to be a convergence in my research for problems and applications related to using nonlinear algebra for difference and differential equations.

• NLDE(with sub-packages for D-algebraic sequences and the multivariate setting)
• FPS
• HyperTypeSeq

The differential equation in ADE encodes the Weierstrass elliptic functions. The command invDalg from the package NLDE computes a differential equation for the functional inverses of Weirstrass elliptic functions.

The FPS command from the FPS package is used to find a closed-form representation for the power series expansion of the expression in the argument. This yields a formula in the variable z and the summation index n, as provided in the arguments. Note that this is purely symbolic algebra: it consists of finding and solving differential equations.

The first command solves the recurrence equation with the initial values in the list, and the second command simplifies the given trigonometric expression. The terms denoted with the Greek symbols represent the interlacements (or interleavings) involved in these sequences. The commands are from my package HyperTypeSeq.

Research Notes

• On 'Best' Rational Approximations to $\pi$ and $\pi+e$.
  Preprints 2020, 2020050268. DOI: 10.20944/preprints202005.0268.v2.
  Maxima code. (General mathematics manipulations. Draft of an idea!).