### Introduction

I recently completed my Ph.D. in Mathematics, in the field of Computer Algebra at the University of Kassel, some details are given below. I have obtained a master's degree in Mathematics at the African Institute for Mathematical Sciences (AIMS) - Cameroon in 2018, and another in Computer Engineering at Ecole Nationale Supérieure Polytechnique (ENSP) de Yaoundé in 2016.

**Address:** University of Kassel, Germany. Heinrich-Plett-Str.40. 34132 Kassel

**Email:** bteguia@mathematik.uni-kassel.de / bertrand.teguia@aims-cameroon.org

**Tel: **+49 1521 2117745 / +237 676915434

### Power Series Representations of Hypergeometric Type and Non-Holonomic Functions in Computer Algebra

**Ph.D. (Dr. rer. nat.) in Mathematics, Computer Algebra, from August 2018 - Mai 2020, University of ****Kassel, Germany.**

I worked under the supervision of Prof. Dr. Wolfram Koepf.

I give below brief details of my major results.

**1.** An algorithm, say mfoldHyper, that computes bases of the subspaces of all m-fold (m being a positive integer) hypergeometric term solutions of holonomic recurrence equations. This algorithm is new, and it has the advantage to linearize the computation of Laurent-Puiseux series: every linear combination of hypergeometric type series, even for many different values of m, is detected.

**2. **An algorithm that computes normal form representations for non-holonomic functions. A very important consequence of this algorithm is its ability to prove difficult identities.

**3.** A variant of van Hoeij's algorithm for computing hypergeometric term solutions of holonomic recurrence equations. Following the main steps of van Hoeij's algorithm, our variant computes hypergeometric term solutions of holonomic recurrence equations as fast as the original algorithm while using other methods. This algorithm is an integral part of mfoldHyper mentioned in **1.**. Download this algorithm here.

PS: papers related to these achievements will soon be available.

The thesis is available at meine Dissertation.

### Maxima implementations

Maxima is a free computer algebra system (CAS). I use it for most of my symbolic computations. In particular, Maxima was the CAS used during my Ph.D. work.

The pictures present some outputs obtained with my Ph.D. algorithms.

My package FPS.mac is available by email request.

**Teaching Assistant **

**AIMS-Cameroon, March 1st - May 31st, 2019.**

Tutoring students in mathematical sciences at the African Institute for Mathematical Sciences (AIMS) of Cameroon, Limbe.

**Workshops and Conferences**

ICMS 2020, TU Braunschweig, Germany, July 13-16, 2020

I was one of the software demo presenters. My algorithm, a variant of van Hoeij's algorithm, was accepted upon peer review.

Workshop on Applied Algebra, TU Braunschweig, Germany, June 7-8, 2019

I was accepted to present a poster from my paper on randomness and the distribution of primes.

**Papers**

On rational approximations to pi+e, May 2020 (submitted, the fun during my quarantine time): what rationals approximate pi and pi + e best? Maxima code

Observation on the distribution of Prime numbers, May 2019 (appeared): Primes and Randomness

**Game**

P&C Game, a game inspired by mathematics, April 2019: Play P&C Game online. Documentation.

### My Essays

**AIMS-Cameroon, Limbe, Cameroon, April - Mai 2018:**

Automatic Computation of Laurent-Puiseux series of Hypergeometric Type.

This is my first contact with the subject of my Ph.D. thesis. Notice that in this essay the hypergeometric type series is reduced to those whose recurrence equations with only two terms are immediately found.

**ENSP Yaounde, Cameroon, January - June 2016:**

Classification non Supervisée et Suivi des Processus de Dynamique Forestière. (French)

The main purpose here is to model the birth, growth, and mortality of species of trees in the forest. The EM algorithm is used for clustering. Concerning the regression, the growth and the mortality are modeled using the binomial distribution, and the birth is modeled using the Poisson distribution.

**R codes**:

Simulation of data:

Estimation of parameters with the EM algorithm:

**Extension, August 2017 (pdf): **I wrote a proposal that gives an approach to extend this work by considering data collected from satellites and estimate the stock of carbon.

### Where am I from?

I got a master's degree in computer engineering at Ecole Nationale Superieure Polytechnique (ENSP) de Yaoundé, Cameroun. When I was a student in that school, I was always doing my best to stay close to mathematics. I have then been introduced to Computer Algebra in level 4 for a pre-engineering internship, and I did my master thesis in advanced statistics where I wrote an algorithm for forests dynamic. My stay with pure mathematics books and friends made me known as a pure mathematician computer engineer, and from my mathematician lecturers, I had enough support to go to AIMS-Cameroon where I could pursue my dream. I indeed performed well at AIMS and got my Ph.D. opportunity...