Introduction
Note: please use Teguia (or Teguia Tabuguia) if you want to call me by my name. My first name is Bertrand.
I have a Ph.D. (Dr. rer. nat.) in Mathematics, in the field of Computer Algebra (2020), a master's degree in Mathematics (2018), and another in Computer Engineering (2016).
I am a Postdoctoral Researcher in the Non-Linear Algebra group of Bernd Sturmfels at the Max Planck Institute For Mathematics in the Sciences, Leipzig, Germany.
Research Interests: my research interests combine Symbolic Computation, Computer Programming, Differential Algebra, Algorithmic Number Theory, Algebraic Geometry, and the applications of all that in other scientific areas.
Check this website menu to learn more about my background.
Address: Inselstraße 22, 34132 Leipzig, Germany
Office: F3 07
Email: email@bertrandteguia.com
MPI MiS group member webpage: https://www.mis.mpg.de/nlalg/members/bertrand-teguia-tabuguia.html
UniKassel web page: http://www.mathematik.uni-kassel.de/~bteguia/
Tel: +49 341 9959 768
Download my CV
Bertrand Teguia T.
'Magic' in symbolic computing
I invite you to read an informal presentation on computations based on Mathematics and computer programming in Computer Algebra.
1. Formal power series in Maxima 5.44: PDF, Html
2. Formal power series in Maple 2019: PDF
You can try some computations with my Maple library if you wish to:
Download my implementations at The new FPS package.
News
Talk at the Maple conference 2022: Symbolic powers of functions defined by second-order linear ODEs.
What is new in FPS (Maple version): AddHolonomicDE, MulHolonomicDE, SelfOpHolonomicDE, and the option partialwrt in HolonomicDE.
Assume you have n (valued positive integer) holonomic DEs DE1, ..., DEn, in the dependent variables y1(t), ...,yn(t), respectively. Then you can compute a differential equation for the sum z(t)=y1(t)+y2(t)+...+yn(t) as follows:
FPS:-AddHolonomicDE([DE1,...,DEn],[y1(t),...,yn(t)],z(t));
Similarly for the product z(t)=y1(t)*y2(t)*...*yn(t), one uses
FPS:-MulHolonomicDE([DE1,...,DEn],[y1(t),...,yn(t)],z(t));
Now, if you have a differential equation DE in the dependent variable y(t), and you want to compute a differential equation for a polynomial expression z=p(y(t)), you can proceed as follows:
FPS:-SelfOpHolonomicDE(DE,y(t),z=p(y));
A start for the multivariate case: for computing partial holonomic differential equations with respect to a variable xk for a given multivariate D-finite (holonomic in a sense) function f in x1, ..., xk, ..., xn, one proceeds as follows
FPS:-HolonomicDE(f, F(x1,...xn), partialwrt=xk);
When the argument partialwrt is not specified, the output is a list of n partial differential equations that can be used to write down a canonical representation of the input expression as a holonomic function.
More to come in FPS very soon...