PhD Defense: A computable extension for holonomic functions: DD-finite functions

A computable extension for holonomic functions: DD-finite functions

D-finite or holonomic functions are solutions to linear differential equations with polynomial coefficients. They have been in the focus of attention in symbolic computation during the last decades due to their computability properties. They can be represented with a finite amount of data (coefficients of the equation and initial values) and several algorithms have been developed to work with this representation.In the current thesis we extend the definition of D-finite functions to a more general setting and we focus on extending some of the existing algorithms to this wider class of functions: those that satisfy a linear differential equation with D-finite coefficients. We call them DD-finite functions. Further we show that, by the same principle, those algorithms can be extended to the wider setting of solutions to linear differential equations with coefficients in some computable differential ring. This allows us to iterate the construction,yielding the set of Dn-finite function. We also study their properties and their relation with the differentially algebraic functions (which are an even larger class of functions). All algorithms developed and presented in this thesis have been implemented in Sage (an Open Source system for computer algebra based on Python).

Zoom-Link: https://jku.zoom.us/j/98578158861?pwd=OWZWSjRqUkx0eXpXcVdNU1lHQjF3UT09

Meeting-ID: 985 7815 8861 Code: 364691