Many processes in science and engineering can be modeled by so-called linear functional systems.
To manipulate and analyze such systems, one computes with the corresponding matrices and linear
operators. Properties of systems and operators are expressed by identities. Instead of working with
concrete matrices and operators, symbolic computation works with mathematical objects
represented by symbols. The main goal of the project Symbolic computations for identities of
linear operators is to automatize such formal computations with operators and classes of systems
beyond what is currently possible on the computer. In particular, we are interested in symbolic
methods and computer algebra tools for proving and discovering identities of linear operators and
for solving operator equations.
In the project, we develop methods to analyze classes of dynamical systems in engineered processes
and their control. These systems and their transformations are usually modeled by differential,
delay, and integral operators. To compute with such operators, we work out a unique way of
representing them. Based on these normal forms, we will prove and discover identities of operators
automatically by computer algebra software, which we develop in the course of the project.
If input and output of operators or matrices have different dimensions, they cannot be added and
composed in arbitrary ways. This restricts computations with operators and matrices. In the project,
we will work out new symbolic methods to deal with these restrictions. The idea is to first compute
symbolically without restrictions and then justify the result independent of how it was obtained.