Master of Science (MS)
non-commutative, rational function
The coefficients of a Taylor series expansion of any rational function in one variable satisfy a linear recurrence relation. Our main result is a generalization of this statement for rational functions of multiple non-commutative variables. We show that if such a function is represented in the form of a non-commutative formal power series via Magnus embedding, then the coefficients of this formal power series are determined by a finite set of linear homogeneous recurrence relations. This finite representation of an infinite series allows for efficient computation of operations (multiplication, addition, and in many cases inversion) on non-commutative rational functions.
Zamoruyeva, Olga, "Computation in a Localization of the Free Group Algebra" (2015). Master's Theses. 4615.