Publication Date

Summer 2015

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

Advisor

Timothy Hsu

Keywords

non-commutative, rational function

Subject Areas

Mathematics

Abstract

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.

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