THE BIVARIATE (COMPLEX) FIBONACCI AND LUCAS POLYNOMIALS: AN HISTORICAL INVESTIGATION WITH THE MAPLÉS HELP - Alves, Francisco Regis Vieira; Catarino, Paula Maria Machado Cruz (Acta Didactica Napocensia, 2016)
The current research around the Fibonaccís and Lucassequence evidences the scientific vigor of both mathematical models that continue to inspire and provide numerous specializations and generalizations, especially from the sixthies. One of the current of research and investigations around the Generalized Sequence of Lucas, involves it's polinomial representations. Therefore, with the introduction of one or two variables, we begin to discuss the family of the Bivariate Lucas Polynomias (BLP) and the Bivariate Fibonacci Polynomials (BFP). On the other hand, since it's representation requires enormous employment of a large algebraic notational system, we explore some particular properties in order to convince the reader about an inductive reasoning that produces a meaning and produces an environment of scientific and historical investigation supported by the technology. Finally, throughout the work we bring several figures that represent some examples of commands and algebraic operations with the CAS Maple that allow to compare properties of the Lucas'polynomials, taking as a reference the classic of Fibonaccís model that still serves as inspiration for several current studies in Mathematics.