  The LC method described in this work seeks to approximate the roots of
polynomial equations in one variable. This book allows you to explore the LC
method, which uses geometric structures of Lines L and Circumferences C in the
plane of complex numbers, based on polynomial coefficients. These structures
depend on the inclination angle of a line with fixed point that seeks to
contain one of the roots; they are associated with an error measure that
indicates the degree of proximity to that root, without knowing a priori its
location.
  Using a computer with parallel processing capabilities, it is feasible to
construct several of these geometric structures at the same time, varying the
inclination angle of the lines with fixed point, in order to obtain an error
measure map, with which it is possible to identify, approximately, the location
of all polynomial roots.
  To show how the LC method works, this book includes numerical examples for
quadratic, cubic, and quartic polynomials, and also for polynomials of degree
greater than or equal to 5; this book also includes R programs that allow you
to reproduce the results of the examples on a typical personal computer; these
R programs use vectorization of operations instead of loops, which can be seen
as a basic and accessible form of parallel processing.
  This book, in the end, invites us to explore beyond the basic ideas and
concepts described here, motivating the development of a more efficient and
complete computational implementation of the LC method.
