Eugenio Roanes Lozano

Estimating radial railway network improvement with a CAS

Abstract The Spanish railway network is very complex, with two different track gauges: the broad classic Iberian track gauge and the so called international gauge, the latter used in the extensive high speed network. All new lines have been built with double track and top technologies. But there are controversial opinions among experts regarding how the network should grow. We had developed what we called isochrone circle graphs and a geometric index for radial railway networks improvement estimation, that can be very useful for decision taking regarding the improvement of railway lines. The corresponding paper was illustrated with a sketch constructed with a dynamic geometry system that used sliders to change the input parameters (timing to each peripheral destination and population of these destinations). Although very comfortable to use, altering the number of peripheral destinations considered required to construct a complete new sketch. To avoid this problem and in order to be able to perform symbolic computations and solve equations with the data obtained, we have begun from scratch and have designed and implemented a complete new package in the computer algebra system CAS Maple that takes as input the lists of destinations, timings and populations and builds the corresponding isochrone circle graphs and performs all the corresponding calculations. An important advantage of working in symbolic mode (i.e., of introducing parameters in the computations) is the possibility to work with unknowns (that represent network improvement goals) and consequently obtain the time improvement required in a line in order to fulfil a network specific improvement goal.

“Turtle Graphics” in Maple V.2

We think the “Turtle Geometry” [1] is a useful and convenient way of doing graphics programming. Recently, we have developed brand new implementations of the “Turtle Geometry” in Turbo Pascal [12] and in Maple V [14]. Our implementations include the usual primitives with Turbo-Pascal-like syntax: Forwd(dist), TurnLeft(ang), SetPenColor(color), SetPosition(xl, x2), etc. We shall begin with a brief resume of the implementation developed in Maple V.