Distributed Computing in Algebraic Topology: first trials

Nowadays, Internet appears as a suitable tool for performing scientific computations in a distributed collaborative way. One of the fields where this idea can be applied is that of Symbolic Computation. Computer Algebra packages are being extended to interconnect them. In fact, some Computer Algebra systems are already capable of performing distributed computing. An example is Distributed Maple [7], which is an environment for executing parallel computer algebra programs on multiprocessors and heterogeneous clusters. With this example in mind, it is clear that this trend could be explored in any other Symbolic Computation system, in particular in systems devoted to algorithmic Algebraic Topology. The leader systems in this field are EAT [3] and Kenzo [4]. These systems, created by Sergeraert, can be used to compute homology groups of infinite topological spaces, namely loop spaces. Both systems are written in the Common Lisp programming language and have obtained some results (specifically, homology groups) which had never been determined before using neither theoretical nor computational methods. Since the programs are very time (and space) consuming, it is obvious that they are specially well placed to try making them distributed. EAT and Kenzo are written in the Common Lisp programming language, but Java is the core language in the net-centric mainstream technology. That is the reason why we first thought of reconstructing the systems in the Java language. As an intermediate step, we rebuilt (some fragments of) EAT in the statically typed functional programming language ML [6]. Thus, we have implemented two prototypes to perform computations in Algebraic Topology in ML and Java respectively. The following step we undertook was to interoperate between these systems through the net. Our first attempt was to use MathML (Mathematical Markup Language) [5] (an XML dialect which was the first standard to represent mathematics) as exchange language, but it turned out to be not adequate as the elements of the algebraic structures that EAT