Tools of mathematical service MathPartner for parallel computations on a cluster

In many application areas it is necessary to perform symbolic-numerical calculations with a large volume of data. Examples of such areas are robotics, speech recognition, recognition of graphical information, automation and others. Symbolic computation systems, they also called computer algebra system, actively developed since the late eighties. Well-known systems are Mathematica, Maple, Reduce, and many others. Almost all of these systems were not originally focused any large-scale mathematical objects or on multiprocessor clusters. System FORM is a unique exception. It was conceived as a system which can operate with objects exceeding RAM. Such objects are placed on the hard drive. We give a description of such algorithms of MathPartner web services, which are designed to interact with a computing cluster. We give an algorithm to work a socket server, which is the link between MathPartner and super computers, and which provides the execution of parallel programs on a cluster. We explain in detail the mechanism which abstracts the specific features of super computers and the installed PBS package. The user can run on the cluster or program of MathPartner package, or their own programs. To run its own programs, they are able to send the compiled classes to the computing cluster in a zip-archive through the MathPartner web interface. We show examples of using parallel algorithms included in MathPartner package. Some of MathPartner parallel programs implemented with the paradigm of DDP (dynamic decentralized parallelization). DDP is designed as a framework that allows to write efficient parallel program for working with nonhomogeneous data such as sparse matrix. We demonstrate examples of using DDP-programs that are integrated into MathPartner.