Volkov V. Methods of algebraic programming in development of mahematical software systems

A methodology for coordination of different types of mathematical activities in homogenous programming environment via representation as matematical agents is developed in this thesis. Basic tools of the APS System supporting integration of the main programming paradigms are developed. An architecture supporting the methodology is created, implemented, and applied in development of the VRS system for requirements verification. Algebraic representation for a class of completion by critical pairs like algorithms is developed. Properties of this representation are studied, a workbench for these algorithms is implemented, and a few concrete algorithms are implemented. An approach to integration of symbolic computation with numeric one and artificial intelligence is created. Two computer algebra systems are implemented on a base of this approach. The first one is for support of mathematical training and the second is for numeric-symbolic transformations devoted for studying of applied analysis problems.