Computação algébrica: sistemas de software estrutura e algoritmo de risch.

Abstract

Aplicad mathematics problems, specificaly related to modeling, are generally presented in words, without formulas. This means to do/to choose the physical hypotheses to be taken in account or to verify which are the problem main ingredients. Nowadays the computer can be used as an efficient, way for experimenting and verification in the study of these problems. The current tendency is looking for building integrated enviroments for the solution of mathematics problems (ASP s) what demands man)' experts cooperation. There is a great interest in searching the integration of algebric. numerical and graphic computation that leads the idea of conceiving and algebraic software sistem organized in modules. To avoid rounding up errors, the algebraic software sistems perform the basic arithmetical operations by software. Is necessary then, to choose data structures apropriated to represent the objects (wholes and polinomes) as well as algoritthms that perform these operations efficiently. Real numbers can be represented in order to utilize the algorithms and data structures used for wholes numbers. An algebraic software sistem must offer recourses of simplification and recousers to obtain the primitive of a function. A continuous progress is obtained in the field of interaction and in searching to develop an ' 'expert sistem " in interaction, combining numerical computation knowledge, algebraic computation and artificial intelligence. Risch algorithm contributed significantly to find out a solution for the problem of getting a primitive in its closed pattern. In this work Risch algorithm is analysed in order to show and understand details in this functioning. In reality, this work has a modern view in which you can/must motivate the theory using practical situations applying the computer. It was tried to organize basic knowledges of algebraic computation to serve as orientation to whom desires to implement an algebraic computation sistem or wants to use rational)' some existent sistem.