Illustration from: https://windows-cdn.softpedia.com/screenshots/Computer-Algebra-System_10.pngA Computer Algebra System (CAS) is a sort of software program used in mathematical formula manipulation. The basic purpose of a computer algebra system is to automate laborious algebraic manipulation operations, sometimes challenging. The main distinction between a computer algebra system and a standard calculator is to deal symbolically with equations rather than quantitatively. These systems' specific uses and capacities vary widely from system to system, but the objective remains the same: manipulating symbolic equations. The Algebra computer systems frequently incorporate grabbing equation facilities and enable the user with a programming language to construct his routines.
In addition to changing the way Mathematics is taught at many colleges, Computer Algebra systems have offered mathematicians worldwide a flexible tool. Popular systems such as Maple, Mathematica and MathCAD are some examples. Algebra systems can simplify rational functions, polynomial factories, find solutions to an equation system, and several other operations. They can be used in Calculus to discover the limit, symbolically integrate and distinguish arbitrary equations.
It would be hard to use the binomial theorem manually, almost impossible to make without error. However, this equation may be extended with the help of Maple in less than two seconds. The result can then be differentiated term by term in milliseconds. The usefulness of a system like this is clear: it not only acts as a time-saving device. It also enables challenges that could not be completed hand in seconds.
Leibniz and Newton have established algorithmic calculus. Computer Algebra systems can now take these strategies to remove the human. However, it would seem that computers are extraordinarily inept to do such jobs when studying calculus and even simple algebraic processes. After all, most of us think that mathematics taught at grammar school and beyond is a major issue solving. How can a computer, an unconscious combination of binary numbers, do such complicated tasks? It seems that the computer would not be adequate for such activities, yet that is not the case due to the success of popular Algebra software programs. Instead, computer systems Algebra often know how to conduct more operations on equations than the user!
Rather than discussing the many phases in the development and usage of calculus by computer algebra systems, we were more fascinated by how these systems worked. We started by looking at the theories and questions involved in constructing a computer algebra system. Together with our research, we started to create our algebra computer system in C++. The rest of this part is about summarising our study and the implementation details we have chosen.