# Math used in computer algebra systems

• Avichal
In summary, the conversation discusses the use of computer algebra systems for solving mathematical problems. The basic functions of CAS include algebra, integration, limits, and series, using various algorithms such as the risch algorithm. The conversation also explores the reason for a separate approach in solving math for computers, as CAS is focused on manipulating symbols rather than numerical evaluations. This approach allows for the extension of CAS to do limited numerical evaluations.
Avichal
I am recently very interested in computer algebra systems and was thinking about the maths in it.
Basic things that CAS does is algebra(solve set of equations), integration, limits, series etc.

Various algorithms are used for such operations. For e.g.:- for integration there is an algorithm called risch algorithm.

Now, these algorithms seemed very new to me. They are different from methods we use in solving such problems. Why do we need a separate approach in solving math for computers? Why can't we use normal math algorithms/methods?

For one reason, CAS evolved to manipulate symbols, rather than evaluate expressions numerically. It's a different approach because the goal is different. CAS can be extended to do limited numerical evaluations, since numbers can be represented symbolically.

http://en.wikipedia.org/wiki/Computer_algebra_system

## 1. What is a computer algebra system (CAS)?

A computer algebra system is a software program that is specifically designed to manipulate mathematical equations and expressions symbolically, rather than numerically. This allows for a wider range of calculations and problem-solving capabilities compared to traditional calculators.

## 2. How are computer algebra systems used in scientific research?

CAS are used in a variety of scientific fields such as physics, chemistry, and engineering to solve complex mathematical equations and perform simulations. They are also used to analyze and visualize data, making them a valuable tool for research and experimentation.

## 3. What are the advantages of using a computer algebra system?

CAS can handle large and complex equations that would be time-consuming and error-prone to solve manually. They also allow for symbolic manipulation, making it easier to test and explore different mathematical concepts and relationships.

## 4. How does a computer algebra system differ from a regular calculator?

A regular calculator is limited to numerical calculations and can only provide a numerical answer. A CAS, on the other hand, can handle symbolic calculations and provide a more comprehensive and flexible solution. It also has a wider range of mathematical functions and tools for problem-solving.

## 5. Can anyone use a computer algebra system or is it only for mathematicians?

CAS are designed to be user-friendly and accessible to anyone, regardless of their mathematical background. While they can be a valuable tool for mathematicians, they can also be used by students, researchers, and professionals in various fields for a wide range of applications.

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