Application of Algebra in computing
Algebraic principles are used extensively in computing. In computer science, the computer algebra is called algebraic computation or symbolic computation. This is used mainly in software development and the associated algorithms that are used in the manipulation of mathematical expressions and objects. Kaltofen Erich (1982) noted that the long-known algorithms that were being used proved to be very long and this necessitated the revisiting of classical algebra with the intention of making them effective and efficient. In specific terms, algebra is used in the following fields of computing.
Encoding: in encoding, data that is arranged in arrays or matrices are used to capture information in the computer. For example,
This data can be obtained from an algebraic equation. The coding is done to represent specific information. For example, this is what one sees. It is matrix representation of data that can be understood by the machine.
Similarly any data can be captured using the same procedures as above. For example, the word Wikipedia can be coded as following
Another example may involve the following; a matrix can be created from several values say 6. A 3 by 2 matric is formed in the following code
> matrix(1:6, ncol=3)
[,1] [,2] [,3]
[1,] 1 3 5
[2,] 2 4 6
This can be advanced to form a three dimensional illusion of the data. The following code is two by two by two matrix.
, , 1
[,1] [,2]
[1,] 1 3
[2,] 2 4
, , 2
[,1] [,2]
[1,] 5 7
[2,] 6 8
The usage of the algebraic backing and matrixes form the core methods used to capture and represent data in computers.
References
Kaltofen, Erich (1982). "Factorization of polynomials", in B. Buchberger; R. Loos; G. Collins,
Computer Algebra, Springer Verlag.
