Algorithms on computational algebraic geometry

In this thesis, the algorithms on some algebraic structures are studied in computational algebraic geometry and some basic algebra problems are solved using these algorithms. For example, a Macaulay2 program is an application of these algorithms. Some problems related to primary decomposition of the prime ideals, Hilbert function, Hilbert series, Hilbert polynomials and free resolution are solved using the Macaulay2 program.The historical development and significance of Macaulay2 program is given in the introduction of the thesis. In the second and the third section, the definition of ring and modules, features and fundamental theorems are given and the use of Macaulay2 program is explained.Finally, the basic definitions of primary ideals, primary ideal decomposition of prime ideals and the Hilbert function, Hilbert series, Hilbert polynomial and the free resolution and some theorems are given and some applications are being on the Macaulay2 program.Key words: Noetherian ring, graded ring, graded module, primary ideal, primary decomposition, Hilbert function, Hilbert polynomial