Monomial ordering and a division algorithm for polynomials of two or more variables with software

• Main Authors: Cuaycong, Mark Angelo C., Wong, Coleman
• Format: text
• Language: English
• Published: Animo Repository 1997
• Subjects: Algorithms; Computer software; Polynomials; Ordered sets; Variables (Mathematics)
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16340
• Institution: De La Salle University

This thesis is about monomial orderings and a division algorithm for polynomials in two or more variables. Three types of monomial orderings are discussed in detail: lexicographic order, graded lexicographic order, and graded reverse lexicographic order. Then a method of dividing one polynomial by two or more polynomials is described. Examples illustrating the different monomial orderings and the division algorithm as well as proofs of theorems regarding these concepts are also given. A software is also designed to be able to use the computer in dividing a given polynomial by another in the polynomial ring of two or more variables.