Groebner Bases in Java with Applications in Computer Graphics

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Executive Summary

In this paper, the authors present a Java implementation of the algorithm that computes Buchbereger's and reduced Groebner's basis step by step. The Java application enables graphical representation of the intersection of two surfaces in 3-dimensional space and determines conditions of existence and planarity of the intersection. This application was developed for calculating the Groebner basis of an ideal and for representing it in 3D. The program was written entirely in Java. It can be run from any computer that has an up-to-date version of Sun Microsystems's free Java Virtual Machine (JVM). JVM enables a set of computer software programs and data structures to use a virtual machine model for the execution of other computer programs and scripts.

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