ABSTRACT
This chapter provides a “broad brush” introduction to the subject of Grobner bases including the mathematics behind them. To focus on key ideas instead of computational details, Maple is used as a calculator throughout the presentation. Many fundamental problems in mathematics, the natural sciences and engineering can be formulated in terms of systems of nonlinear multivariate polynomials. Examples include the solution of algebraic systems of equations, symbolic integration and summation of expressions involving special functions, and solution of linear boundary value problems. Grobner bases provide a uniform, powerful approach for solving such problems. Grobner basis theory has gained much attention outside the mathematical community due to the wide variety of applications that have been found in many areas of science and engineering. Many non-trivial, interesting polynomial systems encountered in practice have a lot of structure that makes their Grobner bases relatively easy to compute.
