THE THEORY AND PRACTICE OF GROEBNER BASES
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Franz Winkler

Groebner bases are a central tool in the theory of polynomial
ideals and the solution of systems of multivariate polynomial
equations. They are implemented in every major computer algebra
system. We will provide a thorough introduction to the theory
of Groebner bases, proving the existence and construction.
We will describe the use of Groebner bases for equation solving,
the arithmetic of polynomial ideals, the computation of the
Hilbert function and dimension of ideals, and applications in
robotics and geometry.