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Algebra and number theory have always been counted among the most
beautiful mathematical areas with deep proofs and elegant results.
However, for a long time they were not considered that important in
view of the lack of real-life applications. This has dramatically
changed: nowadays we find applications of algebra and number theory
frequently in our daily life. This book focuses on the theory and
algorithms for polynomials over various coefficient domains such as
a finite field or ring. The operations on polynomials in the focus
are factorization, composition and decomposition, basis computation
for modules, etc. Algorithms for such operations on polynomials
have always been a central interest in computer algebra, as it
combines formal (the variables) and algebraic or numeric (the
coefficients) aspects. The papers presented were selected from the
Workshop on Computer Algebra and Polynomials, which was held in
Linz at the Johann Radon Institute for Computational and Applied
Mathematics (RICAM) during November 25-29, 2013, at the occasion of
the Special Semester on Applications of Algebra and Number Theory.
Resolution of Singularities has long been considered as being a
difficult to access area of mathematics. The more systematic and
simpler proofs that have appeared in the last few years in zero
characteristic now give us a much better understanding of
singularities. They reveal the aesthetics of both the logical
structure of the proof and the various methods used in it. The
present volume is intended for readers who are not yet experts but
always wondered about the intricacies of resolution. As such, it
provides a gentle and quite comprehensive introduction to this
amazing field. The book may tempt the reader to enter more deeply
into a topic where many mysteries - especially the positive
characteristic case - await to be disclosed.
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