Effective Polynomial Computation is an introduction to the
algorithms of computer algebra. It discusses the basic algorithms
for manipulating polynomials including factoring polynomials. These
algorithms are discussed from both a theoretical and practical
perspective. Those cases where theoretically optimal algorithms are
inappropriate are discussed and the practical alternatives are
explained. Effective Polynomial Computation provides much of the
mathematical motivation of the algorithms discussed to help the
reader appreciate the mathematical mechanisms underlying the
algorithms, and so that the algorithms will not appear to be
constructed out of whole cloth. Preparatory to the discussion of
algorithms for polynomials, the first third of this book discusses
related issues in elementary number theory. These results are
either used in later algorithms (e.g. the discussion of lattices
and Diophantine approximation), or analogs of the number theoretic
algorithms are used for polynomial problems (e.g. Euclidean
algorithm and p-adic numbers). Among the unique features of
Effective Polynomial Computation is the detailed material on
greatest common divisor and factoring algorithms for sparse
multivariate polynomials. In addition, both deterministic and
probabilistic algorithms for irreducibility testing of polynomials
are discussed.
General
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