Standard bases over Euclidean domains

In this paper we state and explain techniques useful for the computation of strong Gröbner standard bases over Euclidean domains: First investigate several strategies creating pair set using an idea by Lichtblau. Then methods avoiding coefficient growth syzygies. We give in-depth discussion on normal form resp. a generalized reduction process with many optimizations to further avoid large coefficients. These are combined reach GCD-polynomials at earlier stage computation. Based various examples show that our new implementation in computer algebra system Singular is, general, more efficient than other known implementations.