  In this paper we show how to combine different techniques from Commutative
Algebra and a systematic use of a Computer Algebra System (in our case mainly
CoCoA) in order to explicitly construct Cohen-Macaulay domains, which are
standard $k$-algebras and whose Hilbert function is ``bad". In particular we
disprove a well-known conjecture by Hibi.

Algebraic Geometry;Algebraic Geometry