Computing Toric Ideals
by Lorenzo Robbiano

Toric ideals are binomial ideals which represent the algebraic relations of
sets of power products.  They show up in  many fundamental questions arising
from several fields of Mathematics, such as Integer Programming, Statistics,
Combinatorics, and it is also the basic step of any procedure which computes
SAGBI bases.  In this introductory exposition I explain how naive approaches to
the problem of computing toric ideals may lead to very poor performances, so
that the need of new algorithms will be clear.