CoCoATeam
CoCoA: a system for doing Computations in Commutative Algebra.
Available at http://cocoa.dima.unige.it

John Abbott and Anna Maria Bigatti
CoCoALib: a C++ library for doing Computations in Commutative Algebra.
Available at http://cocoa.dima.unige.it/cocoalib

\def\cocoa{{\hbox{\rm C\kern-.13em o\kern-.07em C\kern-.13em o\kern-.15em A}}}

In particular, if you use some of the following commands, please also cite the corresponding publication:

Factor

J. Abbott, V. Shoup, P. Zimmermann
Factorization in Z[x]: the searching phase

Fat points

J. Abbott, M. Kreuzer, L. Robbiano
Computing Zero-dimensional Schemes

Hilbert, Poincare, Dim, Multiplicity

A.M. Bigatti,
Computations of Hilbert-Poincaré Series

(H)Intersection(List), (H)Colon, (H)Saturation

M. Caboara, C. Traverso, 
Efficient algorithms for ideal operations

IdealOfPoints, IdealOfProjectivePoints, SeparatorOfPoints

J. Abbott, A.M. Bigatti, M. Kreuzer, L. Robbiano
Computing Ideals of Points

Radical, EquiIsoDec, RadicalOfUnmixed

M. Caboara, P. Conti, C. Traverso, 
Yet Another Algorithm for Ideal Decomposition

Res, Betti

A. Capani, G. De Dominicis, G. Niesi, L. Robbiano, 
Computing Minimal Finite Free Resolutions

stat package

M. Caboara, L. Robbiano, 
Families of Ideals in Statistics

Toric, TestSet, intprog package

A.M. Bigatti, R. La Scala, L. Robbiano,
Computing Toric Ideals