For computational algebra, I think there are some more places. You may want to look at
Symbolic Computation Group in Waterloo University (Canada).
Research Institute for Symbolic Computations in Linz (Austria)
Computer Algebra in Kaiserslautern (Germany), where Singular is (Wayback Machine)
Centre for Interdisciplinary Research in Computational Algebra (University of St Andrews, UK). (Wayback Machine)
CoCoA Sytem : Computations in Commutative Algebra.(Italy)
Macaulay2 : Computations in Algebraic Geometry and Commutative Algebra. (USA)
Moreover, I think in US, there are also some other places, like UIUC, North Carolina State Univ. . .
I hope those information may be useful.
Good luck.
Best,
John
