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)][1]

[Computer Algebra in Kaiserslautern (Germany), where Singular is][2]

[Centre for Interdisciplinary Research in Computational Algebra (University of St Andrews, UK)][3].

[CoCoA Sytem : Computations in Commutative Algebra.(Italy)][4]

[Macaulay2 : Computations in Algebraic Geometry and Commutative Algebra. (USA][5])


  [1]: https://risc.jku.at/
  [2]: http://www.mathematik.uni-kl.de/~zca/
  [3]: http://www-circa.mcs.st-and.ac.uk/circa.php
  [4]: https://cocoa.dima.unige.it/
  [5]: https://faculty.math.illinois.edu/Macaulay2/

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