OSCAR is an open source computer algebra system for research in algebra, geometry, and number theory. It is written in Julia, and unifies the systems Gap (group and representation theory), Hecke (number theory), Polymake (polyhedral geometry and combinatorics) Singular (algebraic geometry and commutative algebra). It is featured extensively in my research

Singular is an open source computer algebra system for polynomial computations with special emphasis on commutative and non-commutative algebra. It boasts a large amount of libraries and is known for its speed. A significant amount of its features have been made available in OSCAR.

Polymake is an open source software for research in polyhedral geometry. It has an impressive toolbox for tropical geometry and matroid theory. I also use it for creating 3D prints of tropical models. A significant amount of its features have been made available in OSCAR.