I have implemented the following softwares for the study of algebraic geometry.
Macaulay2 package for enumerating rational points on a given affine / projective variety defined by its ideal. It finds the points by using brute force plus some elimination, no advanced algorithm is involved. (As the name suggests, this is a considerable improvement over its predecessor,
A Julia package for doing computations in intersection theory, built using the components of the
Oscar system. It is still under active development, and is aimed at providing an alternative to the
Schubert2, with better performances and more interesting features. Check out the documentations for some nice examples.
A Sage package for doing computations using Bott’s residue formula. It can be used to compute the Chern numbers of the known families of hyperkähler manifolds.