I might be wrong, however the way I understand the question by Joachim
is rather what useful functionality those objects would bring?

For instance, what would be the use for the basis of a vector space?
Would I be able to define a scalar product to transform the vector
space into an Euclidean vector space where I can use the Gram–Schmidt
process to transform the basis into an orthonormal basis?

What about groups? Are there, for instance, algorithms to enumerate
subgroups of a group, or give the group from only defining some
representation? Check that an action is this and that... Concerning
groups, there is another recent thread about gsoc that you might want
to check.

Anyway, I suppose that such examples will be an invaluable addition to
your application (however do not take me for my word, I am also an
applicant, not a mentor).

Stefan

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