> Great!  Welcome!  What sort of library are you thinking of?

Magnus - a package for finitely presented groups, may be.

> It's a possibility.  If there was a library that only worked for sparse
> matrices, but the user wanted to use a function on a dense matrix, I
> don't see any way around converting the matrix.
>
> Of course, the user could ask for a sparse version of their matrix, then
> call the library routine a thousand times, then convert back to dense,
> if they wanted.

There obviously, will be some common ground between Magnus and GAP, so
the same group can be represented as a GAP object and as a Magnus
object.
I guess, I don't really understand who will be responsible for the conversion.
...
Ahm, I've just looked at Sage's reference manual section on
GAP-Singular connection (http://www.sagemath.org/doc/ref/node100.html)
and I'm kind of unimpressed. It's ugly.
It looks like the only benefit of using Sage is a common runtime
environment across its libraries. Libraries' types are kept completely
disjoint.
Why not to do such translations (from a polynomial to a polynomial)
transparently to the user?

-- 
Best regards,
Yegor
__________________________________________________________
Yegor Bryukhov,
Research Associate
Center for Algorithms and Interactive Scientific Software
City College of New York

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