> Probably other people have a more substantial answer, but let's try...

Thank you, Simon, it did bring some light.
I was thinking about this problem not from an end-user point of view
but as a (potential) developer of one of these libraries.

>
> Firstly, Sage is based on an object oriented language (Python
> respectively Cython).
> For example, having different flavours of matrices (sparse, dense,
> special implementation over GF(2), defined in various interfaces,...)
> will usually not matter to the user, since the code usually relies on
> the methods of the objects. Now, dense and sparse matrices have most
> methods in common. So, your code would not feel any difference between
> dense and sparse matrices.

The problem, as I see, is in the construction of a new matrix.
If user creates just a matrix, and suppose, it is stored as a dense matrix.
Now, s/he starts invoking different methods that end-up C-library that
actually expects sparse matrices.
Suppose, we do a thousand calls, does it mean that our dense matrix
will be converted to a sparse matrix one thousand times?


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

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