GPL - GSL and derivative work.

[Mark Galassi]

    Edwin> An application program does not "require" the GSL just
    Edwin> because it uses the same API.  I don't think that you can
    Edwin> copyright an API.  Anyone could implement the GSL API
    Edwin> without infringing on the GSL copyright.

There is a discussion of these issues on the GNU web pages which
matches what I say and is a legal opinion backed by the FSF's legal
counsel.

If another identical API exists then you have a grey area.  People
have done the trick (in other software) of writing a low-quality
compatible API that was public domain instead of GPLed

Regarding your comments on the use of the GPL instead of the LGPL, we
are a GNU project and there are very clear reasons for the GNU project
to promote using the GPL instead of the Lesser GPL for almost all
libraries.  See:

http://www.gnu.org/licenses/why-not-lgpl.html