I've got some open-source code which I'd like to translate into different programming language (it is a scientific library and it is the only open-source piece of code that does the thing, so I don't have much choice). Parts which I am interested in are GPL, LGPL and BSD (some code is in one, some in another).
This would be a total rewrite, and not a simple modification, but based on the original code. Would I have to use original license for new code?
IANAL, but my gut feeling would be that I have to stick to the terms of the original license.
If it is really a TOTAL rewrite, then you don't have to keep the original license. But if you decide you want to reuse a piece(even with small modifications to fit in the new language), you can do that in BSD without keeping the original license, but not for LGPL nor GPL.
Ideas cannot be copyrighted, only the expression of the ideas. You should therefore be OK to use any license you like, provided you give a completely new expression to the ideas. This implies that a simple machine translation, changing a few variable names, might not be enough, so I would not ist down and slavishly translate the existing code to the new language. absorb the ideas and then write your new version - chances are you'll be able to improve on the original.