The programmer must understand the formula in order to write computer code that implements it. The result is a creative/expressive work which is copyrightable.
Of course not, this is math; it is not copyrightable.
It would have made perfect sense to Euclid.
Some computers can understand this and execute it as if it were computer code. That's amazing! Kudos to those compute language designers and compiler authors. But their ingenuity does not suddenly grant copyright protection to anything their clever compilers can now understand.
Any computable function can be written the way I wrote the function that is equivalent to Euclid's algorithm. Does it means no computable function is copyright-able or not copyright-able if written that way?
The law says nothing about computability (nice straw man) but it does say ideas and math are not protected whereas code is. My point is the API declarations at the heart of this case are not protected by law because they are examples of the former. Like a formula, they are ideas that describe what to do, but not exactly how to do it.
If you code GCD in a low-level computer programming language then of course you can claim a copyright on that code, but nobody owns the idea of the Euclidean algorithm.
Exactly. That argument would never fly in a court. I’m always amused when software people think they have some legal checkmate like “any digital work is somewhere in the infinite digits of pi therefore cannot be copyrighted.” That’s not how law works.
A formula is an idea. It describes the nature of something computable. It does not explain how to compute.
For example: https://en.wikipedia.org/wiki/Euclidean_algorithm
The programmer must understand the formula in order to write computer code that implements it. The result is a creative/expressive work which is copyrightable.