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When transfering a rather complex equation from another authors published article, to a computer programming language such as R, does the intellectual property of the script itself belong to the programmer?

Or would it be like translating, say a quote, to a different language?

Does it depend on the complexity of implementing the model in the script?

I am thinking of this on more of a philosophical level, rather than specific IP laws.

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There are some disgusting cases of patented algorithms, but in a generic case, everyone can translate a formula from a paper to code.

Even more: it's the essence of computer science in how to translate a formula to code. This can be done in various ways, where some are much more efficient (and hence, better) than others. So it's definitely the intellectual property of the person, who wrote the code.

Probably, some implementations can be dismissed as trivial, but most would not be.

Of course, it's still an implementation of your formula / algorithm, which (normally) would be credited as such. But this retains you no rights to the implementation.

You might retain rights for the formula itself, by patenting it or something. Unless it's something big, I would not really bother.

Disclaimer: I am not a layer.

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I expect that there are few equations non-trivial enough that the author has a reasonable claim of ownership, for which the corresponding code implementation is so trivial that the programmer can't reasonably claim a certain degree of ownership of their own.

Here is an analogy to consider. If an author were to construct some great, abstract system of morality, it is indisputable that they could fairly claim ownership over it. However, if another author were to take those abstract ideas and make them concrete by way of accessible language and real-world analogies, that second author could surely claim ownership of their own interpretation of the original author's ideas. Here, I liken the first author to the creator of the equation, and the second to the programmer who implemented it in code.

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