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I want to avoid writing something like:

However, calculating the variable X and solving this equation requires iteration using the Newton-Raphson method [22, p. 45][15, p. 152]:

"equation"
"equation" 1

Here, a means ... and b represents...

This results in:

"equation" 2
"equation" 3

which can be used in equation X ...

I want to inform the reader that they can find the entire process in the source:

However, calculating the variable X and solving this equation requires iteration using the Newton-Raphson method, which can be found in [22, p. 45][15, p. 152].

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    What exactly are you trying to avoid, and why?
    – Bryan Krause
    Jan 4 at 17:26
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    @BryanKrause I don't want to reproduce an entire algorithm or system of equations in my document that is already available in a book. Therefore, I want to inform the reader that the complete algorithm can be found in the book.
    – ed190
    Jan 4 at 17:36
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    Okay, then why not do that?
    – Bryan Krause
    Jan 4 at 17:57
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    How much of the literature have you personally explored? I think it would be difficult not to have seen various ways others have handled this sort of thing. Maybe there’s part of this I don’t understand. Jan 4 at 19:02
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    As someone who has had to create independent implementations of mathematical methods in software based on their descriptions in published papers, I highly recommend that you describe the method rigorously in a supplemental document included with the paper. I have greatly appreciated it when authors did this in their papers. In my opinion, simply pointing to some other reference and saying, "we did it like that" is rather hand-wavy and often misses key details that someone else would need to know in order to reproduce your results.
    – Matt
    Jan 4 at 22:52

2 Answers 2

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There are cases where a mere pointer to the algorithm in the literature suffices, and there are cases where it is better to explicitly walk the reader through the application of the algorithm, with explanations of how exactly it works in your particular case.

To figure out what makes sense for your article, think about who your readers are, what their background is, and what they are trying to get out of your paper. If applying the algorithm is a routine exercise for your readers, and most of them wouldn't actually be interested in the details, it's fine to leave them out. If you do forsee readers who really want to see how your results came about which aren't familiar with the algorithm, you should consider helping them out by spelling it out.

In either case, it is probably prudent to write out the long version, even if you don't intend to include it in the paper. This can be a good way to catch mistakes.

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If it is central to your paper, make it easy to reach, either by adding it in the supplementary material or by writing it in the paper.

The fact that the algorithm can be found in a book may mean two things:

  • it is some kind of base knowledge in your field;
  • something that may be base knowledge in your field in 10 years;

It is up to you to decide which maturity level reached the algorithm. It strongly depends on the journal you are submitting to, too.

Additionally, if the algorithm can be found in only one book, please consider that it is rather unlikely that the algorithm is some basic knowledge.

I as a reader and user of peer-reviewed scientific publications I am usually disappointed when authors keep their papers short by cutting the equation solving steps. Why? It happened to me something along these lines:

  • Find an interesting algorithm in paper P pointing to an obscure book B for the demonstration;
  • acquiring book B;
  • finding the interesting algorithm and development in the book;
  • using the book's algorithm in subsequent work;
  • 2 years later writing a paper X referencing only the algorithm in the book B;
  • 3 years later getting the paper X published;
  • 4 years later getting entangled in a publishing controversy with authors from paper P;
  • 5 years later finding a pdf copy of the paper P in a backup of mine (please note: I changed 3 institutions and 5 homes/offices in the meanwhile) and therefore apologizing profoundly with original authors;
  • 15 years later, the publisher did not yet update the paper references in my paper X (personally, I do not care anymore, I checked now for sake of completeness of this story, I know I have somehwere an email from the publisher stating they will update my paper X, I am done).

So my suggestion is go ahead, be "lazy" now and then spend a lot of your energies in remembering people they first read about the interesting algortihm in your paper.

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