# How to treat the results of symbolic computations in a paper?

I am working with quite complicated (i.e., numerous) trigonometric functions. Let’s say one equation does not fit on an A4 sheet of paper. Rewriting the expressions by hand would be extremly tedious, but thanks to computer algebra systems, I managed to do a symbolic computation and arrive at something like f (0) = 1 (for the sake of the example) as a final and main result.

How can I explain such a thing in a scientific journal (in mechanics)?

A few possibilities, that I considered:

• The calculations yield f (0) = 1

But I feel guilty because I did not make the calculation by myself.

• Using ComputerProgram++, we showed that f (0) = 1.

But should I provide the code in this case?

• but I feel guilty because I did not make the calculation by myself then who did it? For the second possibility: see the answers here academia.stackexchange.com/questions/23237/… Nov 11, 2014 at 0:05
• @seteropere programmers and me, I guess. Nov 11, 2014 at 0:30

## 1 Answer

In an engineering paper, it's not appropriate to have lengthy, non-novel symbolic computations in the body of the article. The requirement however, is that your readers are able to reproduce it in some way. Here are a few options:

• Write all symbolic computations formally in an appendix to the paper.
• If you obtained the results with a software (free or commercial), give the exact name and version of the software you used together with all the necessary parameters you used in the methods section. I don't think there is anything to be 'guilty' about using a faster, controlled way of solving maths providing you know what you are doing.
• If you obtained the results with a piece of code, make it available in some ways (like a public repository or your institution's website). This can sometimes also be done by submitting it to the journal with your article, but few engineering journals host code.

This being said, it's very uncommon to see symbolic maths solved with software in the engineering literature (I don't think I ever read it in any paper). Generally either the concept is well-documented and does not warrant a formal proof in the context (e.g. don't copy the Fourier theorem every time you do an FFT) or it's application-specific and should be written formally.

• TY for your point of view. I think what disturbs me is to make a mathematical proof rely on a computer program... but it probably should not. All the problem is "knowing what you are doing". I'm not sure I actually know what I'm doing when I ask Mathematica to calculate 2+2! Nov 11, 2014 at 0:50
• @anderstood I think it's field-dependent; I've heard for pure math that you shouldn't generally rely on a computation conducted by closed-source software (because you can't review it for bugs; same applies for other software whose correctness is not verified) that isn't easily verifiable with other means (so a pure math paper wouldn't rely on "Mathematica said so" as a key element of a proof). Nov 11, 2014 at 2:12
• @cpast 'Mathematica said so' in unacceptable in any field. Obviously OP is not writing a pure math paper. Nov 11, 2014 at 13:24