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I am writing a paper about a problem that involves solving a certain equation. The problem is that the solution is very long and there are a lot of terms. My question is: Is there a way to present the solution in an attractive manner instead of just typing the solution, which is about a page long? Also, would the fact that the solution is long and looks unattractive affect whether the paper get accepted or not?

1 Answer 1

This happens not just in mathematics but in many other disciplines as well: modeling of biological systems, for example, often involves a vast number of terms in the equations. The best approach that I have found for these sorts of situations is to look for the structure in the system and to build your presentation around that structure.

In most cases that I have encountered, it is not true that there are simply a bazillion essentially unrelated terms. The true story of the equation, then, is not the expanded mathematical form but the process and relations that generate it. This opens up a number of approaches for factoring out the equations in order to make them more tractable to present, including:

  • Abstracting sub-structures as variables (e.g., X^2+XY+Y^2, where X and Y are complex terms presented separately)
  • Separating variables from parameters (e.g., a reaction network where each reaction uses one of several standard Hill equation models, with the parameters of the models presented in a table)

These sorts of factorings also lead to a much more informative and interesting presentation of the equation as well. In fact, the Big Equation itself may often end up being relegated to an appendix, where its page-busting form is of little concern.

There may be, of course, certain systems in which such factoring is impossible---and that fact is quite interesting and worth clear discussion!