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?
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!