I have a couple-page-long, nonlinear system of equations that includes within it many conditionals, which I've found work best when I use Implies[ ]. The mathematical equations are relatively simple algebraic equations--nothing fancy there. I can find out all of the answers by hand if I need to, and this system has only one solution set, yet I like to use FindInstance, specify Reals, and only ask for one example. (I do this because I'm going to expand the system of equations later on--to a magnitude that will not allow me to figure out the solutions by hand, and there may be more than one possible solution set for some of the variables.)
So the problem is that there is one variable that I feel to be a sort of cornerstone of the equation. When I define it as equal to a whole number, the system evaluates in less than 10 seconds. If I define it as equal to a fraction made of whole numbers, the same thing: the system evaluates in less than 10 seconds. But when I define it as equal to a decimal, my computer revs and goes on for several minutes until I abort--even when it's a decimal identical to the successful fraction. Also, if I leave the variable blank and let FindInstance choose an appropriate value, it doesn't--it has a lot of trouble (in all but one useless instance); it just revs and revs, and slowly my computer's real memory gets eaten up by the operation (until I abort).
The big problem is that in the larger system of equations that I will make, I don't know what that cornerstone variable is going to be, and I need the computer to find it. The program is having terrible trouble doing something like that and I don't know why. It must have something to do with the way it accepts fractions but not decimals, mustn't it?