Dissecting these code snippets a little bit.
>//Function. RoD key pairs
>returns one pair for primes two for product of different primes, etc
So this function is only returning the n values. It doesn't seem to be doing anything with t of the correct (e,n). That means there's something inherent to the root of d that is also inherent to n, right? Because that seems to be the point of this function (given e, -f and d, return valid n values).
>given two columns, which values of n are separated by 1, where e(n)>-f(n)
It also means that something about e, -f and d tells us the number of factors that a number has. Every n value in the entire positive e space has a corresponding n-1 somewhere in the negative f space, but obviously all the ns in one e column aren't going to all be in the same -f column. So it returns every instance of an n in a given e having an n-1 in the given -f of our c. That means it returns every possible n value for our c. That means it knows how many n values there are for our c (and thus how many factors it has).
I don't think these are the same function. This starts with an open parenthesis, but the last piece of code he posted was comments followed by a variable. That variable from the last one was the list of n and n-1 values for a given e and -f. That's definitely a local variable rather than a global variable, so those comments were inside its function. That means this has to be the beginning of a separate function. So we have one function to find all of the n values for our c, and another to do whatever this one's doing (which seems to be creating a list of BigIntegers (as opposed to a list of BigInteger arrays with 2 values each) and doing something to them that has something to do with sqrt(2d)).