Feature proposal: Factorization as an abstract integer?

[cmichelenstrofer]

It would be cool if Factorization could be a representation of an abstract integer so that one could do arithmetics with them, etc.

f1e2 = factor(100)
f1e4 = f100 * f100

[reinermartin]

Just a small comment, I find the following convenient sometimes:

using Primes
import Primes.Factorization

*(p1::Factorization, p2::Factorization) = Factorization(merge(+, p1, p2))

@show factor(12) * factor(21)

[rfourquet]

Yes I also had this idea once in a while. I find both behaviors (dict and integer) useful; we could probably allow multiplication of Factorization objects, even when they are not <: Integer. If we made them <: Integer, there would be some questions to sort out, like for +, do we implicitly factorize the sum, or return a non-factorized integer?

[cmichelenstrofer]

I see your point. If it is <: Int inevitably some operations would simply require promoting to Int and some thought is needed as to which operations should be defined specifically to return Factorization. Obviously the most useful is multiplication (including division, exponentiation, etc). If this approach is chosen I would argue it would make sense to define the basic arithmetic operations (including + even if its use is not immediately obvious). Anything else could be promoted to an integer. Support for other operations or functions can be added later if they make sense.

If the <: Int approach is not taken, I like your idea of allowing multiplication of the Factorization objects.

I'm completely new to Julia (coming from Python) but would be willing to give either of these a shot as a first issue.