How to specify conditions within Julia's composite types?

Question

I am trying to create a composite type in Julia representing points on an elliptic curve. Point are valid if satisfying y^2 == x^3 + a*x + b OR both x and y are equal to nothing. Note that the later case represents point at infinity.

I have come up with the below code but can't figure out how to account for point at infinity.

• Is there a way to handle different exceptions in struct?
• Can exception simply return a valid type instead of an error? eg if x == nothing && y == nothing then Point(nothing,nothing,a,b)

IntOrNothing = Union{Int,Nothing}
struct Point
    x::IntOrNothing
    y::IntOrNothing
    a::Int
    b::Int
    Point(x,y,a,b) = x == nothing || y == nothing || y^2 != x^3 + a*x + b ? error("Point is not on curve") : new(x,y,a,b)
end

Answer 1

I would define two inner constructors for Point like this:

IntOrNothing = Union{Int,Nothing}
struct Point
    x::IntOrNothing
    y::IntOrNothing
    a::Int
    b::Int
    Point(x::Nothing,y::Nothing,a,b) = new(x,y,a,b)
    Point(x,y,a,b) = y^2 != x^3 + a*x + b ? error("Point is not on curve") : new(x,y,a,b)
end

as this would be most readable in my opinion.

Note that you will get MethodError if you call Point(nothing,2,1,3) but I guess from your code you do not care about the type of exception thrown as long as it is thrown on invalid data.

Does it solve your problem?