The discussion revolves around proving a property of functions defined on a finite field, specifically that for a prime p, any function from Fp to Fp can be represented by a polynomial of degree at most p-1. The participants explore the implications of polynomial interpolation in this context.
The discussion is active, with participants exploring different interpretations of polynomial interpolation and its relevance to the problem. Some express uncertainty about the connection between the function and polynomial representation.
There is a noted confusion regarding the linearity of the function f and the implications of working within a finite field. Participants are also considering the constraints of polynomial degrees in relation to the number of values in Fp.
Have you tried it? What happened?brru25 said:Would polynomial interpolation work here?
Polynomial interpolation works over any field... or is there something else you see that I don't?HallsofIvy said:I don't see how you could interpolate.
Well, I think of "interpolation" as finding values between given values. And since this is a finite field, there is nothing "between" values.Hurkyl said:Polynomial interpolation works over any field... or is there something else you see that I don't?
http://en.wikipedia.org/wiki/Polynomial_interpolationHallsofIvy said:Well, I think of "interpolation" as finding values between given values. And since this is a finite field, there is nothing "between" values.