How to plot points of a finite plane?
Given a prime field GF(p) -- not GF(p^n) for n>1 -- I would like to plot the affine plane A=GF(p)^2 and in this any given set of points, given either as a list or coming from a function. Especially I want to plot just lines, say, the graph of f: x -> x+1.
- What would be the most elegant way to do this?
- How could I switch to central representatives in the coordinate system for the plot, i.e. instead of e.g. GF(5)={0,1,...,4} use GF(5)={-2,-1,0,1,2}, in the most elegant way?
A few remarks :
"(T)he most elegant way" has no precise (= algorithmically usable) definition. A better question would be "the way most emphasizing the properties you want to exhibit", Which you do not define.
I am not sure that a "line" has any meaning on the (discrete) cartesian product of two (discrete) finite fields. The (argument, value) points have a meaning, but any "line" joining them is but a (possibly misleading) visual aid.
The representation should be done on a torus, to visually represent the cyclicity of
GF(p)and "break" the intuitive visual ordering of the usual Cartesian plane axes.The "change of coordinates" is probably just a question of labeling.
HTH,