# fourierToProbability -- map from Fourier coordinates to probability coordinates

## Synopsis

• Usage:
fourierToProbability(S,R,n,M)
• Inputs:
• S, a ring, of probability coordinates
• R, a ring, of Fourier coordinates
• n, an integer, the number of leaves
• M, an instance of the type Model,
• Outputs:
• , from Fourier coordinates to probability coordinates

## Description

This function creates a ring map from the ring of Fourier coordinates to the ring of probability coordinates, for the four predefined models, CFNmodel, JCmodel, K2Pmodel or K3Pmodel. It will not work with user-defined models. The ring of probability coordinates must have at least $|G|^n$ variables where $G$ is the group associated to the model. The ring of Fourier coordinates must have at least $|G|^{(n-1)}$ variables.

 i1 : M = CFNmodel; i2 : S = pRing(3,M) o2 = S o2 : PolynomialRing i3 : R = qRing(3,M) o3 = R o3 : PolynomialRing i4 : m = fourierToProbability(S,R,3,M) o4 = map (S, R, {p + p + p + p + p + p + p + p , p - p - p + p + p - p - p + p , p - p + p - p - p + p - p + p , p + p - p - p - p - p + p + p }) 0,0,0 0,0,1 0,1,0 0,1,1 1,0,0 1,0,1 1,1,0 1,1,1 0,0,0 0,0,1 0,1,0 0,1,1 1,0,0 1,0,1 1,1,0 1,1,1 0,0,0 0,0,1 0,1,0 0,1,1 1,0,0 1,0,1 1,1,0 1,1,1 0,0,0 0,0,1 0,1,0 0,1,1 1,0,0 1,0,1 1,1,0 1,1,1 o4 : RingMap S <--- R