fourierToProbability -- Map from Fourier coordinates to probablity coordinates

Synopsis

• Usage:
g = fourierToProbability(S,R,n,M)
• Inputs:
• S, a ring, The ring of probability coordinates
• R, a ring, The ring of Fourier coordinates
• n, an integer, The number of leaves
• M, an instance of the type Model, The model (CNFmodel, JCmodel, etc)
• Outputs:
• N, , The map from Fourier coordinates to probablity coordinates

Description

Creates a ring map from the ring of Fourier coordinates to the ring of probability coordinates. 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) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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 }) 2 0,0,0 2 0,0,1 2 0,1,0 2 0,1,1 2 1,0,0 2 1,0,1 2 1,1,0 2 1,1,1 2 0,0,0 2 0,0,1 2 0,1,0 2 0,1,1 2 1,0,0 2 1,0,1 2 1,1,0 2 1,1,1 2 0,0,0 2 0,0,1 2 0,1,0 2 0,1,1 2 1,0,0 2 1,0,1 2 1,1,0 2 1,1,1 2 0,0,0 2 0,0,1 2 0,1,0 2 0,1,1 2 1,0,0 2 1,0,1 2 1,1,0 2 1,1,1 o4 : RingMap S <--- R```

See also

• pRing -- Constructs the ring of probability coordinates
• qRing -- Constructs the ring of Fourier coordinates

Ways to use fourierToProbability :

• fourierToProbability(Ring,Ring,ZZ,Model)