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fourierToProbability -- map from Fourier coordinates to probability coordinates

Synopsis

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

See also

Ways to use fourierToProbability :

For the programmer

The object fourierToProbability is a method function.