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inverseMarginMap -- inverse of the marginMap

Synopsis

Usage:

inverseMarginMap(i,R)
Inputs:
- i, an integer, the index of the variable for which to undo the "margin trick"
- R, a ring, a markovRing
Outputs:
- a ring map,

Description

This method computes the inverse of the marginMap.

i1 : R = markovRing (3,2)

o1 = R

o1 : PolynomialRing

i2 : F = marginMap(1,R)

o2 = map (R, R, {p    - p    - p   , p    - p    - p   , p   , p   , p   , p   })
                  1,1    2,1    3,1   1,2    2,2    3,2   2,1   2,2   3,1   3,2

o2 : RingMap R <-- R

i3 : G = inverseMarginMap(1,R)

o3 = map (R, R, {p    + p    + p   , p    + p    + p   , p   , p   , p   , p   })
                  1,1    2,1    3,1   1,2    2,2    3,2   2,1   2,2   3,1   3,2

o3 : RingMap R <-- R

i4 : gens R

o4 = {p   , p   , p   , p   , p   , p   }
       1,1   1,2   2,1   2,2   3,1   3,2

o4 : List

i5 : F*G -- we see that the composition is the identity map:

o5 = map (R, R, {p   , p   , p   , p   , p   , p   })
                  1,1   1,2   2,1   2,2   3,1   3,2

o5 : RingMap R <-- R

See also

hiddenMap -- linear map between the ring of a model with one hidden variable and the ring of the corresponding fully observed model
marginMap -- linear map on joint distributions for discrete random variables replacing marginals for indeterminates

Ways to use inverseMarginMap :

inverseMarginMap(ZZ,Ring)

For the programmer

The object inverseMarginMap is a method function.