mapToProbabilityRing -- ring isomorphism to the given probabilityRing from the corresponding markovRing

i1 : R = probabilityRing {2,3,4};

i2 : markovR = toMarkovRing R;

i3 : F = mapToProbabilityRing R

o3 = map (R, markovR, {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, 0, 2}   {0, 0, 3}   {0, 1, 0}   {0, 1, 1}   {0, 1, 2}   {0, 1, 3}   {0, 2, 0}   {0, 2, 1}   {0, 2, 2}   {0, 2, 3}   {1, 0, 0}   {1, 0, 1}   {1, 0, 2}   {1, 0, 3}   {1, 1, 0}   {1, 1, 1}   {1, 1, 2}   {1, 1, 3}   {1, 2, 0}   {1, 2, 1}   {1, 2, 2}   {1, 2, 3}

o3 : RingMap R <-- markovR

i4 : target F

o4 = R

o4 : PolynomialRing

i5 : source F

o5 = markovR

o5 : PolynomialRing

i6 : isInjective F

o6 = true

i7 : F.matrix

o7 = | p_{0, 0, 0} p_{0, 0, 1} p_{0, 0, 2} p_{0, 0, 3} p_{0, 1, 0} p_{0, 1,
     ------------------------------------------------------------------------
     1} p_{0, 1, 2} p_{0, 1, 3} p_{0, 2, 0} p_{0, 2, 1} p_{0, 2, 2} p_{0, 2,
     ------------------------------------------------------------------------
     3} p_{1, 0, 0} p_{1, 0, 1} p_{1, 0, 2} p_{1, 0, 3} p_{1, 1, 0} p_{1, 1,
     ------------------------------------------------------------------------
     1} p_{1, 1, 2} p_{1, 1, 3} p_{1, 2, 0} p_{1, 2, 1} p_{1, 2, 2} p_{1, 2,
     ------------------------------------------------------------------------
     3} |

             1      24
o7 : Matrix R  <-- R